The Semantics of Prepositions: From Mental Processing to Natural Language Processing 9783110872576, 9783110136340

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The Semantics of Prepositions

Natural Language Processing 3

Editorial Board Hans-Jürgen Eikmeyer Maurice Gross Walther von Hahn James Kilbury Bente Maegaard Dieter Metzing Makoto Nagao Helmut Schnelle Petr Sgall Harold Somers Hans Uszkoreit Antonio Zampolli

Managing Editor Annely Rothkegel

Mouton de Gruyter Berlin · New York

The Semantics of Prepositions From Mental Processing to Natural Language Processing

Edited by

Cornelia Zelinsky-Wibbelt

Mouton de Gruyter Berlin · New York 1993

Mouton de Gruyter (formerly Mouton, The Hague) is a Division of Walter de Gruyter & Co., Berlin.

© Printed on acid-free paper which falls within the guidelines of the ANSI to ensure permanence and durability.

Library of Congress Cataloging-in-Publication

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The Semantics of prepositions : from mental processing to natural language processing / edited by Cornelia Zelinsky-Wibbelt, p. cm. — (Natural language processing ; 3) Most papers were presented at a workshop held Feb. 1990 at the Institut für Angewandte Informationsforschung. Includes bibliographical references and index. ISBN 3-11-013634-1 1. Grammar, Comparative and general — Prepositions — Congresses. 2. Semantics — Congresses. 3. Cognitive grammar — Congresses. 4. Computational linguistics — Congresses. I. Zelinsky-Wibbelt, Cornelia. 1 9 5 2 II. Series. P285.S46 1994 415 —dc20 93-30213

Die Deutsche Bibliothek — Cataloging-in-Publication

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The semantics of prepositions : from mental processing to natural language processing / ed. by Cornelia Zelinsky-Wibbelt. — Berlin ; New York : Mouton de Gruyter, 1993 (Natural language processing ; 3) ISBN 3-11-013634-1 NE: Zelinsky-Wibbelt, Cornelia [Hrsg.]; GT

© Copyright 1993 by Walter de Gruyter & Co., D-10785 Berlin. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Typesetting: Arthur Collignon GmbH, Berlin. — Printing: Gerike GmbH, Berlin. — Binding: Lüderitz & Bauer GmbH, Berlin. Printed in Germany

Preface

I wish to express my thanks to all authors who have contributed to this book. The majority of the papers in this volume were presented at a workshop on the semantics of prepositions held at the Institut für Angewandte Informationsforschung in February 1990. The range of the book, however, has been enlarged by the contributions of several colleagues who could not participate in the original workshop, but who kindly complied with the editor's request for further submissions. On behalf of all authors, I should like to express my gratitude to the following institutions and individuals for their role in the production of the present volume. The financial prerequisites for the holding of the workshop were provided by funding from the BMFT (Bundesministerium für Forschung und Technologie, Förderkennzeichen 08B3213 8). The encouragement of the project manager Johann Haller was an essential factor in getting the workshop off the ground and in ensuring that the papers were able to be published in a common volume. Finally, I should like to acknowledge the assistance of my husband, who, in addition to his own busy schedule, helped with the compilation of the index. The broader topic of this book is the conceptualization of space. It was the editor's intention to shed some light on this topic by bringing together different approaches to the mental process of interpreting prepositions. In particular, the editor wanted to open windows for the computational processing of prepositions as predications in different cognitive domains. While it was a complex matter to get all these different perspectives under one heading, the editor is aware that it is by far not the whole area of current research on prepositions that has been covered. No presentation of a subject, however, can ever claim to be exhaustive, and there will always be room left for other perspectives. In this vein we hope that this book, with all its valuable insights as well as its inevitable flaws and gaps, will inspire future discussions on a major topic within Cognitive Linguistics. Saarbrücken, July 1993

Cornelia Zelinsky-Wibbelt

Contents

Introduction Cornelia Zelinsky-Wibbelt

1

1. Lexicalization patterns of prepositions The Dutch spatial preposition "in": A cognitive-semantic analysis Hubert Cuyckens

27

Dividing up physical and mental space into conceptual categories by means of English prepositions Rene Dirven

73

On the grammar of lexical and non-lexical prepositions in English Gisa Rauh

99

Prepositions: patterns of polysemization and strategies of disambiguation John R. Taylor

151

2. Semantic categorization of prepositions and context Prepositions and object concepts: A contribution to cognitive semantics Priska-Monika Hottenroth

179

Semantic and conceptual aspects of the preposition durch Ingrid Kaufmann

221

The meaning of German projective prepositions: A two-level approach Ewald Lang

249

3. Contrastive implications of prepositions German temporal prepositions from an English perspective Martin Durrell — David Bree

295

On universality and variability in the semantics of spatial adpositions Bruce W. Hawkins 327

viii

Contents

Interpreting and translating prepositions: A cognitively based formalization Cornelia Zelinsky-Wibbelt

351

4. Image understanding and prepositions A three-level approach to the semantics of space Michel Aurnague — Laure Vieu

393

Computing the meaning of localization expressions involving prepositions: The role of concepts and spatial context Simone Pribbenow

441

A contribution to reference semantics of spatial prepositions: The visualization problem and its solution in VITRA Jörg R. J. Schirra

471

Index

517

Introduction 1 Cornelia Zelinsky-

Wibbelt

1. The linguistic relevance of prepositions What makes up the meaning of words has long concerned linguists both from a general and from a typological point of view. In order to make the necessary semantic distinctions between different meanings of a word, an adequate typing in terms of semantic features is indispensable. Without being able to make these distinctions, natural language analysis, synthesis and generation as well as machine translation will be futile. One aim of this book is to show which types of information are necessary in order to arrive at these distinctions. While all authors achieve this aim by proceeding from the idea of the human mind as an information processing system, they differ with respect to their assumptions of necessary types of information and possible uses of a word as well as their computation. This makes it clear that the achievement of this aim is far from being trivial. This volume deals with the semantics of a lexical category which had long been neglected in linguistic inquiry. Recently, however, interest in prepositions has grown steadily, such that now we are witnessing a veritable plethora of investigations into the semantics of prepositions. So now seems a good time to reconsider this area of investigation. It is the intention of this volume to approach this issue firstly from a more general perspective, namely: how far do insights into the meanings of prepositions give clues to the semantic structure of lexical units and its processing in general? We also feel, however, that the time has come to see how natural language processing (NLP) can benefit from the insights of theoretical linguistics, especially with respect to machine translation (MT) and image understanding. We think that it is particularly important to deal with the meanings of prepositions from precisely these two perspectives: M T requires a model of translation which takes into account the relation between potentially different encodings of one and the same state of affairs. This phenomenon is especially characteristic of prepositions, as we will see below. Many of the articles in this book offer a model for interpreting the typological differences in the distribution of information

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in general. Both MT and the interpretation and linguistic encoding of visual information require a comprehensive model of what knowledge resources lie behind the use of linguistic expressions and which processes operate on the knowledge resources in order to instantiate a specific use of linguistic expressions. Certain techniques for interpreting the real world can be explored by investigating the kind of information that prepositions encode. Only a model of natural language processing can give valid insights into the information encoded by lexical units. Different linguistic theories arrive at different models by assuming different techniques for understanding the real world. Among the most important of these is the technique of abstracting from the vast amount of highly complex and variegated information, which would exceed the processing and storage capacities of the human mind. Thus the human mind, as an information processing system, reduces this abundant information by focussing on those aspects which, according to conventional experience, figure as salient, essential or relevant in a particular type of situation, as well as from the speaker's perspective. This focussing implies that the remaining information is neglected as being non-salient, non-essential or non-relevant in the respective type of situation. With prepositions this abstraction of information can be studied in a fairly transparent way: in their prototypical meaning most prepositions are spatial predicates and as such they can focus on different aspects of our physical environment. In fact, the selection from among different prepositions or from among different senses of a preposition depends on the possibility of focussing on a state of affairs in different ways.

2. New ways of analyzing prepositions The recent interest in prepositions is connected with the emergence of a new philosophical climate in linguistics. The radically positivist and realist climate which still dominated the early years of the 1970s prevented extensive investigations into the problems related to prepositions, although there were exceptions such as Bennett 1975; Lehrer 1974; Wierzbicka 1972 and 1976; Bolinger 1977; Chafe 1968; Fillmore 1975 and 1977. Apart from these "lonesome riders" formal aspects of language, as dealt with in syntactic and model-theoretic analyses, were and in part still are the sole topic of linguistic investigation. It was in the second half of the 1970s, however, that in the wake of Rosch's psychological experiments

Introduction

3

(cf. Rosch 1973 and 1978) an increasing number of linguists have changed their basic attitude with respect to what constitutes the nature of linguistic meaning. Only a few reasons for this change in approach can be given in this introduction. The categorical all-or-none relation between meaning and form, which was defined by discrete categories and absolute conditions, was only partly successful precisely because language is, to a great extent, gradient and vague rather than absolute and precise. The predominance of all-or-none categories in language is mirrored in the artificial distinction between semantics and pragmatics and in the exclusion of such phenomena as metaphorical and semantic extension in general, both of which have become central to linguistic description within the conceptual reorientation. In addition, the usual way in which semantics is conceived in formal theories, i. e., by reconstructing the extension ("meaning") and the intension ("sense") of a linguistic expression in a strictly parallel manner, has been criticized as inadequate. Thus Langacker (1987: 2) claims that, in accordance with the conventional setting of the speaker's environment, one and the same real situation may be associated with different mental representations, and hence it may be assigned different semantic values. As distinct mental images may give rise to different expressions, the problem of how to account for these distinctions in a semantic representation becomes especially important for the contrastive perspective taken by MT. Instead of being considered as contingent, as was the case before the cognitive breakthrough, language-specific encodings are motivated by conventionally based conceptualizations. Linguistic conventions correspond to a certain overall behaviour, which has developed in the physical, social and linguistic context of the respective speech community. This means that the meaning of a word relies on all knowledge resources which may be accessed by the speakers of the respective speech community at a specific point in time, linguistic meaning only being processed as part of a more comprehensive cognitive routine. Hence Cognitive Grammar assumes a wide notion of context, which constrains the use of words and their meanings. As a corollary, semantics and pragmatics have turned out to be inseparable. This holds particularly for semantic extension to novel word senses. In accordance with the overall context, speakers construe the perceived information into focus, foreground, and background. It is not only in different languages that the overall context results in different conceptualizations and hence different expressions of the same real situation.

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Also in one and the same language the same scene may be highlighted in different ways and hence result in different expressions. That this applies especially to the use of prepositions is illustrated abundantly in the contributions to this volume.

2.1. Prepositions and semantic categorization Following the tracks of Gestalt psychology, Cognitive Grammar associates semantic categories with mental gestalts. Depending on the specific situation, these gestalts can be good or less good representations of the respective category. The boundaries between less good, bad, and inadequate cannot be conclusively defined by necessary and sufficient conditions, as they depend on the pragmatic conditions of the respective situation and hence may vary synchronically or be subject to change over time. In other words, category membership is not an absolute but a gradient phenomenon (cf. Langacker 1987: 48; Lakoff 1987). The subjective nature of linguistic meaning does not imply total inconsistency between speakers of a language. The overall context, on which linguistic conventions are based, continuously constrains these. The important point is that we can only interpret natural language if we explore these overall contextual constraints and thus consider how meaning is humanly relevant. This procedure offers the possibility of a semantic interpretation which is psychologically real: what is meant by this is simply that if one interprets language from a human perspective, one can not fail to explain what it actually is that linguistic expressions refer to. The cognitive reorientation has given birth to different paradigms which all claim to be psychologically real. Two major paradigms are focussed on in this volume: Cognitive Grammar, whose most prominent exponents are Lakoff and Langacker, and the two-level approach to semantics, as advocated by Bierwisch and Lang. The centrality that prepositions have gained within the framework of Cognitive Grammar relies on the fact that prepositions as spatial expressions are highly representative of the nature of linguistic meaning: conceptualization in this paradigm comprises linguistic meaning or, put the other way round, linguistic interpretation equates with conceptualization. The essential point is that all conceptualization, that is all mental experience, is ultimately based on physical experience gained from our physical functioning in a spatial environment. This is what Lakoff calls preconceptual experience (cf. Lakoff 1987: 267). It is mentally encoded in image

Introduction

5

schemata, which function as cognitive models for all higher-order mental constructions, that is, they give meaning even to those utterances which deal with the most abstract and complex situations: every thought is ultimately linked to the structure of spatial concepts which grow out of our preconceptual structure of experience. In this view, all abstract concepts are metaphorizations and metonymies of semantically concrete spatial predications. Abstract expressions are indirectly understood in terms of directly meaningful, preconceptual models which are constrained by the perception of physical relations.

2.2. The expressive force of prepositions In conceptualizing the physical world and communicating about it we are confronted with an immense number of spatially significant entities, which have a specific extension in three-dimensional space according to their dimensionality, their internal and external bounding (i. e., whether they are bounded towards their surroundings and whether they are internally continuous or discrete), their shape and orientation and their mobility (i. e., whether they can change their position or not). Unbounded, i.e. mass entities are associated with spatial properties in a restricted sense, as they have no boundaries marking their gestalt and their absolute extension in space and time. It is by these spatial properties that the conceived entities constrain the possible relations between them and hence the possible spatial predications expressed by prepositions. All understanding, communication and experience is thereby constrained. Indeed, understanding and communication only become possible via the schematic, relatively simple structure imposed by spatial concepts on the vast amount of information provided by the physical and non-physical world. 2.2.1. The expression of spatial orientation It is the characteristic capacity of the human species to move freely in the horizontal dimension, normally in an upright position; thus human beings can perspectivize spatial scenes from their own point of view, thereby assigning an orientation to the objects at issue (for the following cf. Lang 1989 and Lang this volume, as well as Langacker 1987: 122 ff. and Vandeloise 1984: 71 ff.). The theories represented in this book agree on the assumption that the concept of spatial orientation is determined

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by the surface of the earth and by gravity as well as by our normally upright posture. Lang therefore claims the vertical axis to be dominant in spatial orientation (cf. Lang 1989; Lakoff — Johnson 1980; Lakoff 1987). Speakers conceptualize objects in space to be oriented along their own axes and/or in relation to another object in their surroundings. Thus speakers assign an intrinsic orientation (cf. Vandeloise 1984: 96) to objects which, independent of context, i.e., independent of the neighbouring objects and independent of the dimensional grid, may receive side assignments in every position. Examples are blouse, trousers, cupboard. We have 'anthropomorphized' (cf. Vandeloise 1984: 97) these objects by categorizing them according to their intrinsic parts which we associate immanently with them. That is, the objects are categorized with the human body and hence with human spatial orientation as a model (cf. Wunderlich 1985: 75). Objects may be contextually oriented either in relation to the speaker's or hearer's orientation or in relation to some other object which is intrinsically oriented as in the chair is in front of the table or Peter is in front of the table (cf. Vandeloise 1984: 96 ff.). In both examples the front may be assigned to the table both by the observer's point of view and by the function of the located object. Lang distinguishes between contextually induced orientation, which is assigned in relation to the vertical axis of the surrounding space and contextually induced perspectivization, which is assigned relative to the actual or potential "observer's line of sight" (cf. Lang 1989: 277). When intrinsic and contextual orientation are in conflict, intrinsic orientation prevails. The resolution of this conflict depends on the relation by which the orientation is assigned. Vandeloise (1984: 88 and 1991) notes that human trajectors are stronger in orienting the landmark contextually. Lang's approach to resolving this conflict is to assume a more finegrained object categorization by what he calls "object-constitutive primary identification" (cf. Lang 1989: 277). He distinguishes between objects which are inherently oriented and those which are canonically oriented. Inherently oriented objects have specified sides and can be interpreted as being in normal position, regardless of how they are localized in relation to the surrounding space. Examples are coin, book. Canonically oriented objects must be in normal position in order to fulfil their function. Objects like wardrobe, chest, tower fall into this category. Langacker uses the term actual orientation for scenes in which the canonical orientation is violated either by an unusual orientation of

Introduction

7

the speaker or by an object orientation which deviates from the norm (cf. Langacker 1987: 123). Finally there are objects which are neutral as to spatial orientation, since they have no specified sides; hence they are assigned sides by contextual cues in any position. Examples are ball, cube, star. The speaker's position and the speaker's asymmetrical perception of the front-back dimension comes into play with canonically oriented entities. Thus in the sentence The table is standing in front of the cupboard the cupboard may be given a canonical or actual orientation (the latter may coincide with the canonical orientation if it is in line with the speaker's/observer's point of view). The canonical orientation is independent of the speaker's point of view, but merely depends on the intrinsic front and rear of the cupboard. This is what is generally called the intrinsic use of the preposition in front of Actual orientation occurs in accordance with the speaker's/observer's perspective, i.e., it arises from his point of view, which in turn depends on his spatial or mental position. Depending on his line of sight the speaker may assign actual sides to the cupboard and thereby locate the table in front of the rear of the cupboard. In this interpretation the projective preposition in front of is used deictically. Projective prepositions are generally ambiguous with respect to deictic vs. intrinsic use. The example given with respect to this distinction is taken from Lang (in this volume), who deals extensively with the problems of perspectivization and orientation. To summarize, it is movable entities that speakers can perspectivize; they thereby assign actual orientations which may deviate from the canonical ones. Mobile or movable entities may undergo both what is called positional, static or topological relations and directional, dynamic or projective relations. The first type of relation expresses a position of one entity in relation to another. The topological prepositions on, at, in for instance relate an entity to the upper surface, the exterior side, or the interior of a second entity. The second type of relation expresses a motion or orientation of one entity towards another. As such, the prepositions into, out of, from express motion or orientation into, or out of a container, or away from an entity. In many cases there is also a topological sense beside the projective one, as in the German equivalent of English into: German in is used both in the topological and in the projective sense, whereas English is lexically more specific in expressing these spatial relations: prototypically in may be used of topological relations and into in the projective sense; some motion verbs, as for instance go, come, walk,

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run require into. Otherwise both in and into can be used in the projective sense. Immobile entities may constitute only static relations. Cognitive Grammar and the two level-approach agree on the assumption that these structure-imposing processes are crucial for the interpretation of and communication about the world. Their relevant hypotheses, however, about how these processes come about, differ considerably. The two-level approach, being object-oriented and axes-based, proceeds from the question of how linguistic structures are determined by the orientation of objects and by the speaker's line of sight. Cognitive Grammar departs from the question of how linguistic expressions are determined by conceptualization and how this conceptualization is constrained by the speaker's environment, his perspective and his purposes. Cognitive Grammar thus explains by cognitive, biological and pragmatic principles how the speaker attributes a certain salience, relevance and typicality to the objects and their parts which belong to a given scene, and how in accordance with this attribution the objects participate in certain relations (for a comparison between the two-level approach and Cognitive Grammar cf. also Dirven — Taylor 1988; Vandeloise forthcoming). 2.2.2. The expression of the foreground-background structure Prepositions, being relational predications, profile a relation with respect to a certain base. The base is that part of the domain which is in the scope of the predication which is conceptually covered (cf. Langacker 1988: 58 ff. and 70 ff.). It is the function of a predication — traditionally known as head of a given construction — to single out a specific aspect of a base so that it gains special prominence. Different profilings of the same base may be expressed by alternately valid expressions, as the following PPs exemplify: (1) the lorry in front of the car (2) the taxi behind the lorry (3) the greengrocer in front of the taxi In these semantically contrasting expressions a common base is assumed both with the conception of the lorry, which is of a certain type, and with the conception of a car, which is also of a certain type, and finally by the conceptualization of a certain spatial relation between the two objects. A relational predication profiles the "interconnections" between those parts of the scene which are salient in the respective discourse situation, whereby the parts can be either "things" or some other relation.

Introduction

9

These interconnections represent the relative position, orientation or motion of the parts within the domain for which the predication holds. The relativity of some part's position or orientation is not only effected by its entering different relations to other parts of the scene, but also by the point of view taken by the language user: by focussing on different parts of the same scene he moves them mentally in the foreground against the other parts which constitute the background. This foregrounding and backgrounding is exemplified in examples (1) to (3): whereas (1) focusses on the location of the lorry with respect to the car, (2) turns round the relationship and focusses on the location of the car with respect to the lorry. (3) is metonymic in relation to (1) in that it focusses on a specific aspect of the lorry, namely its function of transporting vegetables. It localizes this with respect to a specific type of car, a taxi. In each profiled relation a different part of the real scene is focussed on as foreground; this Cognitive Grammar refers to as the trajector (tr). This is also what is "new" in the situation of discourse. The relation implies how the trajector is localized with respect to some presupposed background, referred to as the landmark (lm). This establishes the "old" or "given" part of information in the discourse situation. This mental foregrounding and backgrounding is an old idea of Gestalt psychology, where it became known under the terms of figure and ground, respectively (cf., e.g., Koffka 1935; Köhler 1958). However, Langacker uses the terms trajector and landmark for the mental profilings which are specifically constructed for expressive purposes, the trajector preferentially corresponding to linguistic realizations such as subject or verb and the landmark corresponding to the object. Other linguists such as Schirra and Hottenroth in this volume, and especially proponents of the two-level approach (see Lang, Kaufmann and Pribbenow in this volume) use the term located object (LO) instead of trajector and reference object (RO) instead of landmark. Although it is normally the focus of attention which determines the partitioning of a scene into foreground and background, this partitioning is not totally arbitrary, because certain mental organizations are highly improbable either for gestalt reasons, or because they are unnatural or pragmatically unusual. If, for instance, in an illustration a dark region contrasts with its surroundings it will most probably be conceived as the figure and not as the ground (cf. Langacker 1987: 121). The moving or moveable object of a scene is also the one which is likely to be conceived as foreground: in the scene in which a cat is located on a mat the cat will usually, that is under normal pragmatic conditions, constitute the fore-

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Cornelia Zelinsky-Wibbelt

ground, expressed by the subject NP, while the reversed expression the mat is under the cat sounds unusual, because the normal situation is that the cat gets itself on the mat and not that somebody puts a mat underneath the cat.

3. The structure and use of the lexical category preposition The cognitive breakthrough in linguistics as initiated by Langacker, Lakoff and other proponents of this paradigm gained its strength primarily through the conviction that the shortcomings of previous semantic theories consisted in their adherence to absolute conditions on linguistic meaning and their neglect of the vagueness and flexible use of semantic categories. This cognitive reorientation was triggered by Rosch's psychological experiments on categorization (cf. Rosch 1973 and 1978), which showed that lexical categories cannot be defined in terms of necessary and sufficient conditions, but instead structure as sets of family resemblances. Thus the old philosophical debate about necessity, which Wittgenstein had entered with his notion of family resemblances, was rediscovered empirically. Prepositions constitute a lexical category the elements of which are highly polysemous. Not only do different conceptualizations of trajector and landmark — for instance with respect to bounding, dimensionality and shape — determine the respective differences between the senses of the same relational expression, but these different polysemes are also exploited by metaphorical and metonymic extensions into abstract target domains so that an increasingly higher number of polysemes and increasingly abstract ones are created for the same relational expression. Dirven in this volume illustrates this in detail. This is why prepositions can be taken as exemplary in the study of the semantic representation and processing of lexical units in general. The contributions to this book approach this problem from different theoretical perspectives by touching on the following aspects: — Which are the criteria which define the degree of conventionality, genericity and intrinsicness by which word meaftings become established (cf. Zelinsky-Wibbelt)? — Which are the dimensions of meaning that determine the usage patterns of prepositions (cf., e. g., Hottenroth; Dirven; Zelinsky-Wibbelt; Lang; Kaufmann)?

Introduction

11

— How finegrained is each dimension of meaning according to the functional requirements imposed by the overall context (cf. ZelinskyWibbelt; Lang; Kaufmann; Hottenroth)? — Which are the criteria for distinguishing genuine lexical ambiguity with different readings in the lexicon from lexical vagueness (see Hottenroth; Lang; Zelinsky-Wibbelt)? — How can we provide for all possible uses of a word? This question relates to the problem that meaning may not be predicted in terms of necessary and sufficient conditions, but rather by general lexical rules and principles which can also account for unforseen word meanings (cf. Hottenroth)? — Which are the different communicative conditions which make available different word meanings of different relevance and salience (cf. Zelinsky-Wibbelt)? From a translational point of view this book focusses on the mappings between the language-specific lexicalization patterns in addition. These may consist for instance in (cf. Givon 1978): (a) different mappings of the same content onto different syntactic structures (cf. Zelinsky-Wibbelt; Hawkins; Durrell — Bree); (b) mappings between different contents of source and target language equivalent, e. g., mappings between different degrees of expressive specification (e.g., the German preposition seit which translates into the English prepositions since and for as specialized sub-senses), or incongruence in some dimension of meaning (as with German Bus vs. bus in English; the English equivalent still seems to keep a SURFACE sense contrasting with German in certain situational contexts); (c) language-specific gaps with respect to expressing some universal semantic structure; with prepositions this problem is highly relevant: compared to English and French German is underdetermined with respect to expressing spatial relations by prepositions (cf. Taylor 1988 for the relation between English and Italian; Hawkins this volume).

3.1. Categorization and context The questions which have just been raised can only be solved by an empirically grounded theory specifying how the content and the structure of lexical representation is determined by the conveyance and interpretation of linguistic utterances.

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3.1.1. Prototypes and schemata Linguistic utterances occur in certain situational contexts which provide the conditions for the use of a lexical unit in a specific meaning. This statement implicitly presupposes a division of labour between two qualitatively different components of meaning: (i) meaning that is anchored in a lexical unit; (ii) meaning that is evoked, specialized, constrained or overridden by its specific use in a certain context. How this distinction is made and what status is attributed to it derives from hypotheses about the processing of linguistic meaning and it will crucially determine the design of a particular natural language system. This can be observed by comparing different linguistic theories with respect to their way of drawing the line between lexical and contextual knowledge. In particular, different theories draw different conclusions from this division with respect to the interpretation process. We can only touch on this in this introduction by contrasting some basic assumptions of Cognitive Grammar with those of the two-level approach. The basic difference between these theories in modelling the interpretation of language derives from the following contrasting axioms: The guiding assumption of Cognitive Grammar is the holistic and continuous nature of all human behaviour and its underlying structure. Linguistic behaviour is inextricably interrelated with its underlying structure, and language in turn is continuously related to overall human behaviour and its structure. Language is only considered as a more specific faculty embedded in a more general psychological faculty. In contrast to this holistic view, the two-level approach considers the organization of human behaviour to be basically modular (cf. Lang 1987: 291). In particular, semantic and conceptual knowledge are seen as constituting relatively autonomous though interacting systems. In a very general sense it can be said that semantic representation and interpretation generalizes over specializations which are only instantiated by the context on the conceptual level. Cognitive Grammar, in line with Prototype theory, retreats from abstracting only one common semantic representation from all possible polysemes of a lexical unit in the lexicon, as done by the two-level approach. Instead it pays the price of a redundant representation by enumerating several senses in the lexicon, while additionally generalizing over regular polysemy relations holding between word senses in the form

Introduction

13

of rules. Cognitive grammarians often emphasize that language is less economical and systematic than it is generally claimed to be and that in this respect a purely generative approach will not work (cf., e. g., Langacker 1987: 369 f.; Lehrer 1990). Thus Cognitive Grammar defends the mental abstraction of a word's meaning from its instantiations (cf. Langacker 1987: 401 ff.) by categorization both in terms of prototypes and schemata as being constitutive of the interpretation of word meaning. Both prototypes and schemata are economical abstractions and function as patterns of comparison in evaluating the meaning of actually used linguistic units. 2 A prototype represents the most typical instance of a semantic category, while a schema represents a generalization over two or more instances. The two abstractions are closely interrelated, for instance a schema generalizes over the prototype and its semantic extension^). Cognitive Grammar neither distinguishes between levels of knowledge, such as linguistic and world knowledge, nor does it single out the lexicon or any other component as autonomous on nonarbitrary grounds (cf., e.g., Langacker 1987: 2,20). Instead, linguistic meaning is claimed to be encyclopedic in nature, comprising knowledge about basic as well as specific domains, knowledge about language use, which is related to knowledge about social conventions and other behavioral constraints. All knowledge structures are thus coherent with general conceptual structures. The lexicon is only seen as a more specific part of the grammar as a whole. As such, it takes a central position within our encyclopedic knowledge, as it relates to all types of knowledge. A two-level model of the interpretation of meaning can be said to be in contrast to Cognitive Grammar in all its basic axioms (for the following cf. Bierwisch 1987 and 1989; Lang 1987 and 1989). The research paradigm developed by Bierwisch and Lang assumes several knowledge systems which are relatively autonomous as they have their own representations, rules and principles. For one thing, they argue in favour of distinct systems, because words, without being polysemous, may refer to a "whole family of interrelated conceptual complexes" and therefore the lexical meaning of a word should establish a "pattern generating the family of conceptual complexes" (Lang 1989: 270). Among all systems, the conceptual system has intermodal status, as it has an integrative function with respect to the other systems. The semantic representation of the lexicon is constituted by the semantic system only. The conceptual system does not constitute the representation of the lexicon, but the structure of lexical entries and the

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structure of the lexicon as part of the grammar, as there is a mutual interaction between the conceptual and the semantic system. As the semantic system is a proper subsystem of the grammatical system, semantic representations mediate between the grammatical and the conceptual system. A semantic representation of a lexical unit consists of parameters which establish the potential of interpretation. This semantic potential provides a schema for the generation of a family of concepts. From this family a particular concept is selected depending on contextual conditions for conceptual values which instantiate parameters of the semantic representation. The division between semantic and conceptual information is correlated with a division of the interpretation process into two phases. In contrast to this, a more holistic approach assumes that all components of knowledge interact during the whole process of interpretation. Thus specific senses may be preferred right from the beginning. Cognitive Grammar also assumes lexical meaning to be schematic in that one single sense of a word is the result of a mental abstraction from all its occurrences that speakers have met in language use. However, lexical meaning is itself conceptual and hence abstract, schematic meaning encoded in the lexicon and its more specialized instantiations in language use cannot be distinguished by their representation and the principles and rules working on them. Moreover, as we have shown above, Cognitive Grammar assumes that lexical meaning is not purely schematic, but that prototypes also establish lexical meaning abstractions. The assumptions of these contrasting theories will lead to different implementations of a language system. This book is an attempt to throw some light on these differences. Many authors focus on the distinction between lexical and contextually instantiated meaning while investigating the process of interpreting the meaning of prepositions. 3.1.1.1. Categorization by schemata As one of its originators, Lang presents a clear defense of the two-level approach. In this paper he finds evidence for his approach in the necessity to distinguish intrinsic from extrinsic uses of projective prepositions. His essential point is that these different uses do not depend on different semantic representations of the respective prepositions. Instead he claims that one semantic representation is sufficient, and that the interpretation of different concepts is the result of an interaction between the two distinct levels representing semantic and conceptual information respectively. During this interaction the parameters which are part of the

Introduction

15

semantic representation of the preposition are assigned values by being mapped — via identification and specification — onto the conceptual representation of the reference object. On the conceptual level, spatial objects are represented as Object Schemata, which embody information about the object's dimensionality, shape, sidedness and orientation. The position and location of objects in space is basically determined by what Lang calls Primary Perceptual Space. This is a perceptually anchored system comprising the three axes — the Vertical establishing the dominant axis, the backbone of spatial orientation, the Observer Axis and the Horizontal. The study continues Bierwisch and Lang's work on dimensional adjectives and is meant as an example in that the semantic properties assumed for prepositions are claimed to have cross-categorial validity. Adhering to the same theoretical assumptions, Kaufmann illustrates the interpretation of prepositions with an exhaustive analysis of the manifold uses of the German preposition durch {through). The semantic representation generalizes over all possible uses of durch by two components of meaning: the INCLUSION component, which is the same as the representation of the preposition in, and the PATH component, containing the essential path parameter D (x). The inclusion component is responsible for the interaction of the dimensionality properties of the located object and the reference object. The information specific to the path properties of durch is provided by the second component. The path parameter D (x) has to be fixed by a path provided by contextual information about the located object x. The actual course of the path is then determined by the further interaction of the conceptual information associated with the located object and the reference object. At least three types of information are encoded by the concepts associated with nouns denoting objects: gestalt properties, functional properties (at least as far as artifacts are concerned) and structural properties of the object. This information can be used to fix the parameter D (x). Pribbenow develops a two-level model of the computational interpretation of localization expressions. This has been implemented in the LILOG prototype LEU 2, a text understanding system with the ability to answer questions. Localization expressions are defined by their function of predicating the static or dynamic localization of entities, which is typically designated by prepositions. The paper focusses on the conceptual analysis of localization expressions, exemplified by prepositions, and on the influence of the textual and situational context. The adequate processing of knowledge is achieved by using picture-like representations,

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Cornelia Zelinsky-Wibbelt

referred to as depictions. The depictions are combined with a propositional formalism, which interprets general regularities between spatial concepts and non-spatial, e. g. functional aspects of meaning. The representation of the conceptual meaning of localization expressions is assessed by areas functioning as search domains with respect to the entities to be located. Each search domain consists of a primary area describing the basic meaning of the localization expression and priorizations which take into account expectations about the typical localization of the entity to be located. The search domain is the result of the depictorial interpretation working on the concept combination, which has been computed by the propositional rules. 3.1.1.2. Categorization by prototypes The semantic model proposed by Hottenroth is a hybrid model in the sense that, on the one hand, she also starts from the assumption of a two-level model of semantics, but on the other hand, she does not assume that the semantic representation of the preposition has to be an abstraction from all possible contextual interpretations, but only from a certain range of "prototypical" uses. In a detailed analysis of the spatial uses of the French preposition dans (in), Hottenroth shows that the adoption of such an "overspecified" semantic representation turns out to be quite a natural and psychologically plausible assumption. The analysis of the process of interpretation gains its plausibility by taking into account the part played by certain general cognitive principles known from the domain of object conceptualization and categorization, as well as certain systematic manipulations of object concepts. The paper shows how these principles determine the interpretation of prepositions dependent on their different possible reference objects. Within this model the author makes explicit what "similarity" or "tolerance" means in linguistic categorization. In analyzing the semantics of the Dutch preposition in, Cuyckens proceeds from the view that meaning is encyclopedic in nature. Thus he describes the differing senses of in as a family resemblance structure and explains the fuzziness at the borderline of the senses as a natural consequence of man's functioning in his social environment. On the one hand he assumes that the abstract relation COINCIDENCE generalizes over the different relations between trajector and landmark expressed by the preposition in. On the other hand he assumes that Hawkins' spatial configuration MEDIUM subsumes differing, but related, configurations of the landmark. Cuyckens analyzes these subconfigurations in terms of

Introduction

17

internal and external bounding and in terms of the dimensionality of the landmark. He concludes that porous, three-dimensional bounded mediums figure as prototypical in the family of senses of in. The sense of in which refers to a part-whole relationship is outside this family resemblance structure, but is still related to the chain of meaning via the configuration of the landmark. The path uses of in copy the family resemblance structure analyzed for the non-path uses of in and the two are related by transformations as well as by conceptual intersection. In dealing with image understanding Schirra explores and models an experientialist relation between natural language and perception. The topic of this paper is how the experientialist relation is processed by the SOCCER system, the aim of which is the interpretation and German verbalization of visual information provided by soccer games. This is achieved by visually perceiving locations and movements, interpreting conventions, assuming intentions and plans and finally selecting events for adequate verbalisation. All this is achieved in relation to the participants of the game. By translating visual percepts into prototypically structured spatial concepts defined by a conjunction of graded functions of essential parameters, SOCCER represents conceptual vagueness: each spatial preposition is associated with a core meaning very similar to Herskovits' ideal meaning; from this core meaning actual meanings are derived by algorithms, resulting in a classification function, which associates SOCCER's percepts to a graded Spatial Concept corresponding to the usage of a spatial preposition. Based on a function over applicability degrees in generation, linguistic hedges are used to express good or less good instances of such a graded concept. Schirra shows how in reverse these structures can be used for the construction of mental images during the interpretation of PPs. Aurnague and Vieu present a text analysis system in which inferences are drawn in analogy to human reasoning. Although their semantics is modularized into three qualitatively different levels, the authors rely heavily on Herskovits and Yandeloise. At the geometrical level, purely objective topological and projective properties are represented. This knowledge is used for the interpretation of the orientation and structure of entities as well as some common sense spatial relations at the functional level. The internal structure of entities is described in terms of several part-whole relations and their ordering relations, which the authors explain by Link's lattice theoretical analysis of entities. By these relations

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Cornelia Zelinsky-Wibbelt

Aurnague and Vieu can distinguish functionally different senses of the preposition dans (in) and sur (on). The representation of geometrical and functional relations is done in first-order predicate logic. While the knowledge represented at these two levels is indefeasible, this does not hold for the third level, which represents pragmatic principles. Relying heavily on the function of objects, these pragmatic principles filter out relations wrongly inferred and add information by using knowledge about the typical use of objects, their relevance in relation to other objects and the quantity of objects. By taking into account these additional conceptual relations, Aurnague and Vieu succeed in inferencing relations which could not be accounted for in purely geometrical and functional terms. As there may always be highly marked situations in which the typicality and relevance normally attributed to a sense may be defeated, the pragmatic knowledge may only be manipulated by non-monotonic logic; this, however, was still being developed at the time of writing. 3.1.2. Semantic extension of lexical meanings The phenomenon of semantic extension has currently undergone a revival not only in Computational Linguistics with respect to the implementation of a lexicon, but also in Linguistics in general. It is being discussed in regard to the options of an economical vs. a more redundant lexical representation. The economical representation would generalize over different senses of a lexical unit by representing only the most abstract meaning in the lexicon, and by representing the polysemous structures by rules which generate the polysemous senses. The latter is obviously very helpful for the interpretation of novel senses which are not foreseen in the lexicon. Still, it may be asked whether such a redundancy-free representation is sufficient. Many linguists, often those who proceed from an empirically grounded work, refute this position (cf., e. g., Lehrer 1991) with the argument that language — although regular to a high degree — is not completely regular. This is especially true of Cognitive Grammar. Cognitive Grammarians generally agree that meaning extension by metaphor and metonymy constitutes productive processes operating on the lexicon (cf. Lipka 1988: 357). Yet, it contradicts the philosophy of Cognitive Grammar to set up categorical rules for patterns of meaning extension which can predict each possible meaning extension with complete certainty (cf. Taylor 1989). Rather, these predictions should hold for preferred patterns of meaning extension. Dirven gives a good example of this in this volume. He illustrates chains of meaning resulting from

Introduction

19

meaning extension. Meaning extension proceeds from a prior meaning which is projected onto increasingly abstract senses in various cognitive domains. It is the intention of this article to point out the semantic regularities holding between different cognitive domains such as time, state, area, manner or means, circumstance, cause or reason on the one hand. On the other hand each domain is investigated with respect to the relations existing between the concepts expressed by different prepositions. The result is that there are gaps in meaning extension in some abstract domain, because of the underlying spatial sense relations of the respective preposition which have conventionalized a particular structure. Taylor's article allows for a related conclusion: he analyzes polysemy relations for an extensive set of English prepositions and sets up patterns which, though they are realized by a large class of prepositions to a high degree, do not hold without exception. In fact, he discovers many meaning extensions which pertain to one preposition only. He classifies prepositions with respect to the extensions they can undergo on the basis of the profiled relation. Both simplex (on, under, at) and multiplex prepositions (around, along, through) can be categorized with respect to the characteristics of their trajectors on the one hand and their landmarks on the other. Multiplex prepositions are more productive and variegated with respect to the semantic extensions they can undergo. The paper closes with a catalogue of knowledge types, which Taylor assumes as necessary for the selection of the intended lexical meaning: (1) world-knowledge; (2) knowledge about the valency of other constituents in the sentence, especially the verb; (3) knowledge about the sentential aspect; (4) knowledge about the informativity of the utterance. In the framework of X-bar theory Rauh analyzes English prepositions by the relational properties which they exhibit in the grammatical constructions in which they participate. By analyzing the different types of uses of prepositions according to their relational properties, she points out the heterogeneous functions of prepositions. First, lexical prepositions are distinguished from non-lexical prepositions by the syntactic and semantic properties which they have as heads of constructions and by their co-occurrence restrictions, which they impose on other constituents within their maximal projection. Non-lexical prepositions are analyzed as constituting different intermediate stages in the bi-directional processes of lexicalization and gram-

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maticalization originating in a marked metaphorical use of a form and ending in a lexical variant. Case prepositions are an instance of grammaticalization of originally autonomous lexical forms. Prepositions in fixed phrases are grammatical functions taking part in "adjectivizing" or "adverbializing" lexicalization processes. These multi-word units are associated with lexical entries of their own as well as with lexical rules which describe their syntactic and semantic regularities. Existing metaphorical extensions of the spatial meanings of prepositions may be observed in different stages. Transfer into the temporal domain results in a reanalysis of the lexical properties in accordance with the temporal domain and in lexical variants with individual lexical entries. Other metaphorical extensions such as scalar and sequential uses of basically spatial prepositions constitute lexicalized conceptual variants which are the result of a reinterpretation by imposing the spatial structure on the target domain. Rauh's analysis concludes that an account of grammatical structures only in terms of the cognitive principles imposed on them is insufficient, as the same metaphorical processes which are determined by the cognitive principles, result in different grammaticalizations. Therefore it is rather the grammaticalization process itself which restricts grammar.

4. Contrastive implications of prepositions Cognitive Grammar offers particular benefits for machine translation as it allows for both universal and language-specific semantic structures to be analyzed and related. It assumes that there is universality of meaning on the one hand resulting from a cognitive endowment which is common to all language users of the world. On the basis of cross-cultural differences, however, which provide a different environment to the language user, this common cognitive endowment is exploited in different ways: different distributions of universal dispositions are mirrored in different patterns of meaning in different languages. Hawkins studies the interaction of both universal and language-specific meaning from a contrastive point of view: he analyses the spatial adpositions of the two languages English and Japanese, the cultural environments of which are maximally distinct. Not surprisingly, he finds that the two languages make different use of certain semantic resources, while being compatible with respect to others. He obtains this result by assum-

Introduction

21

ing profilable structures which correspond to the common cognitive endowment and which are not developed with respect to specific cognitive domains. These innate structures comprise the basic spatial relations of SAME and DIFFERENT and the two parameters of relation and configuration. By contrasting this universal structural potential against the actually profiled structures of the specific languages Hawkins brings out their differences and correspondences in configurational and relational information. Zelinsky-Wibbelt confronts the problem of cross-language variations and correspondences with the translation of prepositions. She claims that in natural language processing and in machine translation in particular a semantic representation needs to be conceptually constrained in order to interpret and generate different usage patterns in different languages. By proceeding from the assumption that the conceptualization of mental space is perceptually driven she illustrates how pragmatic principles concerning the function of entities determine the salience, relevance and typicality of the entities constituting the conceived situation. These principles determine the process of schematization, in which the spatial relation expressed by the preposition follows from the spatial properties of the related entities. These in turn are derived from prototypical and schematic categories encoded in the lexicon, all in accordance with the utterance situation and the domain of discourse. Zelinsky-Wibbelt assumes that Hawkins' PLACE relations of COINCIDENCE and SEPARATION constitute the "tertium comparationis" which is necessary for translating prepositions between different languages. These relations are abstracted from the profiled relation of the source language and handed over to the target language. The target language uses this transferred information together with its own specific lexical and compositional rules for the generation of the correct preposition. Zelinsky-Wibbelt formalizes in a model how the different knowledge resources are dependent on each other in mapping prepositions from German into English in a machine translation system. Not committing themselves to a specific theory, Durrell and Bree explain the use of temporal conjunctions and prepositions by selection procedures which they represent in selection trees. They proceed from Bree's earlier proposals for English and Dutch and develop a framework for German. The selection trees determine the decision process for the correct use of a temporal conjunction or preposition by temporally relating the time of the state or event expressed by the matrix and subordinated clause and by the time of discourse. The cross-language

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comparison as to the expressive distinctions by temporal conjunctions and prepositions systematically contrasts the differences and explains them as the result of — different conditions being focussed on in the decision processes in different languages; — different conceptualizations of the temporal extension referred to by the nominal governed by the preposition. The high number of German prepositions which are used both in a durative and a non-durative sense has led to two selection trees in German. The validity of the trees might be tested by adapting them to an NLP system, which would be easy to do as the format of the trees is very near to computer interpretable rules. Letting the reader now go in medias res, we hope that this introduction has shed some light on the area of research presented in this book. In particular, seeing the area of research in terms of mental space, we hope that it has become clear how different semantic viewpoints or perspectivizations of the topic of research can lead to different theoretical conceptualizations. The editor apologizes for a presumably biased presentation, due to the fact that she herself subscribes to the theory of Cognitive Grammar.

Notes 1. I would like to thank all colleagues who have discussed these introductory notes with me. I am especially indebted to Ewald Lang, Rene Dirven, John Taylor, Hubert Cuyckens, Claude Vandeloise, Erich Steiner and Michael Grabski for their time and advice which is reflected in this introduction. Thanks are also due to John Taylor and J. A. Charlton for giving the finishing touches to my English. Of course I am responsible for all remaining errors. 2. Langacker uses the term usage event for this comparison.

References Bennett, David C. 1975 Spatial and temporal uses of English prepositions — An essay in stratificational semantics. London: Longman. Bierwisch, Manfred 1987 "Semantik der Graduierung", in: Manfred Bierwisch — Ewald Lang (eds.), 91-286.

Introduction 1989

23

"The semantics of gradation", in: Manfred Bierwisch — Ewald Lang (eds.), 71-261. Bierwisch, Manfred — Ewald Lang (eds.) 1987 Grammatische und konzeptuelle Aspekte von Dimensionsadjektiven. Berlin: Akademie-Verlag. 1989 Dimensional adjectives. Grammatical structure and conceptual interpretation. Berlin: Springer. Bolinger, Dwight 1977 Meaning and form. New York: Longman. Chafe, Wallace L. 1968 "Idiomaticity as an anomaly in the Chomskyan paradigm", Foundations of Language 4: 109-127. Cole, Peter — Jerrold M. Sadock (eds.) 1977 Syntax and semantics. Volume 8: Grammatical relations. New York: Academic Press. Dirven, Rene — John Taylor 1988 "The conceptualization of vertical space in English: The case of taW\ in: Brygida Rudzka-Ostyn (ed.), 379^102. Fillmore, Charles J. 1975 Santa Cruz lectures on deixis. Bloomington: Indiana University Linguistics Club. 1977 "The case for case reopened", in: Peter Cole — Jerrold M. Sadock (eds.), 59-81. Givon, Talmy 1978 "Universal grammar, lexical structure and translatability", in: Franz Günthner — Monica Günthner-Reutter (eds.), 235-272. Günthncr, Franz — Monica Günthner-Reutter (eds.) 1978 Meaning and translation. Philosophical and linguistic approaches. London: Duckworth. Hüllen, Werner — Rainer Schulze (eds.). 1988 Understanding the lexicon. Meaning, sense and world knowledge in lexical semantics. Tübingen: Niemeyer. Köhler, W. 1958 Dynamische Zusammenhänge in der Psychologie. Bern: Huber. Koffka, K. 1935 Principles of Gestalt Psychology. London: Harcourt, Brace & World. Lakoff, George 1987 Women, fire, and dangerous things. What categories reveal about the mind. Chicago/London: University of Chicago Press. Lakoff, George — Mark Johnson 1980 Metaphors we live by. Chicago: Chicago University Press. Lang, Ewald 1989 "The semantics of dimensional designation of spatial objects", in: Manfred Bierwisch — Ewald Lang (eds.), 263-417. Langacker, Ronald W. 1987 Foundations of cognitive grammar, Vol. 1. Theoretical prerequisites. Stanford: Stanford University Press. 1988 "A view of linguistic semantics", in: Brygida Rudzka-Ostyn (ed.), 49-90.

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Lehrer, Adrianne 1974 Semantic fields and lexical structure. Amsterdam: North Holland. 1991 "Polysemy, conventionality and the structure of the lexicon", Cognitive Linguistics 1-2: 207-246. Lipka, Leonhard 1988 "A rose is a rose is a rose: On simple and dual categorization in natural languages", in: Werner Hüllen — Rainer Schulze (eds.), 355-366. Moore, Timothy Ε. (ed.) 1973 Cognitive development and the acquisition of language. New York: Academic Press. Rosch, Eleanor 1973 "On the internal structure of perceptual and semantic categories", in: Timothy E. Moore (ed.), 111-144. 1978 "Principles of categorization", in: Eleanor Rosch — Barbara B. Lloyd (eds.), 27-47. Rosch, Eleanor — Barbara B. Lloyd (eds.) 1978 Cognition and categorization. Hillsdale, N. J.: Erlbaum. Rudzka-Ostyn, Brygida (ed.) 1988 Topics in cognitive linguistics. Amsterdam/Philadelphia: John Benjamins Publishing Company. Schweizer, Harro (ed.). 1985 Sprache und Raum. Ein Arbeitsbuch für das Lehren von Forschung. Stuttgart: Metzlersche Verlagsbuchhandlung. Taylor, John 1988 "Contrasting prepositional categories: English and Italian", in: Brygida Rudzka-Ostyn (ed.), 299-326. 1989 Linguistic categorization: Prototypes in linguistic theory. Oxford: Clarendon Press. Vandeloise, Claude 1984 Description of space in French. Doctoral Dissertation, University of California, San Diego: L . A . U . D . T . 1985. 1991 Spatial prepositions: A case study in French. Chicago/London: The University of Chicago Press. in press "Methodology and analyses of the preposition", in: Leuvense Bijdragen. Wierzbicka, Anna 1972 Semantic primitives. Frankfurt: Athenäum. Wittgenstein, Ludwig 1953 Philosophical investigations. Oxford: Blackwell. Wunderlich, Dieter 1985 "Raum, Zeit und das Lexikon", in: Schweizer, Harro (ed.), 66-89.

1. Lexicalization patterns of prepositions

The Dutch spatial preposition "in": A cognitive-semantic analysis Hubert

Cuyckens

1. Setting the scene This paper provides a lexical-semantic analysis of the spatial senses of the Dutch preposition in, or, in short, of the spatial preposition (SpP) in, as it is exemplified in (1): (1)

a. De vaas Staat in de kast. 'The vase is in the cupboard.' b. Hij woont in onze buurt. 'He lives in our neighborhood.' c. Teken een lijn in die cirkel. 'Draw a line in that circle.' d. De knik in de curve is heel significant. 'The dip in the graph is very significant.'

Before embarking on the analysis proper of in, we will (a) look at the nature of spatial prepositions in general, and (b) briefly present the lexicalsemantic framework within which this study is situated.

1.1. Spatial prepositions defined Spatial prepositions indicate the spatial relation between two arguments χ and y, i.e., how χ and y relate to each other in space.1 (In cognitive linguistic studies, it has become customary to utilize the terms trajector (TR) and landmark (LM) 2 for the arguments χ and y, respectively.) More specifically, in a large number of cases, spatial prepositions describe the place/location of χ (in other words, they assign χ to a particular place) by using the argument y as reference, or still, they serve to locate χ with respect to y, or rather, the place of y. Examples are: (2)

a. the books on the table b. He washed his car in the garage.

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On in (2 a) locates the books (argument x) with respect to the table (argument y): it assigns χ to a place or location which coincides with the the place taken up by top of the table (a place which is assumed to be known). The English SpP in (henceforth inE) in (2 b) stipulates that the location of the event expressed in the sentence He washed his car coincides with the interior of the garage. In a number of cases, though, SpPs serve not to locate the entire entity χ with respect to y, but an element in its semantic structure. Consider (3): (3)

a. The children were drawing on the wall, b. the sign to Brussels

In (3 a) it is only the result of the children's drawing which is located with respect to the wall. In (3 b) not the sign is assigned a particular location, but the direction this sign adopts.

1.2. Classical vs. cognitive lexical semantics Irrespective of the lexical-semantic framework we adopt, we take lexical meaning or lexical-semantic information to be conceptual in nature. Word meanings or lexical concepts are mental entities that link, or mediate between, words and their (extralinguistic) denotata. More precisely, a lexical concept X (labeled by the word x) establishes a class/category "X" of denotata that fit the conditions (or conceptual information) in X. 3 Interesting proposals for the semantic analysis of lexical items have recently been put forward within cognitive linguistics. Indeed, cognitive lexical semantics has become a widely accepted alternative to the socalled classical 4 view of word meaning. On the whole, these two lexical-semantic approaches differ in three important respects: 5 (a) Classical lexical semantics advocates the existence of an autonomously linguistic level of word meaning and, concomitantly, the separation of linguistic-semantic and encyclopedic information in the conceptual content of a word. Cognitive lexical semantics, in contrast, suggests that all conceptual information associated with a lexical item is broadly encyclopedic in that it is part of, and needs to be understood against the background of, broader cognitive structures. On this view, word meaning

The Dutch spatial preposition in

29

is not determined by the language system itself, but reflects how people interact with, perceive, and conceptualize the world. (b) With respect to the structure of word meaning, the classical approach holds that (autonomous) lexical concepts are well-delineated entities whose definitions are couched in terms of an invariable set of necessary and sufficient features applicable to all the instances in that concept. From this definitional perspective, then, all instances are completely identical. 6 Now, on the cognitive view, instances of a concept may be linked not because they all share the same features, but because they share different sets of features with each other; in other words, because they are similar to each other in different respects (or along different dimensions), very much like the members of one family. As such, what links the various instances of a lexical concept is a family resemblance relationship. The structure of lexical concepts must capture this family resemblance relationship between instances. A simple list of (encyclopedic) features is an inadequate representation of a family resemblance concept (even when allowance is made for the fact that none of these features need be necessary and/or sufficient), because it does not sufficiently convey that different (yet, mutually related) featural configurations may apply to different subsets of instances of the concept. Therefore, as Geeraerts (1989) suggests, family resemblance concepts can be represented as a cluster of overlapping featural configurations. 7 Instead of representing lexical semantic structure in terms of featural configurations, one might also resort to imaginal representations (depictions of the physical world), with overlapping imaginal representations corresponding to overlapping featural configurations (cf. Brugman 1981; Lakoff 1987). (c) While classical lexical concepts are made up of an invariable set of criterial features, all of which have an equal status in defining the concept, some featural information in cognitive concepts may be more salient or prototypical than other (extensionally, some concept instances are more prototypical, salient, or representative than others) (cf. Rosch 1975, 1978; Rosch - Mervis 1975). It has been amply shown elsewhere that the classical account of word meaning runs into a number of serious problems and that the cognitive approach constitutes a far more satisfactory framework for lexical-semantic analysis (Haiman 1980; Lakoff 1982, 1987; Geeraerts 1985: 82148, 1986: 112-115, 1988, 1989; Cuyckens 1991). It goes without saying, then, that also the lexical item in should be analyzed within this cognitive framework. While it is beyond the scope of this paper to dwell at length

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on the merits of the cognitive approach, it might be instructive, given that in is an SpP, to look at some evidence from earlier studies of SpPsemantics against classical and in favour of cognitive lexical semantics. (a) Also in the semantic study of SpPs the autonomy requirement (typical of classical lexical semantics) is no longer tenable. (i) A significant number of (allegedly) non-encyclopedic SpP-deflnitions exploit the properties associated with either one of the SpP's arguments (usually of argument y). I doubt, though, whether these properties can be considered to be properly semantic (i. e., non-encyclopedic) ones, when χ or y are not part of a prepositional construction. InE and on, for instance, are often said to describe a COINCIDENCE relation between χ and a 3DIM container or 2DIM surface y, respectively. (4)

a. the keys in the cupboard b. the statue on the Marketplace

I have a strong hunch that advocates of the classical view would have to regard these physical and functional attributes of y (cupboard: potential container, 8 3DIM; Marketplace: 2DIM, surface) as encylopedic. Now, advocates of the classical view could still argue that otherwise encyclopedic information associated with a lexical item becomes non-encyclopedic when this item is the argument of an SpP. In my mind, though, one cannot seriously maintain that the same conceptual information is now encyclopedic then semantic. Similar examples can be found in (5): (5)

a. The child crossed the street in front of my car. b. the trees along the road

In (5 a)'s most likely interpretation, χ (i. e., the child crossing the street) is located at some point on the axis defined by the inherent front of the car. Now, the fact that a car has an inherent front would, on the classical view, fall outside the strictly semantic information associated with car.9 In (5 b) along exploits an encyclopedic attribute of x, viz., its significant extension in one dimension. (ii) The encyclopedic information associated with y may also play a crucial role in resolving the ambiguity of prepositional expressions. Consider (6): (6)

a. a ring around the bathtub b. a ring around the collar (example taken from Hawkins 1985: 287)

The Dutch spatial preposition in

31

Strictly speaking, the prepositional constructions in (6) involving around are ambiguous: χ may describe a circular path (i) which coincides with y (e. g., in (6 a) the visible residue of soap or dirt that is left when the water in the tub has drained and in (6 b) the residue of dirt when a shirt has been worn for too long) or (ii) which is separate from y (e. g., when the householder has drawn a circle around the bathtub). Now, the first reading is the preferred one because it is part of our practical (or encyclopedic) knowledge that rings of dirt/soap residue are a typical feature of bathtubs. (iii) I pointed out above that on the cognitive view, all conceptual information associated with a lexical item is broadly encyclopedic in that it is part of, and needs to be understood against the background of, broader cognitive structures. In Langacker's terminology, the semantic structure of a word necessarily takes the form of a profile or figure which is characterized relative to a base or ground. With respect to SpPs now, it seems quite obvious that physical space has a prominant role in the base of or the background against which SpPs must be understood. How do we understand physical space? First of all, there is the Newtonian conception of space "as an infinite, continuous, stationary, three-dimensional box [that] enables the speaker to label locations by their coordinate values ... (given a point of origin)" (Miller — Johnson-Laird 1976: 380). However, ordinary languages deal with relativistic space, space in which the location of objects is determined relative to other objects. Our three-dimensional conception of space can be attributed to our visual appreciation of depth and of the horizontal and vertical relations between objects (cf. Miller — Johnson-Laird 1976: 57-76). Now, neither actual physical space nor our conception thereof has an inherent orientation. Oriented physical space requires laying out a three-dimensional coordinate system relative to an origin. Not all SpPs talk about space relative to an origin and coordinate axes (e.g., inE, on, at). Yet, in front of, behind, to the left of, to the right of, above, and under crucially involve the imposition of a three-dimensional matrix on physical space. Furthermore, in front of, behind, to the left of, and to the right of can be interpreted relative to a speaker's egocentric origin (deictic use) or relative to coordinate axes derived from the intrinsic parts of y itself (intrinsic use). Another element in the base of SpPs is the observer. In He lives across the bridge, he ( = x) must be located at the end of a mental path that initiates at the location of an observer (on this end of the bridge) and that terminates at the other end of the bridge. Also past in He lives past

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Hubert Cuyckens

the post office and the deictic uses of in front of, behind, to the left of, and to the right of involve this observer. (b) The second "classical" requirement, viz., that lexical items be characterized in terms of a set of necessary and sufficient conditions, also presents difficulties for the semantic analysis of SpPs. (i) For quite a few SpPs, a description in terms of criterial features can simply not be found. An amply studied example is over, which involves at least three senses: "above and across", "above", and "covering" (cf. Brugman 1981; Lakoff 1987). (7)

a. We flew over the Atlantic. b. the picture over the door c. the tablecloth over the table

Also the Dutch SpP op, a number of whose uses are exemplified in (8), is not amenable to a necessary and sufficient description. (8)

a. Het pakje op de tafel 'the package on the table' b. de mooie fresco's op de zoldering 'the frescos on the ceiling' c. het ongeval op het kruispunt 'the car accident at the intersection' d. Hij is op zijn kantoor. 'He is at his office.'

Given, on the one hand, the highly polysemous nature of most SpPs and the difficulty to find a single set of criterial features on the other, classical lexical semantics would be forced to treat the different senses of SpPs as homonyms. I find this a position hard to maintain. (ii) The necessary and sufficient descriptions that are actually proposed are not adequate. Let us have a look at inE, for which Bennett (1975) and Cooper (1968) propose an analysis in terms of the notion 'interior'. This description is neither necessary nor sufficient. First, the feature "interior" is not involved in all uses of inE, as the examples in (9) show: (9)

a. the oasis in the desert b. He got a kick in the stomach.

Moreover, not all spatial configurations that can be classified as an interior give rise to inE. Consider the following situations taken from Vandeloise (1986: 232-233):

The Dutch spatial preposition in

33

Figure 1. The smoke in the cheese-cover

In Figure 1, cheese-cover features an interior, viz. the 3DIM, non-porous space bounded by its outer edges and the table. The same spatial configuration occurs in Figure 2; still, under is the preferred SpP. (iii) The classical description of SpPs creates the impression that SpPs are clear-cut, well-delineated concepts. However, a fair number of SpPconcepts are fuzzy: (10)

a. The plane flies over the mountain, b. Y is behind X.

When the path of the plane in (10 a) is directly above the peak of the mountain, the use of over is sanctioned. Suppose now that the path of the plane is rather to one side of the mountain (cf. Figure 3). If it is reasonably near the top, over is still appropriate, but there is no clear demarcation line indicating where the use of over is still sanctioned and where it no longer is. Similarly in (10 b), if y is not directly behind x, it is unclear from exactly what point onwards the spatial relation between χ and y must be lexicalized by means of to the right of or to the left of instead of behind (Figure 4). Summing up, from the preceding remarks, it must have become clear that it certainly seems justified to adopt a cognitive-semantic framework for the analysis of the Dutch SpP in.

1=1

Figure 2. The pear under the cheese-cover

34

Hubert Cuyckens

in f r o n t

to

the

left

of

X

Figure 4. Y is behind X

of

to

t h e right

>

of

The Dutch spatial preposition in

35

2. The analysis of "in": An outline In the rest of this paper, I will be concerned with the cognitive-semantic analysis of the spatial relation expressed by the preposition in. More in particular, I will concentrate on the lexical-semantic structure of in and on the isolation of a prototype. Here are a number of representative examples: (11)

a. De vaas Staat in de kast. 'The vase is in the cupboard.' b. Let op voor de nagels in de plank. 'Watch out for the nails in that board.' c. Hij woont in onze buurt. 'He lives in our neighborhood.' d. Teken een lijn in die cirkel. 'Draw a line in that circle.' e. Hij woont in Duitstand. 'He lives in Germany.' f. Hij zette de champagne in de ijskast. 'He put the champagne in the fridge.' g. De knik in de curve is heel significant. 'The dip in the graph is very significant.'

It is obvious from these examples that in expresses a relation of COINCIDENCE between the arguments χ and y (i. e., y constitutes the place where χ is located). Sentences (11 a-f) differ from (11 g) in that the latter, next to expressing COINCIDENCE, also involves a part-whole relation between χ and y. Furthermore, it can be observed that in lexicalizes static spatial relations (11 a-e, g) as well as relations denoting a path (in the latter case, COINCIDENCE holds only between the terminus of the path traversed by χ and y). The analysis of in will be organized as follows. The first, and largest, part (Section 3) will address the static or non-path uses10 of in (cf. (11 a e, g)). Within this section, the following issues will be dealt with: 1. I will first describe in expressing non-part-whole (NPW) relations. In this respect, (a) I will shortly look at existing analyses of the equivalents of the Dutch in in cognate languages. From this survey it should become clear that (i) the two main elements in the semantics of in are the relation COINCIDENCE and the spatial configuration "medium" associated with the

36

Hubert Cuyckens

entity y; and that (ii) this spatial configuration should not be described by way of necessary and sufficient conditions, but in terms of a family resemblance structure (i. e., in terms of different, yet interrelated subsets of features). (Section 3.1.1.) (b) I will examine in detail the various types of medium, or, as the meaning of in crucially hinges on the notion "medium", the different meanings of (NPW-)/w. (Section 3.1.2.) 2. I will then briefly go into the use of in expressing part-whole (PW) relationships. 3. I will demonstrate how the different types of NPW-senses and the PWsense of in interrelate, that is, what combines them into a family resemblance structure. 4. Although the family resemblance concept "medium" is the backbone of the semantics of in, a number of additional semantic aspects of in (e.g., fuzziness) will also be looked at. 5. I will isolate the prototypical instances of the static SpP in. In a second part (Section 4), I will briefly examine the uses of in expressing a path 1 1 and investigate how they complement the family resemblance structure arrived at for the static uses of in.

3. The analysis, of "in" as a static SpP 3.1. In this first part, I will largely concern myself with the analysis of in lexicalizing the spatial relation between two discrete arguments χ and y.

3.1.1. Although we described (11 a-e) earlier as clearly expressing a COINCID E N C E relation, it is equally obvious from these examples that a semantic characterization of in in terms of C O I N C I D E N C E alone is not sufficient: in (12) the arguments χ each enter into a COINCIDENCE relation with the arguments y, but SpPs other than in are employed. (12)

a. De boeken liggen op de tafel. 'The books are on the table.'

The Dutch spatial preposition in

37

b. Er hangt een briefje aan de deur. 'There is a note on the door.' In (12 a) χ coincides with an argument y exhibiting a spatial configuration different from the one normally attributed to in ; in (12 b) the relational content of the SpP involves ATTACHMENT rather than mere COINCIDENCE. 12 What, then, constitutes an adequate semantic description of in (and, concomitantly, what distinguishes in from the other SpPs involving COINCIDENCE)? Before presenting my own proposal, I would like to look at a number of possible characterizations of the Dutch SpP in based on existing descriptions of its counterparts in other, cognate languages, viz., in in English and dans in French, and examine whether these analyses provide an adequate account of the semantics of in (in Dutch). 13 (So, when we refer below to "Bennett's analysis of in", for instance, we regard that as short for "the analysis of the Dutch SpP in based on Bennett's findings".) 3.1.1.1. One obvious way to come to grips with the semantics of in is to describe it, along with the SpP op 'on, at', in terms of a rather abstract COINCIDENCE relation between χ and y. What seems to distinguish in from these other prepositions is the spatial (in particular, the dimensional) characteristics of the entity y. (As such, the dimensional properties of χ are considered irrelevant.) Clark (1973) and Quirk and Greenbaum (1973) describe inE in this fashion: they claim that inE lexicalizes a COINCIDENCE 1 4 relation between χ and (a) a 3DIM entity (Clark) or (b) a 3DIM volume or a 2DIM area (Quirk — Greenbaum). Neither of these descriptions provides an adequate basis for the semantics of in. (a) Clark's analysis is probably the most rudimentary. First, his requirement that y be a 3DIM entity clearly does not account for the use of in with 2DIM and 1DIM entities: (13)

a. In de woestijn vind je heel wat slangen. (2DIM) 'There are quite a few snakes in the desert.' b. Pas op voor die bocht in de weg. (1DIM) 'Watch out for that curve in the road.'

Quirk and Greenbaum score considerably better in this respect: although they do not explain the use of in with 1DIM entities either, their char-

38

Hubert Cuyckens

acterization of inE in terms of a COINCIDENCE relation with a 3DIM volume or a 2DIM area offers a sounder basis for the analysis of in. In fact, it covers the large majority of spatial relations lexicalized by in, because, as we will see further, the use of in with 1DIM entities is restricted to a specific type of part-whole relations. (b) Neither Clark's nor Quirk and Greenbaum's characterizations make it sufficiently clear that, when the entity y is seen in its full-fledged dimensionality,15 often only a particular portion of y, and not the entire entity as such, is involved in (or enters into) the COINCIDENCE relation with χ expressed by in. In other words, the potential range of locations that an SpP such as in assigns to χ constitutes only a portion of y. In this respect, consider (14). (14)

a. Het geld zat verborgen in de kluis. 'The money was hidden in the vault. b. Teken een lijn in die cirkel. 'Draw a line in that circle.'

The place where we would look for the money in (14 a) is the porous interior of the vault, and not its solid outer shell; the possible location of the line in (14 b) is the area circumscribed by the geometrical figure "circle", but not the circular line itself (though this line may be considered as a limit of the relevant area). In short, in (14) y's boundary does not enter into a COINCIDENCE relation in with x. It can be observed that the internal consistency of y's boundary in (14) is different from the material it circumscribes. As such, the entities y in (14) — when seen in their full-fledged dimensionality — can easily be thought of as consisting of two mutually exclusive parts, viz., the boundary and the interior; and both parts cannot be simultaneously involved in a COINCIDENCE relation. Then, again, the entire entity y (seen in its full-fledged dimensionality) may be involved in the following instances: (15)

a. de worm in de appel 'the worm in the apple' b. de nage I in de plank 'the nail in the board' c. de melk in de koffie 'the milk in the coffee' d. de auto in de mist 'the car in the fog'

The Dutch spatial preposition in

39

The entities y in (15) can be seen in their entirety because there is little or no difference in consistency between their boundaries and the material they circumscribe (15 a-c) or because y does not feature any clear boundaries at all (15d). 16 In sum, in sometimes lexicalizes a COINCIDENCE relation with the entire entity y (15), sometimes with a portion thereof (14). Following Hawkins (1988: 251), we will refer to that particular part of y (whether it be the entire entity y or a portion thereof) that is involved in a COINCIDENCE relation such as in as the "active zone". Given that it is not necessarily the entire entity y that enters in the COINCIDENCE relation expressed by in, it is not the spatial characteristics of y as such that define in (as Clark and Quirk and Greenbaum wrongly suggest),17 but those of the relevant active zone associated with y. In what follows, we will refer to such an active zone of y with its spatial characteristics as a spatial configuration.18 As such, in lexicalizes a COINCIDENCE relation between χ and a specific spatial configuration. What, now, is the spatial configuration characteristic of iri> We will examine three possibilities: the spatial configuration associated with y is (a) a 3DIM entity (based on Clark 1973); (b) a 3DIM volume or 2DIM area (based on Quirk — Greenbaum 1973); or (c) an interior (Bennett 1975; Cooper 1968). (a) Describing in as a COINCIDENCE relation of χ with a 3DIM spatial configuration is clearly insufficient. As we have already pointed out, also 2DIM and 1DIM entities y — which, as a matter of course feature 2/1 DIM active zones — can give rise to in. (b) A spatial configuration characterized as a 3DIM volume or a 2DIM entity gives a fairly exhaustive picture of in. Still, I have a few reservations about Quirk and Greenbaum's approach. For one thing, it does not account for the (admittedly infrequent) use of in with 1DIM entities (cf. above). More importantly, it does not indicate why 3DIM and 2DIM entities alike can give rise to in, in other words, what the link is between 3DIM volumes and 2DIM areas. This is all the more important, because not all 2DIM entities trigger off in: (16)

Hij zat op de vloer. 'He sat on the floor.'

(c) In Bennett's (1975) and Cooper's (1968) view, inE lexicalizes a COINCIDENCE relation between χ and the spatial configuration interior. To my mind, the notion "interior of y" is inextricably linked to the presence of boundaries in y in that it refers to that particular portion of

40

Hubert Cuyckens

y that is enclosed by its boundaries (e. g., the porous interior of the vault in (14 a) or the area circumscribed by the circular line in (14 b)). A semantic description of in along these lines definitely meets the objection against Quirk and Greenbaum's analysis. Indeed, the notion "interior" establishes the link between 3DIM volumes and 2DIM areas: when 2DIM areas, like 3DIM volumes, feature a bounded interior, they may give rise to in (compare (14 a) and (14 b)). However, equating IN (x, y) with COINCIDENCE (x, interior(y)) seems too restrictive. Indeed, I fail to see what sort of interior one would attribute to the entities y in (17), all of which enter into a COINCIDENCE relation expressed by in. (17)

a. Wij hebben heel wat vrienden in de buurt. 'We have a lot of friends in the neighborhood.' b. Ik had die schop in mijn maag niet verwacht. Ί was not prepared for that kick in the stomach.' c. Kinderen begraven graag hun vaders in het zand. 'Children like to bury their fathers in the sand.'

Of course, one might retort that these entities y do not have interiors, but that in some way they are interiors, but this makes the notion "interior" devoid of all meaning. 19 Indeed, I fail to see how the entity named by the stomach in (17 b), for instance, can be seen as an interior. One reason why the incorporation of "interior" in the semantics of in runs into problems might be that it too strongly suggests the presence of a boundary in y (cf. Hawkins 1985: 96). It can be observed, though, that in is non-committal with respect to the existence of such a boundary: the entities y in (14) have definite boundaries, but in (17) no such boundary is apparent. So far, we have analyzed in as a COINCIDENCE relation between an argument χ and a specific spatial configuration associated with y. The descriptions of the spatial configuration we looked at so far all proved to be inadequate in that none covered all the spatial relations lexicalized by in. Relatively speaking, Quirk and Greenbaum provide the most thorough analysis; yet, they do not indicate what links the differing spatial configurations (3DIM volume, 2DIM area) that all give rise to in. 3.1.1.2. Instead of describing in as the combination of the rather abstract relation COINCIDENCE and the spatial configuration associated with y, one might also turn to a more specific characterization of the relational content of in. Here are some definitions of inE and dans:

The Dutch spatial preposition in

41

Leech: "/« expresses the concept of'enclosure' or 'containment' as applied either to two-dimensional or three-dimensional locations" (1969: 162). Miller and Johnson-Laird: "IN (x,y): A referent χ is 'in' a relatum y if ... [PART (x, z) & INCL (z, y)]" (1976: 385). Moreover, they state that the relatum y must be the kind of thing that has an interior. Vandeloise: "a est dans ... b si le site [i.e., y] contient (partiellement) ... la cible [i.e., x]" (1986: 224). Somewhat further (p. 225) he specifies this containment relation as follows: "Le contenu est inclus, au moins partiellement, dans le contenant ou dans la fermeture convexe de sa partie contenante." I do not think that a semantic description of in based on the definitions above (i. e., making use of any one of the relations CONTAINMENT, ENCLOSURE, or INCLUSION) is drastically different from the previous definitions combining the relation COINCIDENCE with a specific spatial configuration associated with y. For one thing, CONTAINMENT, ENCLOSURE, and INCLUSION each entail COINCIDENCE. Furthermore, the extra information (extra, that is, with respect to the abstract relation COINCIDENCE) that in the previous definitions was relegated to the spatial configuration of y is here part of the relational information itself. Consider the following example. A spatial relation between de juwelen 'the jewels' and de doos 'the box', for instance, can — on the basis of the earlier definitions — be lexicalized by means of in because the box (y) features a 3DIM active active zone, viz., its 3DIM interior. The semantic representation CONTAINMENT (jewels, box) of IN (jewels, box) signals that the jewels coincide with an active zone of y that can be described as the containing part of y (possibly the entire entity y). In sum, then, in both types of definitions, the spatial configuration present in y is of crucial importance. Now, I must admit that the characterization of this spatial configuration in the earlier definitions differs from that of the present ones: the former often included dimensional properties, whereas the latter is expressed in terms of "containing part", "including part", "enclosed part". Let us now look at each of these definitions. (a) The semantic representation ENCLOSURE (x, y) or COINCIDENCE between χ and the spatial configuration "enclosed part of y" definitely does not cover all the spatial relations lexicalized by in. It singles out those relations between χ and a clearly bounded entity y, which is precisely the type of entity that features a spatial configuration "enclosed part". In fact, the spatial configuration "interior" experiences

42

Hubert Cuyckens

the same difficulties. As such, ENCLOSURE (x, y) cannot account for the following instances: (18)

a. de auto in de mist 'the car in the fog' b. de oase in de woestijn 'the oasis in the desert' c. Wij hebben heel wat vrienden in de buurt. 'We have a lot of friends in the neighborhood.' d. Ik had die schop in mijn maag niet verwacht. Ί was not prepared to that kick in the stomach.' e. Kinderen begraven graag hun vaders in het zand. 'Children like to bury their fathers in the sand.'

(b) INCLUSION (x, y), or COINCIDENCE between χ and the spatial configuration "including part of y", covers both bounded and unbounded 3DIM entities y, but it seems a less apt description of spatial relations in between χ and a 2DIM entity y. (c) In (19), both the glass and the tree feature a spatial configuration "containing part", which enters into a COINCIDENCE relation with the fly and the birds, respectively. (19)

a. de ν lieg in het glas 'the fly in the glass' b. de vogels in de bomen 'the birds in the trees'

This is what led Vandeloise (1986) to put forward his semantic description of dans, founded on the concept CONTAINMENT, instead of the ones above. However, CONTAINMENT, like ENCLOSURE and INCLUSION, hinges too much on the presence of boundaries in y, which makes it a less felicitous characterization of the spatial relations in in (18). In view of this, it is quite significant that Vandeloise's discussion of dans largely confines its examples to relations between χ and bounded entities y. Indeed, it is only those that are preferably associated with the spatial configuration "containing part". In the foregoing, we have reinterpreted CONTAINMENT, INCLUSION, and ENCLOSURE as a COINCIDENCE relation between χ and a specific spatial configuration associated with y. Basically, we did this because an SpP such as in first and foremost serves to locate an entity χ

The Dutch spatial preposition in

43

with respect to y. I think this locative function is best captured by the abstract relation COINCIDENCE (which is then further supplemented with extra information about y). If we do not reinterpret INCLUSION/CONTAINMENT/ENCLOSURE, we encounter an extra problem. At the beginning of this section, I pointed out that in shares the relational information COINCIDENCE with other SpPs such as op. Defining in in terms of a specific relation such as INCLUSION, 20 for instance, compels us to describe op in terms of another specific relation, viz., SUPPORT. As such, we seem to lose out on the obvious fact that in and op share the relational information "COINCIDENCE". Now, it is not only relational information that in shares with other prepositions. The spatial configuration of y that features in in also occurs in a number of other prepositions such as uit 'out of and door 'through': (20)

a. De vogel is in zijn kooi. 'The bird is in its cage' b. De vogel is uit zijn kooi. 'The bird is out of its cage.' c. De trein rijdt door de tunnel. 'The train passes through the tunnel.'

It can be observed that, although the relational information in these examples varies (COINCIDENCE in (20 a), NON-COINCIDENCE in (20b-c)), the same 3DIM spatial configuration 21 of y is involved. This semantic similarity between in, uit, and door can only be revealed when the spatial configuration of y is an integral part of the definition of in (in other words, when in is not described in terms of INCLUSION/ CONTAINMENT/ENCLOSURE). 3.1.1.3. Two conclusions can be drawn from the above discussion. First, preference should be given to a treatment of in in terms of a rather abstract COINCIDENCE relation between χ and a specific spatial configuration associated with y over a description in terms of more specific relational information. Second, we have seen that existing descriptions of this spatial configuration (viz., 3DIM, 3DIM volume/2DIM area, interior, enclosed part, containing part, including part) are not satisfactory. There is no spatial configuration with one single unitary definition that enters in all CO-

44

Hubert Cuyckens

I N C I D E N C E relations in, but each one is involved in a number of them. This means that the semantics of in, which crucially hinges on this spatial configuration, cannot be characterized in necessary and sufficient terms. 2 2 Consequently, I think we should give up on the idea of trying to find one single unitary (i.e., necessary and sufficient) definition of in. If we wanted to present " C O I N C I D E N C E between χ and the spatial configuration interior", for instance, as a necessary and sufficient description of in, we would have to stretch the term "interior" in order to account for instances such as those in (18). I admit that the spatial relations in in (18) are not wholly unrelated to cases such as (11 a) and (14 a), but the former do not express containment in the same way the latter do. W h a t we are dealing with, then, is differing yet related uses of in. In order to capture this, we submit that the spatial configuration of y that gives rise to in consists of a number of interrelated subconfigurations which can be described in terms of a n u m b e r of interrelated subsets of spatial attributes (each subset contains a number of attributes (possibly one) that is shared by other subsets). M o r e specifically, the spatial configuration characteristic of in can be assigned a family resemblance structure. This spatial configuration will be labelled "medium". This term is introduced by Hawkins (1985: 95), who defines "medium" as "a condition, atmosphere in which something may function or flourish" (Webster). 23 One might object that this definition is too vague or too general, that it is in need of further explanation. But that's precisely the point: in lexicalizes a number of differing, b u t interrelated C O I N C I D E N C E relations, and that is what the term " m e d i u m " is intended to capture. In sum, we submit that in lexicalizes a C O I N C I D E N C E relation between χ and the spatial configuration " m e d i u m " associated with the entity y. I N (x, y) = C O I N C I D E N C E (x, medium (y)) The question now is: What spatial (sub-)configurations can be called "medium"? W h a t are its spatial characteristics, and concomitantly, what entities y show the spatial configuration "medium"? In this section, we will restrict ourselves to the different types of medium. 2 4 It is only in Section 3.3. that we will explore how the different types of medium are related, that is what makes them into a genuine family resemblance structure.

The Dutch spatial preposition in

3.1.2.

45

What are the different mediums?

3.1.2.1. Consider the following examples: (21)

a. de boeken in de kast 'the books in the cupboard' b. de Juwelen in de doos 'the jewels in the box' c. Mijn voet zit nu in mijn schoen. 'My foot is now in my shoe.' d. De stoel Staat in de hoek van de kamer. 'The chair is in the corner of the room. e. De vogels bouwden een nest in het gat van de muur. 'The birds built a nest in the hole in the wall.'

In (21 a-c), the active zone of y that enters into the C O I N C I D E N C E relation expressed by in is the interior of y; in (21 d), it is the space defined by two planes; and in (21 e) it is the hole denoted by y. In each of these examples, the active zone of y is a 3DIM, porous, bounded space. It is this active zone that constitutes the first type of medium. Incidentally, in (21 a-d), the active zone takes up part of y, while in (21 e) it denotes the entire entity y. Let us now look at this in somewhat more detail. (a) The first type of 3 D I M , porous, bounded medium associated with a particular entity corresponds with the interior defined by its solid outer shell. All entities that can be characterized as "shells or frames with a solid external boundary circumscribing a three-dimensional interior with a consistency quite different from that of the b o u n d a r y " (Hawkins 1988: 253) feature this medium. Examples are: cupboard, closet, room, grave, building, various sorts of smaller containers (bottle, barrel, box), etc. Now, as Herskovits points out, shell-like entities with complete closure are relatively rare, "so that some boundaries of the interior will usually be imaginary" (1986: 151). Obvious examples are: (22)

a. We zijn nu in de tunnel. 'We are now in the tunnel.' b. De kerstboom Staat in de woonkamer. 'The Christmas tree is in the living room.'

Two sides of the interior of a tunnel (22 a) are planes through its ends. Rooms in a house (22 b) may be separated from each other by an imaginary line instead of solid walls. Also the entities y (with incomplete

46

Hubert Cuyckens

Figure 5. D e vis in zijn hand

closure) in the following instances may be attributed an interior or, more generally, a 3DIM, porous, bounded medium: (23)

a. de vis/de pen in zijn hand 'the fish/the pen in his hand' b. de voet in de stijgbeugel 'the foot in the stirrup' c. de vogel in de boom 'the bird in the tree' d. de aardappels in de kom 'the potatoes in the bowl'

The medium that bears a COINCIDENCE relation with the fish or the pen in (23 a) is a porous, 3DIM space bounded by the palm of the hand and a number of imaginary planes through its edges (see Figures 5 and 6). Similarly, the medium defined by a torus-shaped object such as stirrup (23 b) is an interior bounded by the material object itself and imaginary planes through its sides. In (23 c), the interior (and medium) of the tree

Figure 6. D e pen in zijn hand

The Dutch spatial preposition in

47

is the 3DIM space bounded by its outline. Entities with partial closure also typically include open containers and vessels such as vase, glass, cup, etc. (cf. also 23 d). Their medium consists in the 3DIM, porous active zone that is bounded by a closed bottom, a vertical wall, and an imaginary plane through the rim of the vessel or open container. Along similar lines, a medium may be discerned in "cup-like concavities" (cf. Herskovits 1986: 149) such as cradle, pocket, nostril, armchair, etc. It is important to keep in mind that not all 3DIM spaces bounded by (the external boundaries of) an entity with incomplete closure qualify as an interior (and hence as a medium), or qualify as such in every context. Compare the following situations: (24)

a. de aardappelen in de kom b. de aardappel onder/*in de kom 'the potato under/*in the bowl'

Both in (24 a) and (24 b) the entity y bowl defines a 3DIM porous space bounded by its bottom and vertical walls and an imaginary plane through its rim. Yet, only in (24 a) does this space constitute the active zone of a COINCIDENCE relation in (with x); in other words, only in (24 a) does it qualify as an interior (and correspondingly, as a medium). Why do objectively identical spaces qualify as a medium in one case and not in the other? Ultimately, the answer to this question rests on whether the 3DIM, porous, bounded space at issue is considered part of the entity it is circumscribed by or not. In that regard, it might be instructive to look at shell-like entities with complete closure again. These entities function as containers in that they can hold, carry, or store things. It seems self-evident that their containing part (viz., the 3DIM, porous space or interior circumscribed by the container's outer shell) is an integral part of these entities. As a part of y, then, their interior constitutes (in a COINCIDENCE relation with x) the type of active zone of y that we have labeled "medium". By analogy, those shell-like entities with partial closure that function as containers (cf. 24 a) also circumscribe the type of 3DIM, porous, bounded active zone that we labeled "medium". In (24 b) the bowl is turned upside down, which precludes its functioning as a proper container (conceptually it is no longer fit to hold, carry, or store things, though materially of course nothing would prevent this). In cases such as these, no containing part can be attributed to y; or, to put it differently, the 3DIM porous space defined by the bowl (turned upside down) is not considered a part of y. As such, it cannot serve as

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Hubert Cuyckens

the type of active zone that meets the characteristics of a medium. Other examples illustrating the importance of y's functioning as a container: (25) (26)

de rook in de kaasstolp 'the smoke in the cheese cover' a. de melk in het glas 'the milk in the glass' b. de melk op/*in het glas 'the milk on/*in the glass'

(27)

Afspraak onder/*in de Arc de Triomphe. 'Meet us under/*in the Arc de Triomphe.'

(28)

Wij zaten met onze benen onder/*in de tafel. 'We had our legs under/*in the table.'

All entities with incomplete closure in examples (24)-(28) involve vessels, open containers, or cup-like concavities, though of course only cheesecovers and glasses really function as containers. Now compare the following situations featuring a torus-shaped object: (29)

a. De voet in de stijgbeugel (Figure 7) 'the foot in the stirrup' b. Het muntstuk op/*in de stijgbeugel (Figure 8) 'the coin on/*in the stirrup'

Both in (29 a) and (29 b), the stirrup circumscribes a 3DIM, porous space, but only in (29 a) is this space seen as its containing part, because only in (29 a) is de stijgbeugel actualized as a container. Indeed, containers not only hold, carry, or store things (cf. above), but in doing so, they also control the position of the contained. Stirrups exert physical control over

The Dutch spatial preposition in

49

one's foot in that they hold one's foot in place. As there is no such relation of physical control between the stirrup and the coin in (29 b), the stirrup cannot properly be called a container; hence it has no containing part, which in turn implies that the 3DIM, porous space the stirrup defines cannot constitute an active zone, and medium, of y. Summing up, the first type of 3DIM, porous, bounded medium that we looked at in (a) is the interior of shell-like entities with complete or partial closure. It was shown that the presence of an interior in such an entity is inextricably linked to its functioning as a container; 25 and this functioning, in turn, is linked with there being some form of control from the physical part of the container. 26 (b) A second type of 3DIM, porous medium involves spaces bounded by two planes or two cylinder-like objects meeting at an angle. Here are some examples: (30)

a. De man lag te slapen in de goot. 'The man was sleeping in the gutter.' b. de stoel in de hoek van de kamer 'the chair in the corner of the room'

In (30 b), for instance, the active zone (and medium) of y in the COINCIDENCE relation in with χ is the 3DIM, porous space bounded by two walls of the room. As in (a), these boundaries are not included in the active zone; that is, the medium attributed to y only represents part of y.27 (c) The third type of medium denotes the entire entity itself. In these examples, the active zone of y is a 3DIM, porous space, bounded by

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Hubert Cuyckens

another object: the frame of the door in (31 a), the wall in (31 b), the cheese in (31c). (31)

a. Hij stond in de deuropening. 'He was standing in the door.' b. de muis in het gat in de muur 'the mouse in the hole in the wall' c. Er zitten veel gaten in dit soort kaas. 'There are lots of holes in this type of cheese.'

In this first section, we have looked at three (slightly differing) types of 3DIM, porous, bounded mediums. Not all mediums need to possess these three characteristics. 3.1.2.2. (a) Consider the following examples: (32)

a. de nagel in de balk 'the nail in the board' b. Hij werd levend begraven in de muur. 'He was buried alive in the wall.' c. het gatjde barst in de muur 'the hole/the crack in the wall'

In these examples, the active zone of y that enters into a COINCIDENCE relation with χ is the entire solid chunk of material denoted by y, or more generally, the 3DIM, non-porous, bounded portion of y. It is this active zone that makes up the second type of medium. The entities that feature this particular medium are solid chunks of material such as plank 'board'; muur 'wall'; paal 'pole', etc. Examples such as (32 c) should not pose any special problems: just like any other material object, a hole, gap, or crack may bear a COINCIDENCE relation with a 3DIM, solid medium associated with y. Unlike in the first type of medium (a porous, 3DIM space bounded by solid material), there is no contrast in the internal consistency of this medium and its boundary: both consist of solid matter. Note, furthermore, that, although the active zone or medium associated with y in (32) takes up the entire entity y (i.e., inclusive of its free outward facing boundaries), these boundaries are not highlighted. Note, however, that when they are free, outward facing surfaces, y's boundaries may be actualized as a separate active zone, which enters in a COINCIDENCE relation expressed by op. Compare:

The Dutch spatial preposition in

(33)

a. De nagel 'The nail b. De nagel 'The nail

51

zit in de plank. is in the board.' ligt op de plank. is on the board.'

We stated above that the entities featuring this type of medium are solid chunks of material. This solid chunk may exist on its own (cf. 32), or it may be a shell circumscribing an interior. As such, the following expression is ambiguous: (34)

de nagel in de kast 'the nail in the cupboard'

Two active zones can be discerned in the entity y, viz., its interior (3DIM, porous, bounded) and its outer shell (3DIM, non-porous, bounded), both of which qualify as mediums and, as a result, may give rise to in. (b) Not every 3DIM, non-porous active zone of an entity corresponds to a solid chunk of material. Among the entities featuring a 3DIM, bounded, non-porous medium, also less solid substances occur, which need to be kept in a container so as not to spread incontrollably. (35)

a. Er zit een muis in de haver. 'There is a mouse in the oats.' b. Ik heb nog geen suiker in mijn koffie. Ί didn't put any sugar in my coffee yet.' c. de stenen in de plas 'the stones in the puddle' d. de kruimels in de jam 'the crumbs in the jam'

The less solid entities exemplified in (35) can hardly feature a separate active zone giving rise to op. Precisely because they are less solid and therefore need to be contained, they do not show a free outward surface. And even if they did (e. g., the top surface in (35 b)), this surface may not be solid enough to support another entity. 3.1.2.3. Look at the following examples: (36)

a. Zij zaten met hun benen in het zand. 'They were sitting with their legs in the sand.' b. Alle vissen zwemmen in het water. 'Fish swim in water.'

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Although objectively the entities in y denote an entire body of sand (on the beach, for instance) or water (the sea), conceptually y only equates with a relevant portion thereof without clear boundaries. The active zone of y in the C O I N C I D E N C E relations above corresponds with one such chunk of substance. This third type of medium, then, can be characterized as 3DIM, non-porous, and unbounded. Given that the entire entity y has conceptually been reduced to one relevant chunk, also this medium corresponds to the entire y. The relevant chunk of substance denoted by y may also combine clear and vague boundaries. In (37), the relevant chunk of water has two clear boundaries, viz., its outward top surface and its bottom surface. (37)

de vissen in het water 'the fish in the water'

3.1.2.4. In (38) the active zone of y, and concomitantly its medium, denotes the entity y itself, which is a 3DIM, porous, unbounded space. Allowance should be made for the fact that, if y designates a large body of space, it may reduce to a relevant chunk with vague boundaries. (38)

a. het vliegtuig in de mist j de wölken 'the plane in the fog/the clouds' b. de vogels in de lucht 'the birds in the air' c. Er zijn zwarte gaten in het heelal. 'There are black holes in the universe.' d. Grootvader is nu in de hemel. 'Granddad is now in heaven.'

3.1.2.5. So far, we have dealt with 3DIM mediums with variable specifications for the criteria "boundedness" and "internal consistency". Mediums may also vary along the dimensionality-criterion, that is they may also be 2DIM. Consider the following situations: (39)

a. De kinderen stonden in de cirkellhet vierkant.1% 'The children were standing in the circle/the square.' b. Teken een cirkeltje in de hoek gevormd door de twee rechten. 'Draw a circle in the corner formed by the two lines.'

The Dutch spatial preposition in

53

c. Je kwotering Staat in de marge. 'Your marks are in the margin.' d. Hij woont in Duitsland. 'He lives in Germany.' In all these examples, the active zone, and medium, of y is a clearly bounded, 2DIM area. Now, what entities exhibit this type of medium? (a) A first set, exemplified in (39 a), includes geometrical entities (circle, square, rectangle, etc.). These 2DIM areas are bounded by a 1DIM line, which itself is not part of the medium. Indeed, this 1DIM bordering line constitutes an active zone of its own (De kinderen stonden op de cirkel 'The children were standing on the circle'). (Notice the similarity with 3DIM entities with complete closure.) (b) The entity y in (39b) denotes a set of lines meeting at an angle and circumscribing a 2DIM area. As in (a), these boundary lines are not part of this type of 2DIM-area medium, but they do not make up an active zone by themselves either (see also note 27). (c) The entity y in (39c) designates an intrinsic part of a page, bounded by a(n) (imaginary) line marking the division of the page. Again, this 2DIM medium does not include the dividing line (if it is materially present). (d) A large set of entities featuring a 2DIM, bounded area is geographical and geopolitical entities (cf. 39 d). Conceptually, we think of cities, countries, and the like as 2DIM areas bounded off from the rest of the earth. Just like entities such as circle, the boundaries of geographical/ political entities can constitute an active zone of their own ( H i j woont op de grens 'He lives on the border'). 3.1.2.6. In the previous section, we have seen that 2DIM, bounded mediums may be attributed to 2DIM entities with boundaries that clearly set them off from the rest of the surrounding area or environment. There are also 2DIM entities (geographical or geopolitical entities) which are marked off from the rest of the earth's surface, but not in a well-delineated way. Also these vaguely bounded, 2DIM areas may constitute a medium: (40)

a. Wij wonen in het noorden/de woestijn/de prairie. 'We live in the north/the desert/on the prairie.' b. Er is hier geen Supermarkt in de buurt. 'There is no supermarket in the neighborhood.'

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c. Wij hebben een buitenverblijt in de bergen. 'We have a summer house in the mountains.' 3.1.2.7. Let us, by way of conclusion, sum up the different types of medium and provide a few extra examples. (a) 3DIM, bounded, porous medium: (41)

a. Er ligt veel stof in de kast. 'There is a lot of dust in the cupboard.' b. Laten we afspreken in de luchthaven. 'Let us meet in the airport.' c. De kinderen zitten in de auto. 'The children are in the car.' d. We zijn in de kamer/slaapkamer/badkamer/toilet/kelder/keuken/ hall. 'We are in the room/bedroom/bathroom/basement/kitchen/ hallway.' e. Hij woont in een villaatje. 'He lives in a country house.' f. Hij woont in onze straat. 'He lives in our street.' g. Zij heeft een kind in haar armen. 'She's got a child in her arms.'

(b) 3DIM, bounded, non-porous medium: (42)

a. Hij voelde een scheut van pijn in zijn vinger. 'He felt a twinge in his finger.' b. Hij heeft een ring in zijn oor. 'He has got a ring in his ear.' c. De ketel hangt in het vuur. 'The kettle hangs in the fire.' d. Het goud zit in het erts. 'The gold is in the ore.'

(c) 3DIM, unbounded, porous medium (cf. (38)) (d) 3DIM, unbounded, non-porous medium: (43)

a. Jezus wandelt in het water. 'Jezus walks in the water.'

The Dutch spatial preposition in

55

b. We zitten in het stof. 'There is dust all over the place.' (e) 2DIM, bounded medium: (44)

a. Zij heeft sproeten in haar gezicht. 'She has freckles in her face.' b. De verhalen doen de ronde in het dorp. 'The story is being told all over town.' c. Zij wonen in de stad. 'They live in town.' d. London ligt in Engeland. 'London is in England.' e. Het elftal Staat in het veld. 'The team is out in the field.' f. Hij werkt in de haven. 'He works in the harbour.'

(f) 2DIM, unbounded medium: (45)

Hij is alleen in deze wereld. 'He is all alone in this world.'

So far, we have abstracted from the uses of in that indicate a part-whole relationship. In the following section, we will now explore this somewhat further.

3.2. "In" in part-whole relationships Let us first consider a few examples of part-whole relationships lexicalized by in: (46)

a. de spieren/de botten in zijn been 'the muscles/the bones in his leg' b. de golving in de weg 'the undulation in the road' c. een bocht in de weg 'a curve in the road' d. de knik in de curve 'the dip in the graph'

If we consider cases such as (46 a) only, one might be misled to think that part-whole relations lexicalized by in, analogous to spatial relations

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between two discrete objects, denote a COINCIDENCE relation between the part ( = x) and the medium associated with the whole ( = y). In (46 a), this medium would be the 3DIM, non-porous, bounded active zone that is denoted by y. Now, the spatial configuration "medium" can hardly be assigned to the entities y in (46 b-d): weg in (46 b) is a 2DIM surface; in (46 c) weg is a 1DIM line; also in (46 d), curve is a 1DIM line. As such, in contrast to in expressing a NPW-relation, in in PW-relations does not lexicalize a COINCIDENCE relationship with the medium associated with y. In the next section, we will see, though, that there is a straightforward explanation for PW-in.

3.3. The family resemblance structure of "in" We will first describe the family resemblance structure of NPW-/«, which crucially involves the concept "medium". We will then explain how PWin hooks onto this structure. 3.3.1. We have seen that the concept "medium" cannot be described in terms of a set of necessary and sufficient conditions. On the classical view, the failure to provide a single set of criterial features for a lexical concept would automatically imply that the various featural configurations associated with that concept should be considered as homonymous, and hence unrelated uses of the concept. Now, the various featural characterizations of "medium" that we have given are not unrelated, but they are connected to each other along various dimensions, very much like the different members of a family (some featural configurations share the feature "3DIM", others the feature "bounded", etc.). In other words, the various instances of the concept "medium" are related to each other, not on the basis of their identity, but of their mutual similarity. In short, the concept "medium" can be ascribed a family resemblance structure. Let us first look at the question how the different uses of "medium" are related, in other words, at what the synchronic connections in the language user's conceptual knowledge about "medium" are. The first type of medium we distinguished was characterized as the 3DIM, porous, bounded active zone of y, with a containment function (e.g., de sleutels in de hast 'the keys in the closet'). This medium relates (a) to 3DIM, non-porous, bounded mediums (e. g., de nagel in de plank

The Dutch spatial preposition in

57

'the nail in the board') and (b) to 3DIM, porous, unbounded mediums (e. g., We liepen in de mist 'We were walking in the fog). With the former, it shares the features "3DIM" and "bounded", with the latter, it shares the features "3DIM" and "porous". The fact that there exist 3DIM mediums which are either non-porous or non-bounded motivates the existence of 3DIM mediums which are non-porous and non-bounded at the same time (e. g., met zijn hoofd in het zand 'with his head in the sand'). The feature "boundedness", which so far has gone together with threedimensionality, lies at the basis of another conceptual extension. Indeed, bounded 2DIM mediums may also give rise to in (e. g., in de cirkel 'in the circle', in de marge 'in the margin', in Engeland 'in England'). These 2DIM bounded mediums must mark some division. As Herskovits correctly points out, "the reference object must be one of several areas arising from dividing a surface" (1986: 153). These can be divisions on a page, geometrical figures, geographical and geopolitical entities, and divisions on the human body. The third and the fourth types of division lie at the basis of one more conceptual extension: bounded divisions on the earth's surface motivate unbounded divisions on the earth's surface (e. g., Hij woont in Ohio 'He lives in Ohio' —• Hij woont in de vallei van de Ohio rivier —• 'He lives in the valley of the Ohio'). Similarly, bounded divisions of the human body can motivate unbounded divisions (e.g., Ze sloegen hem in zijn gezicht 'The hit him in the face' —> Hij kreeg een schop in zijn maag 'They kicked him in the stomach'). We see here that it is only a subset of entities featuring a particular medium that motivates another medium (divisions on the earth's surface motivate unbounded divisions), whereas it is, for instance, the entire category of 3DIM bounded mediums which motivates bounded 2DIM mediums. At this point, we have arrived at the edge of the category or concept in. Not every entity featuring a bounded or unbounded medium that marks a division on the earth's surface gives rise to in. Names of islands, for instance, often take op. Op is the logical alternative here because it lexicalizes, among other things, the relation between χ and a 2DIM surface. The choice between in and op may not be as erratic as it seems, though. It seems to me that the more an island can be thought of as a political unit (just like a country on the continent, with well-delineated boundaries), the more the boundedness of the island comes into play and the higher the likelihood of in. Furthermore, unbounded divisions of the human body are preferably lexicalized by means of op. It is indicative that at the edges of categories, languages differ from each other. For

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instance, English allows in for unbounded divisions of the human body, whereas in Dutch we largely have op. Another conclusion we can draw from the variation at category edges is that it is possible to explain the particular use of an SpP (e. g., in in een schop in de maag 'the kick in the stomach'), but it is not always possible to explain why the same SpP is not used in similar cases (e. g., Hij kreeg een schop op zijn borst vs. He was hit in the chest).29 By way of summary, Figure 9 represents the family resemblance structure of the spatial configuration "medium", in which the relations between the different types of medium have been rendered through shared features. In a family resemblance structure (a network of overlapping featural configurations), each of the configurations need not share a number of features with all of the other configurations. A family-resemblance structure may also consist of a chain of related configurations. In the latter setup, a particular configuration at one end of the chain may not share any features with another configuration at the other end of the chain; that is, these two configurations are only indirectly related through the other intermediary configurations.

1 = "3DIM" 2 = "bounded" 3 = "porous"

4 = "non-porous" 5 = "vaguely bounded" 6 = "2DIM"

Figure 9. The family resemblance structure of "medium"

The Dutch spatial preposition in

59

We see that the concept "medium" is a mixture of these two types of family resemblance structure. Each of the configurations which share the feature "3DIM" is related to all of the other 3DIM-configurations. Chaining occurs in the extension from bounded, 3DIM to bounded, 2DIM mediums. Both configurations share the feature "boundedness", but the bounded, 2DIM mediums are not (directly) related to the other, unbounded, 3DIM mediums. 2DIM, unbounded mediums are chained to 2DIM bounded ones, with which they share the feature "2DIM division of the earth's surface". They are only indirectly related to 3DIM mediums through the intermediary link of 2DIM bounded divisions of the earth's surface. 3.3.2. How can we explain the use of PW-in on the basis of the family resemblance structure for NPW-in? Let us consider the following examples of non-part-whole in again: (47)

a. de spijker in de plank 'the nail in the board.' b. Ik wil graag melk in mijn koffie. Ί would like cream in my coffee.'

In our earlier discussion of in (Section 3.1.), we pointed out that in in (47) expresses a COINCIDENCE relation between χ and a 3DIM, bounded, non-porous medium associated with y. What we did not point out then is that such a COINCIDENCE relation conveys that χ is embedded in y. I think it is this "embeddedness" between χ and y that motivates the use of in in the part-whole relations in (46). The undulating part of the road is embedded in the rest of the road (46 b); the curving part of the road is embedded in the rest of the road (46 c). Note that not all part-whole relationships are lexicalized by means of in: (48)

a. de leuning aan de stoel 'the back of the chair' b . de Striemen

op zijn

buik

'the streaks on his belly' Figure 10 shows how the part-whole uses of in are related to its nonpart-whole uses.

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3.4. Fuzziness We have established so far that in can be represented as a family resemblance structure. Now, the fact that in is of a family resemblance nature is not all there is to say about the semantics of in. Indeed, in is also a fuzzy concept. To start with, some subsets of concept instances of "medium" have fuzzy boundaries. For instance, there is the fuzziness of 3DIM containers that are open at the top. Containers such as glass unmistakably ask for in. But, the more the vertical sides of a container decrease in size, the more one might be inclined to use op instead of in. It seems to me that as long as one sees y in its containing function, in is allowed. Consider the following instances. When one sits in the back of a pick-up truck, one can still sit in the pick-up. Op, however, is also allowed when one highlights the flat bed ( = 2DIM surface) of the pick-up. Entities with negligible vertical sides can hardly be assigned a containment function; therefore COINCIDENCE relations with entities y such as ondiep bord 'dinnerplate' and schotel 'tray' are most appropriately lexicalized by

The Dutch spatial preposition in

61

means of op. Still, because of the slightly raised sides of dinnerplates and trays, I feel I cannot exclude in in (49 a): (49)

a. Er lag een aardappel op I in het bord. 'There was a potato on/in the plate.' b. Eet de soep inj*? op je bord eerst op. 'Eat the soup in your plate first.'

Although the vertical sides of a soup plate (49 b) are only slightly higher than those of a dinner plate, soup plates are typically seen as containers for soup and other liquids. Second, fuzziness is also inherent in the semantic element "COINCIDENCE". Indeed, this COINCIDENCE may not be complete. It is complete in cases such as (50 a), but it is not in (50 b-d). (50)

a. Mijn pen ligt in de lade 'My pen is in the drawer.' b. Hij heeft een ring in zijn oor. 'He has got a ring in his ear.' c. Hij is in het water. 'He is in the water.' d. Je loopt voortdurend in het stof. 'You keep running through the dust.'

As can be observed from (50 b-d), the COINCIDENCE can be very partial. Whether we allow partial COINCIDENCE to be lexicalized by in or not may be context-determined. Sentence (51) (51)

De appel is in de kom. 'The apple is in the bowl.'

perfectly describes a situation where χ is on top of other fruit, but technically outside the bowl (Figure 11). It is only in contexts where one

Figure 11. De appel is in de kom

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wants to be very precise about the location of that particular piece of fruit that in is not an appropriate lexicalization. When in (50 c), χ is standing with his/her feet in the water because χ is scared of swimming, then good swimmers would not say that χ is in the water.

3.5. The prototype of "in" Prototype effects in a lexical concept may result from different sources. (a) One major source of prototypes is the degree of family resemblance in a concept: it is those concept instances that show the greatest featural overlap with other instances, and least with those of neighboring concepts, that can be considered the prototypical concept instances. Now, it seems rather straightforward to isolate protoypical information in a concept, or a prototypical concept instance, as long as we are dealing with (i) concepts whose constituent featural configurations are related to all of the other featural configurations (concepts of the type bird would be an example, cf. Geeraerts 1989: 67), or (ii) with chained concepts whose structure is still relatively simple (e.g., vers (Geeraerts 1987: 283) and climb (Fillmore 1982)). In those cases with more complex chaining structures (e.g., over, op), isolating a prototype on this basis of maximal featural overlap might not be straightforward (cf. Cuyckens 1991). In the concept "medium", chaining is fairly limited (it only occurs between 3DIM and 2DIM instances), so it might still be possible to isolate a prototype based on maximal featural overlap. The 3DIM, bounded mediums are probably the most prototypical. Within the set of 3DIM concept instances alone, 3DIM bounded mediums cannot be isolated as the most prototypical (their featural overlap is the same as the 3DIM, non-bounded variant). But, given that 3DIM, bounded mediums also overlap with 2DIM, bounded mediums and that the link between 3DIM, unbounded and 2DIM, unbounded mediums is only indirect, 3DIM, bounded mediums are those with the highest family resemblance, and hence are a good candidate for prototypicality. Second, prototypical instances in a family resembance structure are also those that share the least features with other concepts. This makes all entities featuring a 2DIM medium less prototypical because 2DIM entities may also give rise to op. (b) On the basis of the degree of family resemblance alone, porous and non-porous 3DIM bounded mediums are equally prototypical. Yet intuitively, porous 3DIM bounded mediums seem more prototypical. I tend

The Dutch spatial preposition in

63

to agree with Hawkins (1985: 312), who suggests that: "because the human being ... functions and (sometimes) flourishes in a very porous medium [i. e., air], and because a large majority of physical objects with which the human being comes into contact also function in the same porous MEDIUM, ... MEDIUM configurations with a very porous internal consistency have a certain primacy over [i. e., are more prototypical than] those with a more solid internal consistency." (c) In addition to its degree of family resemblance, there are also other sources of prototypes for the concept "medium". Earlier, we have seen that there is fuzziness with respect to 3DIM containers that are open at the top: the boundaries of the concept "medium" grow fuzzier as the vertical sides of these containers decrease in size. Those instances that least give rise to hesitancy are more prototypical than others. As such, a glass is a more prototypical medium than a plate. (d) A final source of prototypes turns on the relational information in in. As amply pointed out, in lexicalizes a COINCIDENCE relation between χ and the medium associated with y. In this respect, relations involving complete COINCIDENCE are more prototypical than those with incomplete COINCIDENCE. When we combine these four sources of prototypes for the SpP in, it should be clear that spatial relations with complete COINCIDENCE between χ and a 3DIM, bounded, porous medium with relatively high vertical sides are most prototypical. 30 Examples are: (52)

a. de melk in hei glas 'the milk in the glass' b. de juwelen in de doos (Figure 12) 'the jewels in the box'

Figure 12. De juwelen in de doos

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4. "In" as a path-SpP In the following set of examples, in does not assign χ to one static or invariable location, but to a series of locations or a path with respect to y. More specifically, in denotes a path starting at an unspecified point in space and whose terminal location is the medium associated with y. (53)

a. Hij gooide zijn materiaal in de doos. 'He threw his tools in the box.' b. Hij sloeg een nage I in de plank. 'He drove a nail into the board.' c. De struisvogel stak zijn kop in het zand. 'The ostrich put its head in the sand.' d. Het vliegtuig ging de lucht in. 'The plane went up into the sky.' e. We reden Amsterdam in. 'We drove into Amsterdam.' f. We reden de woestijn in. 'We drove into the desert.'

Notice that the types of medium that we distinguished in our discussion of the non-path uses of in also show up here. How do the path-uses of in complement the family resemblance structure that we have established for non-path uses (both part-whole and non-part-whole) so far? First, the set of path uses of in as a whole is transformationally 31 linked to its non-path uses through metonymy. As Taylor (1989: 127) points out, "there is a natural, metonymic relationship between the path followed by a moving entity, and one of the infinite number of points located on the path." Furthermore, non-path-/« has to do with a particular static relation between χ and y, whereas path-/« denotes a trajectory (associated with x) at whose terminal point χ bears the static relation with y lexicalized by non-path-/«. As such, the path and non-path uses of in are interrelated through a mixture of both shared and transformationally linked conceptual information. In our representation of the family resemblance of in, an arrow indicates transformationally linked senses, while a regular line signifies a link based on shared conceptual information. Figure 13 represents the path- and non-path uses of in. Finally, we should consider (54): (54)

Hij woont diep het bos in. 'He lives deep into the woods.'

The Dutch spatial preposition in

Figure 13. The path and non-path uses of in

65

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Hubert Cuyckens

Figure 14.

Although in in (54) assigns χ to one static or invariable location, χ is situated at the terminus of a mental path starting at a vague point outside the forest and moving into the forest. Therefore, this use of in should be seen as an extension from the path-uses of in and not from its non-pathuses. (Actually, this sentence is similar to cases such as Hij woont voorbij het postkantoor 'He lives past the post office.') This use of in is rather restricted: it seems to require an adverb indicating that the terminus of the mental path present in in is relatively far removed from y's edges. Concomitantly, it is probably most acceptable for relations between χ and relatively large mediums: (55)

a. Hij woont heel ver Duitslandjde woestijn in. 'He lives far into Germany/the desert.' b. Hij woont net het bos in. ?'He lives just into the woods.' c. * Hij woont Duitsland in. *'He lives into Germany.' d. *Mijn juwelen liggen ver de la in. *'The jewels are far into the drawer.'

Figure 14 is a pictorial or image-schematic representation of how this use of in relates to the other path-uses of in under (54). (The mental path is indicated by means of a broken line.)

5. Conclusion In this cognitive-semantic analysis of the Dutch SpP in, I explored the following issues. First, the conceptual information in in, along with that in other SpPs, is broadly encyclopedic in that it is part of, and needs to be understood against the background of, broader cognitive structures. Second, I presented a detailed sketch of the family resemblance structure

The Dutch spatial preposition in

67

of in, which does far more justice to the semantics of in than the "classical" set of criterial features. Finally, I argued that some concept instances of in are more prototypical than others (viz., spatial relations with complete COINCIDENCE between χ and a 3DIM, bounded, porous medium with relatively high vertical sides).

Notes 1. The argument y corresponds to that part of the prepositional constituent the preposition combines with, while χ is made up of one or more elements from the rest of the sentence or the neighboring discourse that contains the head of the constituent the prepositional constituent is a complement or an adjunct to. 2. It should be kept in mind, though, that these terms also designate the entities involved in a relation that is expressed by lexical items other than spatial prepositions (cf. Langacker 1987). Furthermore, they are inextricably linked to the notions "figure" and "ground" in that in a spatial relation the landmark can be seen as the ground for the trajector ( = figure) (cf. Hawkins 1985: 48). 3. It would be a misconception to think that only word meaning in cognitive semantics has a conceptual, and hence mental, status. Also on the classical view, word meaning is attributed a conceptual status (cf. Saussure 1916:156-157; Trier's term "Begriffsfeld"; Katz 1972: 38). The reason for this ill-conceived, narrow interpretation probably lies with the fact that it is only in psycholinguistic studies of word meaning and, derivatively, in the cognitive paradigm in linguistics that the mental (i. e., conceptual) status of word meaning has been so clearly brought to the fore. 4. Classical lexical semantics encompasses (a) European componentialism (with Pottier 1963; Greimas 1966; Coseriu 1964, 1966; Geckeler 1971); (b) the tradition originating with Katz and Fodor's seminal paper "The structure of a semantic theory" (1963), which also includes the meaning postulate approach and a number of psycholinguistic studies; and, (c) somewhat less importantly, Lyons' relational method (1968, 1977). Although these studies make up a rather disparate set, they can be subsumed under one common denominator on the basis of their similar approach to the description of word meaning. 5. A more detailed treatment can be found in Cuyckens (1991), which, in turn, is largely based on Geeraerts (1986, 1988). 6. The category of "birds", for instance, is evidently not completely identical, but the classical approach abstracts from the differences between instances, and only has eyes for its common features. 7. For completeness' sake, it should be pointed out that cognitive lexical semantics does not claim that all concepts show a family resemblance structure. Technical concepts, for instance, ("odd number"; "even number"; "plane geometry figure") are perfectly amenable to a necessary and sufficient description. 8. The fact that a cupboard, for instance, may function as a container is not just conceptual information determined by the language system, but reflects our interaction with this object in the outside world.

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9. Also a structuralist such as Bennett cannot but allow this encyclopedic information in his semantic description of in front of (cf. Bennett 1975: 83). 10. As a non-path SpP, in assigns χ (or an element in the semantic structure of x) to a location with respect to y that is essentially static or invariable. 11. In as a path-SpP denotes a continuous sequence of locations (associated with x) relative to y. These locations, when taken together, constitute a specific path or trajectory, i. e., a spatial configuration with significant extension in one single dimension. 12. For a detailed analysis of op and aan, cf. Cuyckens (1991). 13. Indeed, there is significant semantic overlap between the Dutch in and its cognates. 14. The term "coincidence" is mine. The authors cited make use of the terms "location" and "place". 15. When, in a COINCIDENCE relation between χ and y, the spatial/dimensional properties of y are (subjectively regarded as) irrelevant, conceptually autonomous parts cannot be isolated in y. Evidently, the COINCIDENCE between χ and y may (objectively) only bear on a particular part of y, but when y is not seen in its full-fledged dimensionality, this particular part is not subjectively highlighted as a conceptually autonomous part of y, and hence does not trigger off the SpP which typically lexicalizes COINCIDENCE relations with that particular portion. For instance, in Meer informatie kan je verkrijgen op het postkantoor 'You can get more information at the postoffice', normally only the interior of the post-office is involved in the COINCIDENCE relation between χ and y; yet, when this interior part is not hightlighted, op and not in is the appropriate lexicalization. 16. It should be kept in mind that in a number of these entities (especially solid ones with free, outward facing boundaries), the outward facing boundaries constitute, next to the entity y seen in its entirety, a separate portion of y. (In that respect, these entities largely resemble the entities y in (14).) 17. If we accept, with Clark and Quirk and Greenbaum, that in depends on the spatial characteristics of y as such, then the semantic representation COINCIDENCE (x, 3DIM (y)) perfectly applies to the spatial relation between the clothes and the top of the dresser in De kleren liggen op de kast 'The clothes are on the sideboard', yet this relation is lexicalized by op and not by in. 18. "Active zone" and "spatial configuration" are related notions: the "active zone" associated with y denotes that portion of y (possibly y itself) that is involved in a spatial relation with x, whatever its spatial characteristics. A "spatial configuration" associated with y is an active zone of y with particular spatial characteristics. 19. Unless one assigns a family resemblance structure to "interior" in order to capture its various uses, but then, again, there are less misleading terms than "interior" (cf. Section 3.1.2.). 20. For the sake of the argument, we assume that INCLUSION provides a satisfactory account of in. 21. Below, we will refine the characterization of the spatial configuration. 22. Note that Vandeloise (1986) does not present his account of in in terms of the notion "containment" as a necessary and sufficient one. Yet, the fact remains that his description is insufficient; hence "containment" is not a good candidate for a single unitary definition of in. 23. Elsewhere, he states that it is something that has the capacity or potential of encompassing or enveloping other things. This definition may be somewhat misleading in that it focuses on 3DIM configurations.

The Dutch spatial preposition in

69

24. "Medium" (in double quotation marks) will refer to the concept or category "medium". Medium (without quotation marks) will refer to (an) instance(s) of that concept. 25. At this point, due credit should be given to Vandeloise (1986), who first pointed out that functional considerations play an important role in SpP-semantics. However, as I pointed out earlier (cf. also note 22), the notion CONTAINMENT alone does not satisfactorily describe the semantics of in. 26. Indeed, in a sentence such as De kaas ligt onder/*in de stolp 'The cheese is under/*in the cheese cover', onder is the appropriate lexicalization, not because the interior of the cheese cover cannot be seen as a container, but because the physical cover itself does not control the cheese (cf. the smoke-sentence (25), where the cover does control the entity within it). 27. It is probably also possible to conceptualize hoek in (30 b) as a set of lines meeting at an angle and circumscribing a 2DIM area; cf. (39 b). 28. I am not considering the meaning 'the children formed a circular line' here. 29. One possible explanation for the use of in and op in de schop in de maag and de schop op de borst could be that Dutch speakers do not interpret maag and borst as unbounded divisions of the human body. Instead, borst could simply be conceptualized as a 2DIM surface (which, in a COINCIDENCE relation with x, gives rise to op); maag, on the other hand, could be conceptualized as the 3DIM, vaguely bounded part of the body that we refer to as the 'gastric region'. On this view, maag would be a medium of the type exemplified in (43), and hence, in a COINCIDENCE relation with x, trigger the use of in. 30. As is shown in Cuyckens (1991), a prototype cannot be isolated equally easily in other SpPs. 31. In contrast to overlapping featural configurations, transformationally linked semantic information does not necessarily share any common elements. For instance, a 2DIM surface and a 1DIM line — which both trigger off op in a C O I N C I D E N C E relation with χ — do not share any common elements; rather, they are transformationally linked in that one can consider a line as a limiting case of a surface.

References Bennett, David C. 1975 Spatial and temporal uses of English prepositions: An essay in stratificational semantics. London: Longman. Brugman, Claudia 1981 Story of over. [M.A. thesis, University of California, Berkeley.] Clark, Herbert H. 1973 "Space, time, semantics, and the child", in: Τ. E. Moore (ed.), Cognitive development and the acquisition of language, 65-110. New York: Academic Press. Cooper, Gloria S. 1968 A semantic analysis of English locative prepositions. Bolt Beranek and Newman report, no. 1587. Coseriu, Eugenio 1964 "Pour une semantique diachronique structurale", Travaux de linguistique et de litterature 2: 139-186.

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Cuyckens, Hubert 1991 The semantics of spatial prepositions: A cognitive-linguistic exercise. [Ph. D. diss., University of Antwerp (UIA).] Fillmore, Charles 1982 "Towards a descriptive framework for spatial deixis", in: R. J. Jarvella and W. Klein (eds.), Speech, Place, and Action: Studies in deixis and related topics, 31-59. Chichester: John Wiley. Geckeier, Horst 1971 Zur Wortfelddiskussion. München: Fink. Geeraerts, Dirk 1985 Paradigm and Paradox: Explorations into a paradigmatic theory of meaning and its epistemological background. Leuven: Leuven University Press. 1986 Woordbetekenis: Een overzicht van de lexicale semantiek. Leuven: Acco. 1987 "On necessary and sufficient conditions", Journal of Semantics 5: 275-291. 1988 "Cognitive semantics and the history of lexical semantics", in: B. RudzkaOstyn (ed.), Topics in cognitive linguistics, 647-677. Amsterdam: Benjamins. 1989 Wat er in een woord zit: Facetten van de lexicale semantiek. Leuven: Peeters. Greimas, A. 1966 Simantique structurale. Paris: Larousse. Haiman, John 1980 "Dictionaries and encyclopedias", Lingua 50: 329-357. Hawkins, Bruce W. 1985 The semantics of English spatial prepositions. Duisburg: L. A. U. D. paper, no. 142. 1988 "The natural category MEDIUM: An alternative to selection restrictions and similar constructs", in: B. Rudzka-Ostyn (ed.), Topics in cognitive linguistics, 231-270. Amsterdam: Benjamins. Herskovits, Annette 1986 Language and spatial cognition: An interdisciplinary study of the prepositions in English. Cambridge: Cambridge University Press. Katz, Jerrold J. 1972 Semantic theory. New York: Harper and Row. Katz, Jerrold. J. — Jerry A. Fodor 1963 "The structure of a semantic theory", Language 39: 170-210. Lakoff, George 1982 Categories and cognitive models. Duisburg: L. A. U. D. paper, no. 96. 1987 Women, fire, and dangerous things: What categories reveal about the mind. Chicago: University of Chicago Press. Langacker, Ronald W. 1987 Foundations of cognitive grammar. Vol. 1, Theoretical prerequisites. Stanford: Stanford University Press. Leech, G. N. 1969 Towards a semantic description of English. London: Longman. Lyons, John 1968 Theoretical linguistics. Cambridge: Cambridge University Press. 1977 Semantics. Cambridge: Cambridge University Press. Miller, George A. — Philip N. Johnson-Laird 1976 Language and perception. Cambridge: Cambridge University Press.

The Dutch spatial preposition in Pottier, B. 1963

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Recherches stir I'analyse semantique en linguistique et en traduction mecanique. Nancy: Publications linguistiques de la Faculte des Lettres et Sciences humaines de Nancy. Quirk, Randolph — Sidney Greenbaum 1973 A university grammar of English. London: Longman. Rosch, Eleonor 1975 "Cognitive representations of semantic categories", Journal of Experimental Psychology 104: 192-233. 1978 "Principles of categorization", in: E. Rosch and B. Lloyd (eds.), Cognition and categorization, 27^18. Hillsdale, N. J.: Lawrence Erlbaum. Rosch, Eleanor — Carolyn B. Mervis 1975 "Family resemblances: Studies in the internal structures of categories", Cognitive Psychology 7: 573-605. Saussure, F. de 1916 Cours de linguistique generale. Paris: Payot. Taylor, John R. 1989 Linguistic categorization: Prototypes in linguistic theory. Oxford: Clarendon Press. Vandeloise, Claude 1986 L'espace en frangais. Paris: Seuil.

Dividing up physical and mental space into conceptual categories by means of English prepositions Rene Dirven

Introduction Like any other word category, prepositions structure a subjective, language-specific view of relations in our experiential world. The purpose of this paper is to show that the structuring of our experience of physical space by means of prepositions to a large extent determines the languagespecific concepts built up in mental space. More specifically, the paper aims to analyse the following theses: (i) Some, if not all, English prepositions are dividing up physical space in an idiosyncratic, "English" way. (ii) The basic spatial conceptualisations can be and are projected onto "mental space", i. e., they may form chains of meaning covering various conceptual domains such as time, state, area, manner or means, circumstance, cause or reason, etc. (iii) Since each of the prepositions can follow a more or less similar path of extensions in meaning, we may, theoretically speaking, find a number of different concepts of time, state, area, manner, cause etc. The question therefore is to find out how similar or how different are the various concepts in mental space, e.g., the various concepts of circumstance or cause denoted by the different prepositions. Although one may assume that concepts of cause are fundamentally different from concepts of manner or area, the question also arises whether the various concepts denoted by the chain of meanings of one preposition, e.g., at may not be as closely related in meaning to each other as they are to the corresponding senses in the domain denoted by another preposition, e. g., on. More importantly, one may also expect gaps in the meaning extensions for some mental domains because of the specific spatial structuring conventionalised by a specific preposition. These hypotheses will be tested on a sample of twelve prepositions selected more or less at random: the three basic space prepositions at, on, in:1 the two "proximity" prepositions

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by and with; the two "path" prepositions through and about, the two "vertical space" prepositions under and over, and the tree "separation" or "source" prepositions from, off and out of.

1. Characterisation of spatial conceptualisations These 12 prepositions and some of the relationships between their spatial meanings can be brought together as in Figure 1. This representation of the relationships is, of course, too strong in some respects. But what it intends to express is the following: At, on, in are the basic and most general place prepositions. At, as the most "neutral" place preposition, denotes place as a point of orientation, disregarding its physical shape: e. g., at the station takes the station as an orientation point for some trajector, 2 but does not denote whether the trajector is near, inside or on top of the station area. On denotes physical contact between trajector and landmark, and therefore necessitates viewing the landmark as one-dimensional space (a line) or two-dimensional space (a surface). In denotes the enclosure of the trajector in the landmark, and therefore views the landmark as two- or three-dimensional space (a surface or a volume). Similar, but now "separation" spatial configurations hold for the three source prepositions. From denotes separation from a point of orientation, e. g., he comes from the station. Off denotes separation from contact with [1]

[2]

[3]

AT

ON

IN

[6]

[4]

BY

THROUGH

[5]

[7]

ABOUT

WITH

[8]

[91

UNDER

OVER FROM [10]

Figure 1. Some relations between prepositions

OFF [11]

OUT OF [12]

Dividing up physical and mental space

75

a line or surface (thus a somewhat funny sentence like he comes off the station could only mean that he had climbed onto the building) and out of denotes separation from the inside of a landmark as in he comes out of the station. Obviously, on and off are the clearest instances of the spatial sense of all prepositions, which may be a consequence of their basic meaning of denoting physical contact (or breaking it off) between trajector and landmark. Although at and in can be used to fulfil purely spatial functions, they do so in a less concrete or less "spatial" way than on, and therefore they may be more apt to go beyond spatial conceptualisations. The same holds for the "proximity" prepositions by and with, which locate the trajector in relation to a point of orientation just like at does, whereas through and about presuppose a two- or three-dimensional area just like in. More specifically by denotes the idea of "connection", either in a static relationship, e. g., He is sitting by the fire, or in a dynamic relationship, e. g., This bus passes by the sation. With also denotes both a point of orientation and the idea of connection, but it subsumes these notions under the more abstract notion of association and/or accompaniment. Hence in its spatial sense, with can only denote persons as a landmark, e. g., John is sitting with Mary. In contrast with the "point-of-orientation" character of by and with, the two- or three-dimensional prepositions through and about require the landmark to be seen as a surface or a volume as in he walks through the station or he walks about the station (platforms). Thus through structures space as a tunnel or channel, whereas about denotes spatial movement in any direction. The two vertical space prepositions under and over are outsiders in the general picture drawn here. Their inclusion in the discussion has a dual purpose: (i) to show that prepositions denoting a negative polarity — this also applies to the "separation" prepositions from, off and out of are less apt to be extended into all domains of mental space, and (ii) to show that the positive polarity item over behaves differently from under, even to such an extent that it can cover some of the domains expressed by through and especially about. Consequently, the only real outsider in Figure 1 is under (especially in view of the position it takes up in the representation). But its position is somehow justified in that it negates over, which in some of its extensions adjoins about. Needless to say, there is no link between the adjoining

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Figure 2. Sets of prepositions and relationships

items with and under nor between under and from. The various relationships that do hold between the twelve prepositions chosen are therefore rather to be interpreted in the sets or groups as represented in Figure 2.

2. Chains of meaning from physical into mental space The extensions of the meanings of a preposition from physical space via time into more abstract domains do not occur in any haphazard way but follow a path of gradually increasing abstractions, whereby the link with each prior meaning remains obvious and may account for most, if not all, co-occurrence restrictions between trajector and landmark. Note, however, that these notions will gradually come to be used in a more abstract sense, too. 2.1. At extends from an orientation-point in space to one in time, and further into state, area, manner, circumstance and cause, as illustrated below: (a) (b) (c) (d)

point as place: at the station time-point: at six o'clock state: at work area: good at guessing

Dividing up physical and mental space

77

(e) manner (point on scale)

(d) area-·

(a) point in space

(c) state

»-(b) point in time

( 0 circumstance

(g) cause Figure 3. Radial network of extensions of at

(e) manner: at full speed (f) circumstance: at these words (he left) (g) cause: laugh at, irritation at The notion of orientation-point obviously links space (a) and timepoint (b); also the state (c) is a metaphorical orientation-point since it contrasts with other states such as at rest, at sleep, at prayer etc. The notion of "area" is used in Radden's (1989: 448) sense of "the thematic context or field within which an event is seen"; thus one can be "good" within the context or field of "guessing". The fact that at is used with a number of predicates such as good, bad, clever, adept, an expert etc. suggests that the skill in question is a point at which the subject of these predicates is aiming. With the manner expression at full speed (e), at denotes a point on a scale, which can be contrasted with other points. Circumstantial at in at these words (f) is a further abstraction of temporal at, now not with a point on the time continuum but with human actions as a reference-point. Although it is possible to imply a cause-effect relationship with circumstantial at in (f), this is not necessary. When this causal relationship is explicitly given as in (g) laugh at, irritation at, infuriated at, angry at, surprised at etc., what is expressed is that the emotional state follows from a cause or that the cause triggers the emotional state. We propose the following diagram (Figure 3) to represent these relations. 2.2. On is substantially different from at due to its notion of "contact" and can have the following extensions:

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Rene Dirven (e) means

(d) area

(a) contact with line/surface

(b) time-expanse

(c) state

(f) circumstance

(g) reason Figure 4. Radial network of the extensions of on

(a) contact with line/surface: on the floor (b) period of time: on Sunday (c) state: on display (d) topic or area: lecture on history (e) manner/means: dine on snails (f) circumstance: on arrival (register first) (g) cause/reason: congratulate sb. on his performance The notion of spatial contact with a line or surface in (a) is mirrored on the time-axis in (b) and in the continuing state in (c). The idea of lecturing (d) presupposes solid contact with one's subject matter. Similarly, snails or whatever other means of subsistence (e) with dine on, live on etc. form a basis of support. Consequently, the notion of manner seems to be incompatible with on. Only the notion of condition, which can be a subcategory of circumstance, seems to be compatible with on as on her own, on these conditions etc. In contrast with this concept of a supporting circumstance, the notion of circumstance with on in (f) does not form a basis of support, but rather denotes the contact that holds between two successive moments in time or in an action chain. Finally, the notion of contact seems to exclude the idea of cause and effect, but the notion of reason is fully compatible with on, since the reason for the act of congratulation follows from and is based upon the performance delivered. 2.3. In conceptualises space as an enclosure or volume, and this basic characteristic also pervades all its extensions:

Dividing up physical and mental space

79

(e) means

(d) area

(a) spatial enclosure

(b) time-span

(c) state as enclosure

(e) manner as state

(f) circumstance as state

(g) cause as state Figure 5. Radial network of extensions of in

(a) (b) (c) (d) (f) (g) (h)

spatial enclosure: in the station time-span: in one day; in a week state as enclosure: in despair, in search of area: specialise in, rich in coal manner, means: in a loud voice, in English circumstance: she nodded in agreement cause: delight in one's success, revel in

The enclosing space can be physical as in (a) or temporal as in (b): here it can be a time-span within which one is situated or a later time-span (seen from the present time-point). The notion of enclosure is extended to psychological states such as in despair or active states such as in search of (c). Also the notion of area can be an action field {specialise in) or a thematic field {rich in). English categorises all kinds of state as enclosing experiences which may denote manner or means (f), circumstance (g) or even cause (0; in themselves these expressions merely denote an "enveloping" state, and the further specifications arise in the given contexts. This may be summarised in the following diagram. 2.4. By highlights the notion of "connection" between two entitities in physical space or two events or states in mental space.

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(d) area · (lawyer by profession)

(a) connection in place (house by the bridge)

(b) connection in time (by day)

(f) circumstance (by such bad weather) Figure 6. Radial network of extensions of static by

(a) (b) (c) (d) (e) (f) (g)

connection in space: a house by a bridge', pass by a bridge connection in time: by day, by six o'clock area: a lawyer by profession manner, instrument: travel by bus circumstance: by accident, by such bad weather cause/agent: surprised by his appearance, a book by Lakoff

Unlike the three basic prepositions at, on, in, which are mostly static, by can denote both static {a house by a bridge) or dynamic (pass by a bridge) relationships. This also applies to time relations: by day denotes a static relationship, by six o'clock refers to a later moment of time, before which something is to happen. English does not associate a psychological state with by (c), which may be due to its strong notion of connection. Also area is only marginally present in (d). But whenever two entitities, events or states can be seen as strongly in connection with each other, by is very productive as with manner, which is usually conceptualised as an instrument (e), or with circumstance (f) and cause or agent (g). The two diagrams in Figure 6 and 7 are proposed to represent the extensions of static by and dynamic by, respectively: 2.5. With conceptualises the notions of association and accompaniment, which are not physical in nature, though they may denote physical proximity; nevertheless this is not transferrable to time or state: (a) (b) (c) (d) (e) (f) (g)

proximity in space: John is sitting with Mary area: deal with a problem manner, instrument: with great precision, with a key circumstance: (I cannot do it) with everybody laughing cause: tremble with fear

Dividing up physical and mental space

81

(e) means/instrument

(a) connection as path (pass by the bridge)

(b) connection with time-point (finish by six ο 'clock)

Τ (f) circumstance (by accident)

(g) cause/agent (idestroyed by fire/the enemy) Figure 7. Radial network of extensions of dynamic by

All the more abstract meanings of with invoke a metaphorisation of the notion of accompaniment: in the domain of area, the thematic field is seen as a companion one has to deal with; manner or instrument are likewise seen as companions to fulfil an assignment; circumstance is a companion standing by and cause a feeling or emotion leading to visible effects. The diagram in Figure 8 represents these extensions: 2.6. Through is, just like about, a path preposition and typically occurs within dynamic contexts. This basic tendency also prevails in the non(e) manner/instrument as accompaniment

(d) area

(a) proximity/accompaniment in space

(f) circumstance as accompaniment

(g) cause as accompaniment Figure 8. Radial network of extensions of with

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Rene Dirven (a) movement in enclosure

(b) movement in time-span

(e) means as channel

(g) cause as channel Figure 9. Radial network of extensions of through

spatial usages, which are, however, precisely because of the necessity of dynamic contexts, more limited than those of by. (a) (b) (e) (g)

Place as path: walk through the fields Time as path: go on through the next months Means: funded through our budget Cause: killed through accidents

The following diagram can be proposed to represent these extensions: 2.7. About denotes movement in any direction, which also leaves fewer options for figurative extensions: (a) (b) (d) (g)

Place: about the playground Time: about then Area: think/doubt about Cause: excited/crazy about

The notion of mental movement is found with verbs denoting speaking and thinking (d): these activities are seen as movements over a mental area. The same notion underlies emotional state predicates which denote emotional states caused by wandering over certain causes (g). (d) area

(a) movement in all directions in space

(g) cause Figure 10. Radial network of extensions of about

(b) approximative time

Dividing up physical and mental space

83

2.8. Over can denote static and dynamic situations and has similar possibilities to about: (a) (b) (d) (g)

Place: over the mountain. Time: over the whole year. Area: debate over Cause: argue/fight over

Figure 11 represents these extensions of over: (d) area

(a) movement to end of surface

(b) movement in time-span

(g) cause Figure 11. Radial network of extensions of over

2.9. Under denotes a static position at the negative and of a vertical dimension, so that it can easily lead to the expression of negative states or circumstances, too: (a) (c) (f) (g)

Place: under the bridge State: under attack, under arrest Circumstance: under no circumstances, under the premise Cause: under the thought of

Figure 12 represents these extensions: (a) lower point in vertical space

(c) state

(f) circumstance

(g) cause Figure 12. Radial network of extensions of under

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The three "source" or "separation" prepositions are even more strongly limited in their possibilities for metaphorical extensions of meaning. 2.10. From denotes a point of departure either in physical space, in time, or in the domain of causation: (a) Place: He has returned from England. (b) Time: He has been working from 6 o'clock onwards. (g) Cause: He died from drugs. 2.11. Off reduced to of in its area or causal meaning, denotes departure from a surface with which one was in direct contact: (a) Place: He has come off the ladder. (d) Area: Talk of the devil (and he is sure to appear.) (g) Cause: He died of cancer. 2.12. Out of denotes departure from an enclosure, which in a metaphorical sense can be an emotional state causing an effect: (a) Place: He walked out of the house. (g) Cause: He killed her out of despair. In order to summarise the varying possibilities for meaning extensions, let us first survey the twelve prepositions with respect to their values for each of the six areas as in Table 1. Table I. Survey of the meaning extensions of prepositions

at on in by with through about over under from off out of

time

state

area

means manner

circumstance

cause reason

+

+ + +

+ + + +

+

+

+ + + + +

+ + +

+ + + +

+

+

-

-

+

-

-

—

-

+

+ + + —

+ + +

-

+

-

•

-

—

•

-

+ + + +

+

-

-

-

-

-

-

+

-

-

+ +

-

-

-

-

-

+

Dividing up physical and mental space

85

Two conclusions that complement each other can be drawn from this summary and the foregoing analyses: (i) a preposition that denotes a vaguer or more general location is more apt to develop metaphorical extensions; (ii) a preposition that denotes a more concrete location or a specialised visual location or which has a negative polarity meaning is less apt to develop metaphorical extensions. These conclusions do not only apply when larger sets of prepositions or prepositions within sets are compared, but also when single prepositions are compared: — The first five prepositions {at, on, in, by, with) are vaguer in exact location than the seven others, and they show more extensions, too (see Table 1). — Within this set of five prepositions only the first three prepositions {at, on, in) can form "state" prepositional phrases. In fact, this is not surprising, if one takes into account the "proximity" meaning of by and with: a state cannot easily be seen as being near an entitity, but it must somehow "touch" that entity. — Within the set of the three most productive prepositions at, on, in, on is more concrete than at and in, since it has, as a major component, the notion of "physical contact". This feature may explain why on does not form "active" state predicates like at or in can {at work, in search of): on just like under only forms "passive" state predicates such as on display ("being displayed") or under arrest ("being arrested"). Furthermore, on can not form manner phrases, but only expressions of means {diet on bananas), which is in line with the notion of physical contact. Also the circumstance meaning of on is a very special one, since it requires two successive acts touching upon each other {on arrival). The dominating feature of contact may also explain why the "cause-effect" pair is not found with on: cause and effect may be a too complex and too abstract relation to be limited to continuous or even tangent events. But reason is possible, precisely since one event can be supported (via a logical step) by some other event. — Also through and about differ slightly in concrete visualisation: through implies the image of a tunnel or channel and therefore excludes the notions of state, area, or manner, but only allows "passage-like" concepts of means or cause; about is much vaguer due to its visual conceptualisation of "movement in any direction" and allows extension into mental movement required for area {think/speak about) or cause {excited about).

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— Over, though only expressing, in its prototypical senses, vertical location, also implies movement and this may be the reason why it has the same, albeit less productive, possibilities of denoting area and cause. The negative polarity item under, on the other hand, can only be extended to notions of passive state (under arrest) and of circumstance (under the premise). — The three "separation" prepositions are all negative in orientation and, just like under, allow far fewer extensions into mental space. Only the most neutral of these three, from, can be used for time. The fact that all three can be extended into cause suggests that extension into cause, though a fairly abstract notion, poses a more general problem. In fact, all these prepositions except on may denote cause, which again requires an independent explanation, which may be attributable to the notion of cause rather than to the nature of the prepositions themselves. This will be the topic of Section 3.5., but it will be discussed in the context of the differentiated concepts which can be shaped within one domain.

3. Differentiated concepts of place, time, state, area, manner etc. Linguistic description finds no difficulty in distinguishing between various concepts in the domain of place or time. Concepts like point in space or time-point are familiar ones. So are concepts like line, surface, volume, enclosure in space or time. The use of different prepositions for the domains of state, area, manner or means, circumstance, and cause or reason, suggests that linguistic description cannot but make similar distinctions within these domains, too. I shall therefore now examine the paradigm of prepositional phrases within one conceptual domain and investigate how similar or different these expressions are. To facilitate the comparison, I shall quote the same examples as before, but add more instances, and group them according to domains. We can leave out place and time, since here we can assume general agreement, and begin with state. For the numbering of the prepositions, the order given in Section 1 will be used.

3.1. State English prepositional predicates denote four different types of state:

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at: at workjrestjsleep)workjplay)prayer/warjlunch on: on display/show/sale/hire/trial/guard/duty in: in despair/sorrow/love/fun/search of/demand under: under arrest/repair/control/fire/pressure

As the examples suggest, these states incorporate important differences. With at all the prepositional predicates denote a more or less clearly delimited and usually and "active" state, whereby the subject is usually human and engages in some form of organised activity; it is the activity itself which is the point of orientation so that the use of at is fairly normal. With on (and also with its antonym under) the prepositional predicates denote "passive" states: things are or can be displayed, shown, sold, hired etc. Most of these ow-predicates are associated with things, and only a few with persons: also in this case the "passive" state (on trial) or the "commissioned" state (on guard, on duty) are still prevalent. It seems that the on predicates visualise things on a platform for everybody to see or witness. In this respect the under-predicates are slightly different: here we find a stronger suggestion of the presence of an agent who controls (very typical is under control) the situation, /«-predicates, finally, leave room for both passive and/or emotional expressions (in despair/ sorrow/love, in demand), or more active ones (in search of/in a hurry). This may be seen as a consequence of the "enveloping" sense implied in the idea of "enclosure" expressed by in: the emotional state, passive state or active state is viewed as an enclosure in which the subject finds himself. The four prepositions thus help to conceptualise different forms of states: at states refer to (parts of) a larger scheduled network of human activities or states; in states denote feelings, emotions or other individual situations; on states, on the other hand, denote controlled, often passive situations, which in adverse conditions are seen as emanating from higher forces, typically expressed as under states. English thus contrasts at liberty with in freedom: at collocates with oberty since this contrasts with a transient state of captivity, whereas in denotes a person's state of being free; 3 under arrest denotes the control "over" a person, and on trial denotes somebody's being raised for public investigation.

3.2. Area Eight of the twelve prepositions can be used to denote area: (1) at: good/bad/clever/an expert/adept at (2) on: concentrate/meditate/an expert/lecture/a book/a summit/a report/ a comment on

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(3) (4) (5) (7) (8) (11)

in: specialisejrichjlowjpoorjlacking in by: a lawyer by profession with: deallbusylfamiliarlbe engaged with about: think/doubt/speak/say sth./talk/a book about over: debate/a controversy/a dispute! quarrel I argue over of: speak / think/remind/know /dream/read of

The point-of-orientation meaning of at is preserved in its transfer f r o m place to the " a r e a " domain in that this area must be one of practical skills such as good at playing the piano. In this respect at in area expressions is very similar to at "active" state expressions, where both action and h u m a n subjects also seem to be m a j o r co-occurrence restrictions. In contrast with at, the use of on in area expressions presupposes longer and more p r o f o u n d contact with, preferably, a mental area: thus one can be "an expert at repairing pianos" in the sense that one practises this oneself, but be "an expert on (repairing) pianos", which implies knowledge a b o u t the area, which may be the specific field of piano repairing or the more general field related to pianos in general. This also explains the co-occurrence of on with such mental activity verbs as concentrate, lecture, brood, ponder, muse, meditate, etc. The difference between on and in stands out clearly with the item expert, too: one can be an expert on the nineteenth century, but for a larger area English prefers in e.g., an expert in literary history. This notion of area with in is therefore the wider context within which one is an expert, whereas on designates a more specific area (of knowledge) and at an area of practical skills. This specific nature of the enveloping /'«-area also accounts for expressions such as rich/poor/low in: here the notion of richness or scarcity only applies within a specific field. The use of with for area evokes the idea of accompaniment, be it activity as in be engaged with, busy with, knowledge as in familiar with or mental activity as in deal with. But this sense of with is not very productive with verbs. In fact, the four prepositions with verbs denoting mental and/or communicative activity are on, about, over, and of. On and of are, just as in their spatial meanings, clear antonyms: serious, p r o f o u n d mental activity requires on: thus lecture on and speak of are almost antipodes. This also explains that things connected with one's imagination or intuition are expressed with of. dream of, know of, think of, remind of. The same holds for things that have to be retrieved f r o m m e m o r y such as remind of, reminiscent of, oblivious of. The spatial notion of "separation" of the

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preposition o f ( f ) does not guarantee any in-depth concentration on things. As against all these more "specific" conceptualisations of area, the expression of area by means of about tends to be that of a "dispersive" or a "discursive" area. This may be based on the fundamental sense of "movement in all directions", whereby the notion of movement may explain the co-occurrence restriction to mental activities such as speak, write, lecture, think, doubt or mental products such as books, stories, films, articles, papers, studies, songs etc. Although about and over are similar in some respects, they differ in one important respect, too: whereas about denotes movement in all directions, over visualises a two-direction movement, implying the way from and back to the mental starting-point. It is this two-way sense of over that shapes the notion of an antagonist area such as in debate, dispute, quarrel, argue, controversy over. The four prepositions that cannot be used for the domain of area are through, under, from and out of The image schema of a tunnel may block any association with the notion of area and so may the concrete vertical image schema of under do. Separation prepositions seem by nature less apt to denote area, although o f ( f ) can be used for the suggestion of a "distanced" area, an area only vaguely reachable. The question, however, is whether this of can still be considered as one of the senses of polysemous ofif)·

3.3. Manner, means, instrument Only six of the twelve prepositions selected can be used to express one or more aspects of this complex domain: (1) (2) (3) (4) (5) (6)

at: at full speed, at the top of his voice. on: dine on snacks, drunk on whisky, on foot, on horseback in: in agreement, in a loud voice, write in ink/pencil by: by train/bike/car/air/sea with: with precision/care /passion', with a key /a pen through: funded through our budget, obtain sth. through the post.

The domain of manner, means and instrument requires prepositions denoting orientation, contact, enclosure or connection between two entities, situations or concepts.

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The fact that the other six of the twelve prepositions about, over, under, from, off and out of do not form prepositional phrases of manner, means, instrument may be due to the vaguer, dispersive meanings of the former two (about, over), and to the negative polarity of the latter four. The domain of manner, means and instrument can be seen as a conceptual continuum, at one end of which we find more abstract conceptualisations for manner and at the other end the more concrete conceptualisations for instrument; the concept of means, though somewhat closer to instrument stands between the two extremes of manner and instrument, as shown in Table 2. Table 2. Distribution of prepositions over manner, means and instrument MANNER with at,

MEANS

INSTRUMENT with

in,

on, by,

through

The prototypical preposition covering both the concepts of manner and instrument is with: combined with abstract nouns, it usually expresses manner, with concrete nouns it expresses an instrument. The other prepositions tend to favour one of the segments of the continuum: at tends towards the more abstract segment; on and by towards the intermediate segment of means; in covers the abstract manner segment (nod in agreement) or the intermediate "means" (write in ink), and through conceptualises means as a channel. The difference between means and instrument stands out most clearly in the pair write in pencil and write with a pencil: the ί'η-phrase conceptualises the way (manner or means) in which things are done; here the idea of an enveloping state or substance is clearly present, which also accounts for the use of pencil as an uncountable noun; the wzfA-phrase stresses the use of an accompanying instrument and since this is concrete, pencil is used as a countable noun here. The fact that on does not favour a manner interpretation is a consequence of the notion of physical contact of spatial on; in its semantic extension to the manner/means/instrument domain on cannot fully switch to the fully abstract end of the continuum, although such a manner interpretation is never fully excluded in expressions such as on foot, on horseback. But even the other extreme interpretation of instrument cannot be excluded in these two expressions; still the absence of articles or plurals in such idiomatic phrases suggests that these are not comparable to freely

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manipulative instruments, but are rather supporting entities or surfaces with which the user is in physical contact. This notion of a supporting means (which also holds for subsistence by means of food and drink) is different from the "path" expressions denoting means, such as by boatj bike/airjsea or through our budget etc.; here the notions of "connection" (by) or "channel" (through) are extended into that of "means", but this time not a supporting means, but rather a means allowing the passage of entities. Typically, the concrete entities (boat, bike, bus) or the substances (air, sea) are not seen as fundamentally different since they are all treated as uncountable nouns. With through the noun remains countable, however, and therefore such expressions as through our budget never allow a "manner" interpretation, which could still be invoked for ^-phrases.

3.4. Circumstance Five of the six prepositions (i.e., at, on, in, by, with, through) that can express the domain of manner, means and instrument can also be used for the domain of circumstance; through is out now, but under takes its place. (1) at: at these words (he left) (2) on: on arrival, on his death, on my return, on receipt, on the condition that, on the pretext that (3) in: (he smoked) in silence (4) by: by accident, (catch) by surprise, by such bad weather (5) with: (I can't do it) with everybody laughing', with the door wide open, the bugs can get in (6) under: under these circumstances, under the premise As with the former domain, the domain of circumstance requires a more or less clear "location"; this condition is also met by under. Circumstance is a conceptual domain that refers to a situation occurring or holding at the same time as or in a close vicinity of some other situation; though some link between the two situations is implied, the nature of this link is not specified or not clearly specified. In fact, there is not a clear-cut boundary between circumstance and cause or reason, but, as with most conceptual categories, a fuzzy zone of transition is found here. Still, the centres of both categories "circumstance" and "cause" are relatively stable. And even within the domain of circumstance,

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the various prepositions divide up this 'mental space' into quite different concepts of circumstance. With at circumstance is viewed as an orientating activity marking the occurrence of a second activity; as with the other uses of at the notion of activity prevails here, too. With on two meanings of circumstance emerge: either the notion of a bordering action (on arrival) which is to be followed by new action (clearly the notion of contact between the two actions is present here); or else we have a static circumstance (on the condition that, on the understanding that), which implies that one situation is to be conditionally supported by some other fact. As already suggested in Figures 3 and 4, the extensions of at and on go from the time concept to that of circumstance so that we can speak of "temporal circumstance" here. To this we must also add the notion of "conditional" circumstance. In denoting circumstance is an extension of state and manner (see Figure 5). The enveloping metaphor following from the "enclosure" sense of in does not allow the interpretation of successive events with /«-phrases, but only that of simultaneous situations. In such an "enveloping" circumstance, the link between the two situations is always felt to be stronger and the borderline with the domains of manner, purpose, cause, or reason is hard to draw: thus one could interpret she nodded in agreement not only as manner but also as circumstance, or even as purpose or reason. The inherent "connection" sense of by makes this preposition almost into the predestined item to express the neutral domain of circumstance, especially when no visible link between two events is implied, as in the expressions by accident, by chance, by mere coincidence. Also other uncontrollable situations such as weather conditions typically require by (by such bad weather), although here the weather can also be seen as an enveloping factor and thus allows the use of in: in such a bad snowstorm, in the rain, in this heat etc. The "accompaniment" meaning of with, just like the "connection" sense of by, is a very apt candidate for a meaning extension into the domain of "circumstance". The difference is that with requires a clearly delimited situation, which can function as an accompaniment to some other situations. Consequently, mere indications of time or factors of luck are not sufficient, but only a fully spelled out situation (e. g., with the door wide open) can be used for this type of circumstance. Circumstance denoted by under (under these circumstances) is very much the same as static circumstance denoted by its antonym on (on the condition that) in that both tend to express the notion of condition. The

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difference between on and under in this respect is that on constitutes the unmarked, neutral case, whereas under is used for the marked case of adverse situations. Finally, it should be kept in mind that, although there is no clear dividing line between the various domains, their centres stand firm. Thus the expression suffer in translation is unequivocally circumstance, not cause, although one might, logically speaking, imply a causal factor. Still, it is not expressed by in here. Expressing such a causal relationship with suffer requires denoting the source of the process as in suffer from a tendency to exaggerate. The various types of causal relationship are discussed in the next section.

3.5. Cause and reason As already stated before, all the twelve prepositions can denote some type of cause (or reason): (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

at: laugh at, irritation at, angry at on: congratulate on, compliment on, pride oneself on in: delight in, rejoice in, exult/triumph/revel in by: surprised by, a book by with: tremble with fear, hair grey with age, pleased with, besides himself with, blush with pleasure, blind with passion, white with anger through: killed through accidents about: excited/crazy/angry/unhappy about over: argue over, fight over, hesitant over under: suffer under a regime from: die from drugs of: die of cancer out of: kill sb. out of despair

The causal meaning of each of these prepositions is strikingly different and helps to explain the type of verb that can be used in the accompanying verb phrase. The three basic prepositions at, on, in are rather restricted in the expression of causal relations. Thus causal at denotes a cause as a target at which one aims one's emotions such as laughter, irritation, anger etc. implying that the target (person or situation) was the cause of the emotion felt by the subject. Thus cause as target is an extension of the basic spatial sense of at, but taken in its dynamic sense. The fact that at only takes

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predicates denoting an emotional state or action results from the basic target sense of dynamic at: since this image schema of target remains intact, the verb or predicate must be such that it resembles in some respects the pure target verbs such as aim at, drive at, fly at, get at etc. (see Dirven 1989: 548). Causal on is also closely linked to the image schema of support associated with spatial on: thus one situation is felt to be the ground on which the other rests one congratulates, or compliments somebody basing oneself on the achievements of that person. This image schema also explains why on does not denote cause proper but only reason: the fact that one situation rests on another does not mean that the second triggers off the first, at least not in English. But in the two related languages German and Dutch, the closest historical items are an and aan, which are very generally used for the expression of causal relations. But an and aan have only kept the contact notion of on, not the support notion, which in German and Dutch is expressed by auf and op, respectively. Causal in is like all other meanings of in based on the spatial image schema of enclosure and the mental schema of an enveloping state: e. g., in delight in hard manual work the manual work is the state enveloping and causing the emotional state of delight. 4 Consequently, the predicates that can be used with causal in must also denote an emotional state which is caused and kept going by the 'enveloping' state denoted by the in phrase. The list of such predicates is rather limited and only contains predicates which denote a strongly felt emotion such as delight, rejoice, exult, triumph, revel etc. Summarizing these three types of cause, one can make the generalisation that the three basic prepositions only allow a type of cause or reason which determines human or animate behaviour and which is restricted to emotions. A similar, though less strong, restriction holds in the case of causal with: this is mostly used with predicates denoting perceptible animate behaviour such as tremble /grin/blush/beside oneself/blind/ white with (the latter three in their metaphorical senses) or perceptible states or processes: hair grey with age; echo with the clash of cutlery, etc. These co-occurrence restrictions for causal with follow from the basic sense of accompaniment: the cause is seen as an accompanying factor of some behaviour or state and triggering it off. For this reason, causal with strongly contrasts with the causes denoted by the three basic prepositions which do not require perceptible situations such as delight, rejoice etc.

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By and through denote a cause which is seen as a path and therefore have the potential of denoting a more general type of cause. In actual fact, this is only reserved for by in English, through being too much concretely visual in its tunnel image schema. 5 In the sentence Many people are killed through accidents, the through phrase denotes the notion of being involved in an accident with the effect of being killed. This visual configuration is absent in killed by, which therefore is not compatible with circumstantial causes such as accidents. Here English only expresses the circumstance by means of in, e. g., killed in an accident, but not the agentive cause, e. g., * killed by an accident. Consequently, the notion of causal by requires an independently acting cause, often bearing "primary responsibility though not volition" as Lakoff (1987: 66) puts it. This is nicely illustrated in a sentence like The tense situation was resolved by the entrance of the corporal, where the by phrase denotes a cause, but not a willing agent. But it would take us too far to go into the distinction between cause and agent here. Although about and over are also path prepositions, they do not denote a linear path as by and through, but a scattered path in all directions {about) or a path in its back and forth directions {over). This makes these two prepositions apt to be used for emotional causes. Causal about and over are very strongly related to the 'area' meanings of these two prepositions (see Figures 10 and 11). The extension of the area meaning found with verbs of cognition and communication such as know, doubt, wonder, write, speak, talk goes via a transition zone such as worry about to purely emotional states such as denoted by excited/crazy/angryj{un)happy/confident about etc. In all these predicates the subject is human and seems to be moving "emotionally" about the cause of his emotion. Since the movement associated with over is less hectic and implies a two-way or a repeated movement, causal over is limited to reciprocal verbs such as fight, argue, etc. or to predicates implying repeated thought movements such as hesitant over. The image schema underlying expressions such as worked up over may be that of a vertical dimension only whereby the state of being "worked up" is caused by the event situated below it. Causal under denotes a cause working from above so that the state in which the subject is results from the weight of that cause: this image schema is present in suffer under a regime·, her heart sinks under the thought of, stagger under the impact of, agonise under somebody's sarcasm, etc. Of the twelve prepositions under discussion, the three "separation" prepositions from, of and out of, are least restricted in denoting cause.

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Since the differences between a remote cause (die from drugs), an immediate cause (die of cancer) and a non-focussed cause as state (kill somebody out of despair) have already been analysed in great detail by Radden (1985: 88 ff.), we can here dispose of the question of why the image schema of "separation from a source" is so apt to become metaphorised into the expression of cause.

Conclusion The above analysis of the radial networks of meanings of English prepositions and of the differentiated senses within one domain of meaning has amply shown that the uses and possibilities of the prepositions to express other than spatial meanings is not an arbritary or random hocuspocus, but a highly motivated system. The most striking phenomenon is the relationship between the way physical space is divided up in English and the way mental space is structured. It is due to the very specific way prepositions are geared to denote relationships in the domain of spatial experience that English has made differentiations in the domains of mental experience such as area, manner or cause. More generally, we can conclude that languages, even the most related ones, have conceptualised the links between spatial and mental domains of experience in slightly or markedly different ways. The basis of it all is the conceptualisation of physical space. The structurings that have taken place here also determine the later extensions of these spatial concepts into the mental domains.

Notes 1. The terminology used here and in the following paragraphs to characterise the meanings of three English prepositions is the same as that used in Dirven (1989) and is accounted for there. 2. The notions trajector and landmark are used in the specific sense given them by Langacker (1987). 3. Dictionaries are not always very consistent in pointing out this difference, but vaguely imply it. Thus libery is defined in The Shorter Oxford English Dictionary as "exemption or release from captivity, bondage, or slavery", freedom is defined as "exemption or release from slavery or imprisonment, personal liberty". 4. Cobuild English Language Dictionary contrasts delight in hard manual work with delight at the prospect of leaving home; this use of at is necessary since a prospect is not

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conceivable as an enveloping state; the αί-phrase is intermediate between circumstance (at these words he left) and cause and hence a typical example of the continuum scale between circumstance and cause. 5. Note that other languages have the equivalent of through for cause/agent, e. g., German durch (but only for inanimate causes/agents) and Dutch door for all types of animate and inanimate causes/agents.

References Dirven, Rene 1989 "Space prepositions" in: R. Dirven (ed.), 519-550. Dirven, Rene (ed.) 1989 A user's grammar of English: Word, sentence, text, interaction. Frankfurt: R Lang. Lakoff, George 1987 Women, fire, and dangerous things: What categories reveal about the mind. Chicago: University of Chicago Press. Langacker, Ronald 1987 Foundations of cognitive grammar. Vol. I: Theoretical prerequisites. Stanford, CA: Stanford University Press. Paprotte, W. T. — Rene Dirven (eds.) 1985 The Ubiquity of Metaphor, Metaphors in language and thought. Amsterdam: J. Benjamins. Radden, Günter 1985 "Spatial metaphors underlying prepositions of causality", in: W. J. Paprotte - R. Dirven, (eds.), 177-207. 1989 a "Semantic roles" in: R. Dirven (ed.), 4 2 1 ^ 7 2 . 1989 b "Figurative use of prepositions", in: R. Dirven (ed.), 551-576.

On the grammar of lexical and non-lexical prepositions in English Gisa Rauh

1. Introduction Discrepancies and inconsistencies have almost become an integral characteristic of the description of English prepositions. Thus, for example, Poutsma (1926: 761) claims that in English prepositions, in addition to their normal uses, are used "as the analytical equivalents of what in Present or Old English, or some cognate languages is, or at least may be, synthetically expressed by inflection". This applies in particular to of, to, for and by. In the same spirit Curme (1935: 29) introduces the notion "inflectional particles" for these cases, and Deutschbein (1917: 278) even talks of "analytical case", referring to to as dative and of as genitive. Strongly rejecting such views, Jespersen (1924: 186), on the other hand, emphasizes that the so-called "analytical cases" must not be separated from other prepositional groups: "It is much sounder to regard them as what they really are, prepositional groups." Thus Jespersen demands that all prepositions be treated as parts of prepositional groups or phrases; however, the proposals made by Fries (1952) and subsequent structuralists (e.g., Hockett 1958; Gleason 1955; 1963; Stageberg 1965) point in the opposite direction. They regard all prepositions as function or structure words, thus grouping them together with affixes signaling gender or case, with conjunctions, negation particles, auxiliaries and articles. For these authors prepositions are distinguished from nouns, verbs, adjectives and adverbs. Their exclusion of prepositions from the latter group is justified by pointing out their lack of lexical content (e. g., Fries 1952: 106) or by claiming that they form a closed set (Stageberg 1965 [1977]: 239).1 In a similar way Fillmore (1968; 1969) describes prepositions in the framework of Case Grammar as variants of inflectional units. Although he distinguishes three types of preposition — those with lexical content, those dependent on verbs and those expressing underlying case relations (cf. Fillmore 1969: 367) — syntactically they are all described in the same way, i. e., as markers on noun phrases. According to Fillmore (1969: 367)

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the notion prepositional phrase can be done away with altogether since prepositions do not represent the heads of constructions: Thus we see that the distinction between noun phrase and preposition phrase is no longer necessary. This is all to the good of course, since preposition phrase has always been a terminological nuisance. We would really like all constituents labeled X-Phrase to be constituents having X's as their heads.

The opposite view, and thus one similar to that of Jespersen, is taken by Jackendoff (1973, 1977, 1983) who, like others, criticizes Fillmore's position: It is often claimed that prepositions are not a lexical category, but rather that they are simply case markers on noun phrases, possibly even inserted by transformations. This approach is institutionalized in Fillmore's Case Grammar (Fillmore 1968); Postal (1971) trivializes the role of prepositions still further ... Though diachronically the reduction of prepositions to case markers is undeniable, it is not clear that such a process plays a role in synchronic grammar. (Jackendoff 1977: 80)

He, in turn, describes prepositions as elements of an autonomous lexical category on a par with the categories noun, verb and adjective. In general, this view is adopted in the framework of X-bar-syntax (cf. Emonds 1976; van Riemsdijk 1978; Stowell 1983; Chomsky 1986 a, 1986 b; Baker 1988). Emonds (1985), however, again distinguishes prepositions from the lexical categories noun, verb, and adjective since, according to his view, they are "a grammatical rather than a lexical category" (1985: 14), even though they represent the heads of constructions. In this paper it will be demonstrated on empirical grounds that a uniform description of various uses of prepositions, as suggested by Jespersen, Fillmore or Jackendoff, is not justified. It will be shown that, based on syntactic evidence — and with some consideration of semantic properties — prepositional variants can be distinguished which can be divided, to start with, into two classes, lexical and non-lexical. "Lexical" here is intended to mean that these items are elements of a lexical category characterized by syntactic, semantic and phonological properties analogous to those of other lexical categories. Lexical prepositions have their own autonomous lexical entries. Non-lexical prepositions, on the other hand, do not have autonomous lexical entries of their own. They are not autonomous lexical items. They are the result of various grammaticalization processes with syntactic and semantic consequences, as characterized, for example, by Meillet (1912) and, more recently, by Lehmann (1985; 1986/87). Since various processes are involved, the set of non-lexical prepositions is heterogeneous. It is the aim

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of this paper to set up criteria which provide an explicit basis for the identification of lexical and non-lexical prepositions and, furthermore, for a characterization of types of non-lexical variants. In what follows, the properties of lexical prepositions will be indicated. These are comparable to those of elements of other lexical categories and may be considered as conditions on lexical heads. Then two types of variant of non-lexical preposition are discussed whose specific properties are compared to and contrasted with those of lexical prepositions. A brief summary concludes the presentation.

2. Lexical prepositions Elements of lexical categories are both syntactically and semantically the heads of constructions. As syntactic heads they determine syntactic properties of constructions, e. g., syntactic projection properties, the formation of category-specific proforms, the potential for coordination or movement, and Case properties. As semantic heads they determine semantic properties of constructions such as, for example, semantic "projection properties", which include the selection and theta properties of internal arguments, modification properties related to elements in adjunct position and specifying properties related to elements in specifier position. They determine semantic properties of proforms as well as conditions on coordination. As semantic heads, elements of lexical categories also determine their argument structure, rendering possible — via their external arguments — a connexion with the heads of other constructions which cannot be provided on purely syntactic grounds. Finally, as semantic heads, elements of lexical categories are characterized by inherent semantic properties which distinguish them from other elements of the same category in a more or less significant way. The properties indicated hold for elements of lexical categories in general. They also hold for a subset of prepositions.

2.1.

Syntactic properties of lexical prepositions

2.1.1. Projection properties According to the assumptions of the Theory of Principles and Parameters (cf. Chomsky 1981, 1986 a, 1986 b) unmarked phrase structures conform

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to the conditions of X-bar-theory. Thus, categories which are not the head of a construction are projections thereof. The facts for English are expressed by the following schemata (Chomsky 1986 a: 3): (1)

a. X' —• Χ X"* b. X" -»· Χ"* X'

In (1 a) X refers to the head of a construction and X"* to its complements, "*" indicating that their number may be η > 0. In (1 b) X"* refers to the specifier of X. According to Chomsky, the schemata are valid for the lexical categories noun [ + N, —V], verb [—N, +V] adjective [ + N , +V] and preposition [ —Ν, —V] as well as for the non-lexical categories COMP and INFL. Studies by Jackendoff (1973, 1977), van Riemsdijk (1978) and Emonds (1972, 1976, 1985) have provided empirical evidence for the fact that prepositions in English exhibit projection properties of the kind indicated. It is emphasized here that this holds only for a subset of prepositions or their uses, i. e., for lexical prepositions. Just like verbs, these allow various XP-categories as their complements ( = "C-selection", cf. Chomsky 1986 b: 86), whereby — again like verbs — individual prepositions may differ with respect to their C-selection properties. The following examples demonstrate that prepositions, in addition to allowing various XP-complements, may be intransitive: (2)

a. John stayed [PP in [ NP the house]], b. John stayed [PP in].

(2')

a. John [VP cooked [ NP the dinner]], b. John [VP cooked],

(3)

a. John went [PP into [ NP the house]], b. *John went [PP into].

(3')

a. John [VP salted [ NP the dinner]], b. *John [VP salted],

(4)

a. I didn't see him [PP before [ NP the movie]]. b. I didn't see him [PP before [CP the movie began]]. c. I didn't see him [PP before],

(4')

a. Bill [VP knew [NP the answer]]. b. Bill [VP knew [CP the answer was correct]]. c. Bill [VP knew].

Lexical and non-lexical prepositions

(5)

a. Bill stayed [PP until [ NP dawn]]. b. Bill stayed [PP until [CP the day dawned]]. c. *Bill stayed [PP until].

(5')

a. Bill [VP recognized [ NP his friend]]. b. Bill [VP recognized [CP that it was his friend]]. c. *Bill [VP recognized].

(6)

a. John came [PP from [ NP the station]]. b. John came [PP from [PP behind the curtain]].

(6')

a. The pencil [Vp pierced [ NP the paper]]. b. The pencil [VP pierced [PP through the paper]].

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The description of [P + XP]-constructions as PPs, as in (2) to (6'), with XP realized as NP, PP, CP or 0, is based on the observation that they exhibit analogous syntactic behaviour. Thus, for example, each of the PPs may be fronted, inducing what is called "comma intonation" (cf. Emonds 1985: 249): (7)

a. Before the movie, I didn't see him. b. Before the movie began, I didn't see him. c. Before, I didn't see him.

The fronting of directional PPs is accompanied by NP-V-Inversion, as Jackendoff (1973: 347) points out: (8)

a. From the station came John. b. From behind the curtain came John. c. In came John.

PPs with various XP-complements may occur in cleft sentences: (9)

a. b. c. d.

It It It It

was was was was

[PP before [ NP the movie]] that I saw John. [PP before [CP the movie began]] that I saw John. [PP before] that I saw John. [PP from [PP behind the curtain]] that John came.

They can also be coordinated: (10)

a. [PP Before [CP the movie began]] and [PP until your arrival] it was very boring. b. He rushed [PP in] and [PP down [ NP the stairs]]. c. John came [PP from [PP behind the curtain]] and [PP off [ NP the chest]].

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In addition, prepositions with various XP-complements may be replaced by proforms which can only replace PPs, not VPs, APs or NPs: (11)

a. Bill refused [PP before I did] and John before me before refused [PP then] too. b. The first session [VP lasted an hour] and [VP so] did the second session too. *then c. The first meeting was [AP late] and [AP so] *then was the second too. d. Bill loves [ NP the summer] and John loves [ NP it] too. *then

(12)

a. Bill stayed [PP up the hill] and John up stayed [PP there] too. b. Bill [VP lives in London] and [PP so] does * there John too. c. The kitchen is [AP ten feet long] and [AP so] is the living room. *there d. Bill hit [ NP the fence] and John hit [ NP it] too. * there

As an additional piece of evidence for the adequacy of classifying the various [P + XP]-constructions as PPs, Jackendoff (1973: 347) and Emonds (1976: 174; 1985: 257 ff.) cite the fact that in each case right may occur as a specifier: (13)

a. b. c. d.

John John John John

stayed right in the house. stayed right in. came right from behind the curtain. arrived right before Mary did.

It is significant that right is not allowed in the context of VP, NP or AP: (14)

a. *Mary [VP right invited John]. b. *Mary is [ AP right beautiful], c. *Mary is [ NP right a beauty].

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Reference to right as a specifier introduces properties of Ρ beyond the domain of complements, i. e., to properties above the P1 level. According to the Chomskyan schemata presented in (1), lexical categories have two levels of projection, the specifier position in English being defined as the daughter of X 2 ( = Xmax) and the left sister of X1. In (1 b) the number of possible specifiers is determined as η > 0. Thus, iteration of specifiers is allowed, but no principled distinction between the various specifiers and the head is indicated. As Jackendoff s analyses (1977) demonstrate, however, with respect to Ν, V and A at least, this approach is inadequate. Jackendoff, who assumes Xmax = X3, distinguishes for these categories specifiers in X 3 as sisters of X2 as well as specifiers in X2 as sisters of X1. As X3-specifiers he identifies articles like the, a, these, those, etc. for N, degree terms like so, too, as, etc. for A and the subject of a sentence for V. As X2-specifiers he identifies quantifiers like many, few, several, etc., measure phrases, attributes and postmodifying phrases for N, adverbials for V and measure phrases for A and P. X3-specifiers differ from X2specifiers in that they close X max -phrases at the periphery. The position can be filled only once, whereas X2-specifiers may iterate. Although Jackendoff assumes X m = X 3 for Ρ as well as for Α, Ν, V and others, he does not provide examples of P3-specifiers. However, he does not explicitly exclude them either. This is done by Fukui and Speas (1986), not only for Ρ but also for A, Ν and V. These authors make a distinction between functional categories like INFL, DET and COMP and the lexical categories Α, Ν, V and P. They identify X2 as the maximal projection for functional categories and X1 for lexical categories. X1 is assumed to allow recursion. Thus Jackendoff s X2-specifiers and some of his X3-specifiers correspond to daughter and sister of X1 in this model. Emonds (1985) also assumes recursion of X1. In contrast to Fukui and Speas, however, he identifies specifiers of XP (X = Α, Ν, V, P) which close the maximal projection (Emonds 1985: 18 ff.). According to Emonds, specifiers are represented by grammatical formatives which are not heads of constructions, like DETERMINER (this, that, these, those, the, a, each, every, etc.) as SP(N), INTENSIFIER (very, so, as, more, most, too, enough, etc.) as SP(A), AUXILIARY (will, would, can, could, may, might, etc.) as SP(V) as well as the prepositional specifiers right, clear and straight. In addition, Emonds identifies as specifiers measure phrases, which occur especially in the context of A and P. Unlike Jackendoff, Emonds thus does not distinguish specifiers on various levels for Ν, V and A. With respect to P, his solution is de facto the same as Jackendoff s.

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Somewhat different are the suggestions made by Radford (1988). He, too, provides examples for the recursion of X^categories and identifies the position X'-daughter-and-left-sister-of-X 1 as that of premodifying elements including e. g. measure phrases. He calls this position, which corresponds to that of postmodifying adjuncts, "attribute position" and distinguishes it from the specifier position, defined as daughter-of-X max and-sister-of-X 1 , which closes a maximal projection. In addition to determiners for N, aspect for V and determiners for A (e.g., that, so, completely, etc.) Radford identifies right as a specifier of R The examples demonstrate that premodifying elements of Ρ have not been described uniformly in the literature. Further examples of these diverging approaches could be considered (e.g., van Riemsdijk 1978; Bierwisch 1988). For the present line of argument it is not necessary to decide whether elements like right occupy the same position as measure phrases like, for example, two feet in two feet above the door, that is, whether they are specifiers or attributes (in Radford's terms). What counts is simply the fact that prepositions allow premodifying as well as postmodifying elements and thus project beyond the domain of complements. Syntactically these elements may be either grammatical formatives (in the sense of Emonds) like right, measure-NPs, or PPs, as the following examples illustrate: (15)

The store is [PP right [P- across the street]].

(16)

Bill lives [PP two miles [P< down the road]].

(17)

Bill arrived [PP two hours [P< before Mary]].

(18)

a. Bill went [PP down [P- to his friends]]. b. Bill went [PP [P< [P' down] [PP to his friends]]].2

(19)

He stayed [PP [P< [P< at his sister's] [PP near Brighton]]].

Thus, with respect to projection properties, prepositions exhibit the same behavior as elements of the lexical categories V, Ν or A. 3 2.1.2. Case properties In addition to syntactic projection properties, which determine the construction of phrases and thus also make predictions concerning movement, substitution and coordination, prepositions also exhibit Case properties. Pronominal complements as in (20) and (21) provide evidence for the fact that prepositions are Case assigners:

Lexical and non-lexical prepositions

(20)

Mary got the book from him.

(21)

Bill bought a book for her.

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In the Case Theory of the Theory of Principles and Parameters a distinction is made between syntactic structural and inherent lexical Case. The latter is related to theta roles (Chomsky 1986 b: 153). It is postulated that an element α assigns inherent Case to an N P if it theta marks this NP. Since prepositions theta mark their complements, Case assigned by prepositions is considered inherent Case. Assignment of inherent Case is postulated for Ρ, Ν and A, explicitly restricting it to the Genitive for Ν and A, realized by either 's or of in the context of Ν and only by of in the case of A. The assignment of structural Case is postulated for V and INFL and is independent of theta marking. We will see later that there is more to be said about the assignment of Case by prepositions (Section 4.). At this point it suffices to have pointed out that prepositions do assign Case, which in English, if morphologically realized, is identical to the Case assigned by verbs. Therefore, van Riemsdijk and Williams (1986: 229) use the term "accusative" to capture both instances.

2.2.

Semantic properties of lexical prepositions

2.2.1. Semantic "projection properties" Lexical heads of constructions exhibit not only properties of syntactic heads, but also of semantic heads. What is important here is the fact that heads determine or are involved in cooccurrence restrictions which include the whole domain of the syntactic projection and thus exceed the domain indicated by Chomsky (1965: 95ff.), which refers to objects, i.e., complements, and subjects of verbs and adjectives only. (22) gives, for elements of the category V, examples of such selection properties related to complements and determined by semantic properties of the head: (22)

a. Bill read the book. *the boy. her thoughts. b. The lesson lasted an hour. *a door. c. The bug crawled over the wall. *above d. The bug flew over the wall. above

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In (22 a) the semantics of read requires the complement to express something readable. The adequacy of using her thoughts in this context demonstrates that selection properties are not to be understood as restrictions requiring a constituent to inherently provide these properties but rather as transfer features in the sense of Weinreich (1972: 96 ff.) which are provided by the verb and read into the feature matrix of the complement. Thus, due to the selection properties of read, thoughts is interpreted here as something readable. The semantics of last in (22 b) requires a temporally interpretable complement. Other complements are inadequate. In contrast to fly, the semantics of crawl expresses contact with a surface. Since above is marked as expressing distance rather than contact between two entities, it is inadequate in the context of crawl, but adequate in the context of fly. Since over is unmarked with respect to distance, it may head a PP in the context of either verb, as is shown in (22 c) and (22 d). Similar selection properties may be observed for lexical prepositions: (23)

a. Bill stayed above the creek. *an hour, average. b. Bill arrived at the station. five o'clock. c. The hadn't heard of it since last week. *the house. London. King George. d. Chaos reigned through the house. across e. The pencil is on the desk. in

(23 a) shows that above does not take a complement which is inherently marked as temporal. It does, however, take complements which allow a spatial or a scalar interpretation. The preposition at, on the other hand, allows spatially and temporally interpretable complements, as is demonstrated by (23 b). This is a first indication that above and at are characterized by selection properties of two kinds, which means that there are lexical variants. We will return to this point later. The examples under (23 c) illustrate that since has temporal selection properties and takes only complements which are interpretable temporally. 4 London and King George are interpreted accordingly, paraphrased perhaps as since they had been in London or since the times of King George. Examples (23 d)

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and (23 e) illustrate that as a result of different selection properties of the head in question, the same complement is interpreted in different ways. Thus through in (23 d) induces a three-dimensional conceptualization of a house, whereas across induces a two-dimensional one. And on in (23 e) causes the selection of a two-dimensional part of a desk, unlike in, which causes the selection of a three-dimensional one. The following examples demonstrate that elements of the categories N, A and V also determine cooccurrence restrictions between heads and pre- or postmodifying elements, i. e., elements in specifier/attribute and/ or adjunct position: 5 (24)

a. many of the men *milk b. much of the milk *men c. a group of men *milk d. a cup of milk *men e. two feet of rope *milk

(25)

a. so J *pregnant b. utterly incompetent *tall c. six feet tall *pregnant * incompetent d. six months pregnant *tall incompetent

(26)

Bill was drawing a circle. *Bill was knowing the answer.

(27)

Bill liked the woman in the green shirt. *idea

(28)

Mary is pregnant with a boy. *tall

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(29)

Bill believed in the stork for several years. *reached the top

(30)

Bill broke the vase using a hammer. *read the book

As the following examples illustrate, lexical prepositions exhibit the same cooccurrence properties: (31)

a. two meters above the door behind the door *before noon * above average *on the door b. three minutes before noon *above the door * above average c. some degrees above average *above the door *before noon

(32)

a. Bill went past the house along the river. *until noon. b. Bill arrived at five o'clock sharp. *the station c. Bill stood behind the door near the wall. *from the wall. d. Bill arrived at five o'clock in the morning. *at the station. e. Bill arrived at the station near London. *at five o'clock.

In (31 a) the measure phrase two meters can only specify a spatial preposition and, since this measure phrase expresses a distance a, only one which itself expresses a > 0. Since on expresses contact and thus α = 0, two meters is inadequate as a specifier in this context. Examples (31 b) and (31 c) illustrate that a temporal specifier can specify only a temporal preposition and a scalar specifier only a scalar one. The aftove-examples in (31 a) and (31 c) also illustrate that this preposition is polysemous between two interpretations, one spatial and one scalar. Thus, the potential for different specifiers supports the assumption presented earlier that two variants may be identified. As with polysemous expressions in general,

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the semantic variation is evident only in context. If, however, a constituent in the projection is marked for one of the potential variants of a preposition, this variant is the one selected and the remaining constituents of the projection are interpreted accordingly. This condition is illustrated by the examples under (32 b), (32 d) and (32 e), which demonstrate that at is polysemous and has a spatial and a temporal variant. In (32 b) the complement five o'clock is marked for the feature [temporal]; thus the temporal variant of at is selected and sharp interpreted accordingly. The complement the station, however, selects the spatial variant of at. Since sharp cannot be given a spatial interpretation, the sentence is ill-formed. Similarly, in (32 d) only the temporal PP in the morning is possible as an adjunct to temporal at, not the spatial PP at the station. If the latter is analyzed as an adjunct to V, the expression is well-formed. The situation is analogous in (32 e) where, because of the station, the spatial variant of at is selected. In a similar way, in (32 a) the until-PP is incompatible with the head past if the former is analyzed as an adjunct to the latter. In (32 c) the from-PP is inadequate as an adjunct to behind since it expresses a source, which cannot serve as a modification of behind. These examples should be sufficient to demonstrate that lexical heads exhibit what are here called semantic "projection properties". 2.2.2. Semantic substitution properties A related and yet somewhat different property of lexical heads may be seen in the fact that they semantically determine the syntactic proform of their maximal projection. This is illustrated by the nominal proforms in (33) and (34):6 (33)

the boy - he *she

(34)

the girl — she *he

In a similar way, prepositional proforms are marked for either space or time: (35)

a. He stayed in London. there. *then. b. Where did he stay? — In London. *When

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(36)

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a. He came in the morning. then. * there. b. When did he come? — In the morning. *Where

For causal PPs — including what is traditionally classified as a causal clause introduced by a subordinating conjunction — a specific whproform may be identified: (37)

Why did he do it? — Because of the rain. Because it was raining.

In addition, therefore may be considered a causal prepositional proform, showing by its morphological complexity that causal prepositions are always derived and never basic: (38)

Because of the rain he did it. Therefore he did it.

The proform thus, which may also replace [P + NP)-sequences and which is inherently marked for "manner" as is illustrated in (39), (39)

He spoke in a loud voice. thus.

cannot be considered a prepositional proform since as a deictic, especially text-deictic expression, it is predominantly semantically marked and may replace various units of a text, including syntactically unspecified units: (40)

a. b. c. d.

Thus spoke the chief. When thus gentle, Mary was the nicest girl in the world. The legend has thus much of foundation. The new machine will work twice as fast, thus greatly reducing costs.

The same holds for the wh-form how, which represents a semantically rather than syntactically specified proform and may replace various syntactic categories: (41)

a. How did he leave? — In a hurry. — Quickly. — Convinced. — Cursing.

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b. How tall is he? - Six feet. - Very tall. It seems that the set of possible, semantically marked prepositional proforms is relatively small and is by far exceeded by the set of meanings which are attributed to prepositions (cf., e.g., Radden 1982; 1989), including the spatial, temporal and causal ones identified in traditional grammar. 2.2.3. Argument structure and theta properties A further important semantic property of lexical heads is that they determine an argument structure and a theta grid. 7 Thus, for example, the verb put provides three arguments, assigning them the theta roles AGENT, T H E M E and GOAL respectively. What renders argument structure and theta grid so important is the fact that these semantic properties are mapped onto syntactic ones, providing an interface between syntax and semantics. Since Williams (1981 a), a distinction has been made between an external argument and η (n > 0) internal ones; the internal ones being represented by the sisters of the head, the external one being located outside the maximal projection. In the case of verbs the external argument is represented by the subject. Thus, the external role of put, the A G E N T role, is assigned to the subject. T H E M E and G O A L are the internal roles assigned to the complements, which represent the internal arguments. In addition to external and internal roles, a referential role is identified in Theta Theory. Thus, Williams (1981 a: 86) introduces the role "R" in the context of nouns, which is relevant for referential uses of NPs. Higginbotham (1985), following Davidson (1967), introduces the referential event role "E" for verbs of all kinds, not restricting this role to event verbs as Davidson did. It is postulated that with respect to nouns the referential role is identical to the external one whereas this does not hold for verbs. All lexical prepositions determine a two-place argument structure and a corresponding theta grid. It is this property which gives them the relational character which was recognized and emphasized in traditional grammar, and expressed, for example by Curme (1935: 87) in his definition of prepositions in the following way: "A preposition is a word that indicates a relation between the noun or pronoun it governs and another word, which may be a verb, an adjective, or another noun or pronoun." The internal argument is always represented by the complement. According to traditional grammarians, including Curme, this complement

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is always realized as an NP. In Section 2.1.1. it was claimed that it could also be a CP or a PP. The internal argument is assigned the internal role under government, a process described by Higginbotham (1985: 559 ff.) as "theta marking". This role, which behaves like a free variable, is bound by the complement and thus saturated. If a preposition is intransitive, the internal argument is implicit. In this case the internal role is bound by contextual information. The external argument of prepositions, which is located outside their maximal projection, is identified according to the position or function the PP assumes. If the PP is a complement or an adjunct in a construction, then its external argument is lexically represented by the head of the construction. If the PP assumes the function of the predicate, it is the subject. The dependencies may be demonstrated more precisely by considering the assignment, the "discharging" or saturation (cf. Higginbotham 1985: 561) of theta roles. PPs may occur as predicates in socalled "small clauses": (42)

a. [sc Bill in London] is unexpected, b. Bill hates [ s c meetings on Sundays].

In cases like these, the external role of Ρ is assigned under government by theta marking — as in the case of complements — and saturated by the subject. In sentences like the following, (43)

a. Bill is in London. b. The session is in the evening.

the PPs are not predicates but complements of the verb be, which in these examples is not the copula but a lexical verb which determines an argument structure of its own, just like stay or take place. The referential, non-predicative character of such PPs is clearly shown by the fact that they can be replaced by deictic proforms (cf. Jackendoff 1983: 49): (44)

a. Bill is there. b. The session is then.

Sentences like (45), (45) Bill is in pain. in which the sequence [P + NP] is used predicatively, will be considered at a later stage (Section 3.). Anticipating, I claim that in this case the preposition is not lexical.

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115

If a PP assumes the function of an adjunct, its external role is identified with the refential role of the head of the construction. It is this latter role which in turn has to be saturated. In this respect PPs behave like APs, which are described by Higginbotham (1985: 564). (46) and (47) are examples in which the external roles of Ρ and A respectively are identified with the referential role R of the nominal head of the construction: (46)

the day before Sunday the trip on Sunday the book on the table

(47)

the early morning the high board the blonde girl

In the examples under (48) the external role of Ρ is identified with the referential role Ε of the verbal head: (48)

a. Bill met Mary in London. on Friday, b. Bill slept for hours. in the afternoon.

If the PP is the complement of a construction, the external role of Ρ is again identified with the referential role of the head, in (49) with that of a verbal head: (49)

a. The session lasted until five o'clock. b. Bill threw the ball behind the tree. c. Bill jumped on a chair.

Sentence (49 c) is ambiguous between two readings: the PP could equally be an adjunct to V. The difference between the two readings is reflected in the way theta assignment works. A PP as a complement, but not as an adjunct, is assigned a theta role by the verb in addition to theta identification, and is thus connected with the verb in two ways. Haumann (1991: 148 ff.) argues convincingly that this explains the often observed fact that the coherence between verb and complement is much stronger than that between verb and adjunct, prohibiting, for example, certain types of movement. The similarity between PP-complements and PPadjuncts, on the other hand, is explained by the fact that in both cases the external role of PP is identified with the referential role of V.

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A comparison of the connexion between PP-complements or PP-adjuncts and the head of the construction illustrates how important is the task performed by those lexical items which may be the heads of adjuncts, including P. The Licensing Principle formulated in Chomsky (1986 b: 93 ff.) requires that each element in a well-formed structure must be licensed in one of a few possible ways. Thus, for example, complements are licensed by thematic roles which they receive from the head of the construction, predicates in that they require a subject. Adjuncts are not governed by the head of the construction in which they are included and thus cannot receive a theta role from it. They are not required by any constituent and in turn do not require any. The only possible way of licensing adjuncts is via an unsaturated external role which their heads have and which needs to be saturated. This is achieved by theta identification with the referential role of the head. Thus, the external role of its head provides the only connexion between an adjunct and the construction of which it is an integral part. It follows necessarily that lexical items which may be heads of adjuncts must have an external role which is not saturated in their own projections. We shall consider some consequences of this requirement later (Section 3.). With respect to adjunct-PPs a further remark is in place. Since adjuncts are not governed by the heads of constructions containing them, they cannot be subject to the selection properties identified in Section 2.2.1. However, restrictions may be defined on the basis of external arguments. Thus it was claimed that prepositions express relations, the two semantic arguments representing the entities related. Given this prerequisite, a natural consequence is the condition that, with respect to ontological type, the arguments must not differ. It is, in other words, inadequate to relate a spatial entity with a temporal one by means of a preposition. If the internal argument of a preposition is determined by lexical selection properties, then automatically restrictions are imposed on the external argument too: the external role of the preposition of an adjunct-PP can be identified with the referential role of a given head only if the latter provides an external argument for the preposition which is not ontologically distinct from its internal one. This condition explains the wellformedness or ill-formedness of the examples presented in 2.2.1. to the extent that it is related to the semantic correspondence between the two arguments of a preposition in adjunct-PPs and, of course, also in complement-PPs. The discussion of adjunct-PPs and adjuncts in general necessarily leads to a conclusion which will be relevant in what follows. If it is the case

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that adjuncts are licensed only by identifying their external role with the referential role of the head to which they are adjuncts, then all lexical elements which are heads and which take adjuncts must provide a referential role. Since prepositions, as was illustrated in Section 2.1.1., are heads and take adjuncts, it follows that they must provide a referential role, just like nouns and verbs. This would explain the property of referentiality of PPs emphasized by Jackendoff (1983). Jackendoff bases his claim on the observation that PPs can be replaced by "pragmatic anaphors", i.e., deictic expressions (cf. Jackendoff 1983: 49): 8 (50)

a. Your coat is here [pointing] and your hat is there [pointing]. b. He went thataway [pointing].

The following sentence provides evidence for temporal PPs: (51)

Push the button ... now!

It follows that a referential role of Ρ depending on the semantics of Ρ should be specified as either spatial, temporal or something else. Assuming, then, that lexical prepositions in addition to their external and internal roles, provide a referential one, two questions arise: 1. What is the relation between these roles? and 2. How is the referential role saturated? With respect to verbs it is assumed that the external and the referential role are distinct. The referential role is saturated by theta binding via existential quantification. For nouns it is assumed that the external and the referential roles are identical. Saturation is achieved by theta binding either by means of the specifier or by existential quantification (cf. Higginbotham 1985: 559 f.). The uses of PPs which clearly exhibit referential properties suggest that the situation here is neither like that for V nor like that for N. The fact that P1 can be replaced by a deictic proform and the fact that intransitive prepositions can be used referentially provide evidence for the claim that in the case of prepositions the internal role is identical with the referential one. Accordingly, in the context of transitive prepositions the referential role is saturated via theta marking and in the context of intransitive prepositions by contextual information. Since the referential role is identical with the internal role, it is unnecessary to assume several semantically specified referential roles, as indicated above, because an interpretation of the internal argument as a spatial or temporal unit is guaranteed by the selectional properties of the preposition, for example SPATIAL (x) or T E M P O R A L (x) (cf. Section 2.2.4.).

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This section has looked at argument structure and the theta grid, considering how many arguments and theta roles are determined by lexical prepositions and how the roles are saturated. The specific semantic content of the theta roles is part of the specific semantic properties which characterize lexical prepositions as autonomous lexical items. These properties are considered in the following section. 2.2.4. Specific semantic properties By definition, lexical heads exhibit inherent semantic properties. On the one hand, elements of the same syntactic category are distinguished with respect to semantic properties, on the other hand, shared properties allow the identification of semantic classes. Thus, for example, the nouns man and woman differ from each other in that the former is marked by the property MALE (x) and the latter by FEMALE (x). Since both, however, exhibit the properties ADULT (x) and HUMAN (x), they can be assigned to the semantic classes of adults ( = ADULT (x)), humans ( = HUMAN (x)) as well as human adults ( = ADULT (x) & HUMAN (x)). In contrast to statements about prepositions which classify them as structure or function words with only structural meaning (e.g., Fries 1952: 106; Hockett 1958: 153; Quirk 1962 [1968]: 79), numerous contributions to the semantics of prepositions have demonstrated that they exhibit specific lexical meaning. 9 Again it should be noted that this holds for lexical prepositions. Irrespective of which theoretical position is preferred — at present approaches to the semantics of prepositions are characterized by their diversity rather than by unity, as can be seen from the contributions to this volume — in any of the approaches questions of the following kind will have to be central, assuming that expressing relations is a category-specific characteristic of prepositions: 1. What are the properties of the arguments? 2. Which roles are assigned to the arguments? 3. What are the properties of the relation? In connexion with the first question, the relation to a domain is of primary importance, i.e., whether the units related are characterized as SPATIAL (x) or TEMPORAL (x), for example. What is important here is the characterization of the internal argument since, as was pointed out before, the external argument may not differ and thus its properties are derived automatically. If a preposition selects a spatial unit as its internal argument, as do in, on, behind, near, above, etc., for example, then it

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belongs to the semantic class of spatial prepositions. If it selects a temporal one, like, for example, since or until, then it belongs to the semantic class of temporal prepositions. It may be the case that the specific meaning of a preposition also defines further properties of its potential arguments. It is interesting to note that definitions of this kind seem to be restricted to the internal argument, whose syntactic representation is governed by P. Thus it seems that semantic properties are assigned under government, as are Case and theta roles. Semantic properties of the kind indicated include, for example, in the context of SPATIAL (x) 3DIM (x), as in the case of in or through, or 2DIM (x), for example on or across, which define the internal argument as a three-dimensional or two-dimensional spatial unit. These two properties are responsible for the different interpretations constructed for the sentences (23 d) and (23 e), presented in Section 2.2.1. and repeated here as (52 a) and (52 b): (52)

a. Chaos reigned through the house. across b. The pencil is on the desk, in

With respect to the second question, it is assumed here — as suggested in Rauh (1988) — that the set of roles assigned by prepositions is restricted. The external argument always receives the role THEME, whereas the internal argument is assigned either LOCATION, in the context of on, in, at, by, near, etc., SOURCE, in the context of from, since, o f f , etc., PATH, in the context of along, across, through, during, etc., or GOAL, in the context of to, toward(s), for, until, etc. The preposition with assigns its complement the role ACCOMPANIMENT. That lexical prepositions do, in fact, assign roles themselves and do not simply express roles assigned by verbs — as is often assumed — is evident in those cases where the roles assigned by a verb and a preposition in the former's domain differ, as in the following examples: (53)

a. Bill lives along the road. b. Bill threw the ball on the roof.

In (53 a), live assigns its PP-complement the role LOCATION, along its NP-complement the role PATH. This expresses that the place where Bill lives is situated along the path provided by the road. In (53 b), throw assigns its PP-complement the role GOAL, on its NP-complement the role LOCATION. As a result, the goal of the throwing is interpreted as identical to the place expressed by the complement of P: the roof. More

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frequent than examples like (53) are those where the roles assigned by verbs and prepositions in their domain are identical, as in (54 a) and (54 b): (54)

a. Bill walked along the road, b. Bill lives on a hill.

This can lead to the inadequate conclusion that prepositions express rather than assign roles, as is assumed, for example, in the framework of Case Grammar. It should be noted that THEME, LOCATION, SOURCE, PATH and GOAL are considered here as roles independent of any specific semantic domain. If these roles are regarded as properties assigned by prepositions to their arguments just like domain-specific selection properties, e. g., SPATIAL (x) or TEMPORAL (x), then by conjoining both types of property domain-specific roles may be defined. Thus, for example, LOCATION (x) & SPATIAL (x) defines a spatial localization, LOCATION (x) & TEMPORAL (x) defines a temporal localization, SOURCE (x) & TEMPORAL (x) defines a temporal starting point or area, etc. The notions LOCATION, SOURCE, PATH and GOAL signal that the relations they express were originally relevant for the spatial domain and later became transferred to other domains, a development that may be observed for many prepositions diachronically 10 and in language acquisition.11 With respect to the third question ("What are the properties of the relation?"), various criteria are relevant. For spatial prepositions these include, for example, relative distance, such as DIST (x, y) in the case of above or PROX (x, y) in the case of near or by and CONTACT (x, y) in the case of on, verticality, such as ABOVE (x, y) for over and above and BELOW (x, y) for under and below, as well as originally deictically determined horizontality dependent on the perspective of the observer, which may be transposed to intrinsically structured objects, such as IN FRONT OF (x, y) or BEHIND (x, y). Purely topological criteria, expressed, for example, by INCLUDE (y, x) or EXCLUDE (y, x) are also relevant. With respect to temporal prepositions, a relevant criterion for the kind of relation is the position within a linear sequence, i. e., either BEFORE (x, y) or AFTER (x, y).12 Thus, semantic properties of the kind presented may, in fact, be identified for lexical prepositions. We shall not go into the important and yet unsolved problem of how to represent the lexical meaning of lexical prepositions. For the present purpose it suffices to have pointed out that

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the semantics of prepositions always includes three different aspects of meaning, one related to the arguments, one related to the roles and, finally, one related to the relation.

2.3.

When is a preposition lexical?

2.3.1. Conditions The syntactic and semantic properties of lexical prepositions identified in Sections 2.1. and 2.2. provide criteria on the basis of which lexical and non-lexical prepositions can be distinguished. The criteria may be interpreted as conditions on lexical autonomy in the following way: (55)

a.

b. c. d. e. f. g. h.

Conditions on the lexical autonomy of prepositions: A preposition is lexically autonomous iff it exhibits the following properties: syntactic projection properties, i. e., η complements (n > 0) are defined with respect to their categorial realization ( = C-selection, cf. Chomsky 1986 b: 86), adjuncts and attributes and/or specifiers are allowed; determination of a syntactic proform for P 1 ; category-specific movement and coordination properties; Case properties; semantic projection properties, i. e., Ρ is involved in semantic well-formedness conditions within P max ; semantic determination of the syntactic proform; argument structure and theta grid; definition of properties of the arguments, of theta roles ( = Sselection, cf. Chomsky 1986 b: 86 f.) and of the relation between the arguments.

In the following sections it will be demonstrated that non-lexical prepositions fail to fulfill some of these conditions in a significant way. Before turning to non-lexical prepositions, however, examples of lexical prepositions will be presented. 2.3.2. Examples Lexical prepositions first of all include the primary spatial ones. This is not surprising since, as language historians have repeatedly observed, they have developed from spatial adverbials and thus from elements of

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a lexical category (cf. e.g., Whitney 1989 [1969]: 414ff.; Brugmann 1911: 758 ff.; Paul 1920: 3 f.; Behaghel 1924: 29 ff. or Wackernagel 1924: 165 ff.). Thus, prepositions like in, on or at all exhibit the properties listed above, though only when used spatially. This may be the case when Ρ represents the head of a complement or adjunct to Ν, V or P. Deadjectival spatial prepositions, like near or round, also exhibit these properties. Next is interesting because its adjectival origin is obviously responsible for the fact that it is incapable of assigning Case and thus requires a preposition, to, to assign Case to the NP-complement. Except for this Case property, next exhibits all the properties listed. Denominal spatial prepositions, mostly phrasal with a nominal element, e.g., in front of, on top of, or developments of such a construction and now merged like beside, across or aboard, also exhibit these properties. Interesting here are examples like in front of or on top of, which represent transitive prepositions to which there is an intransitive equivalent, as is illustrated by the following examples: (56)

a. Go in front of me! b. Go in front!

(57)

a. Put the book on top of the others! b. Put the book on top!

It is evident in examples like these that of, as was suggested with respect to to in the context of next, compensates for the inability of the [ + N]category — Ν in this case — to assign Case. Thus, only the first two elements of on top of and in front of represent the lexical preposition, which — because of its deviant Case properties — differs from other lexical prepositions. Similar observations hold for the denominal form ahead, merged from the sequence [P + NP]: (58)

a. Go ahead of me! b. Go ahead!

At a later stage it will be demonstrated that examples like these provide further relevant insights (cf. Section 4.). It is a well-known fact that numerous prepositions of spatial origin may be used non-spatially. Only a few forms, however, may be identified as autonomous lexical prepositions which fulfill the conditions listed above. The following examples illustrate that temporally used spatial prepositions are a case in point:

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(59)

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a. Bill arrived on Friday in the afternoon at about five o'clock, b. Bill arrived then.

In (59 a) on is the head of a PP with a temporal complement modified by a temporal i'w-PP in adjunct position, which in turn is modified by a temporal αί-ΡΡ. Thus, the in-PP and the a/-PP illustrate that the o«-PP and the /«-PP take temporal adjuncts and thus must provide a referential role. The prepositions on, in and at differ with respect to the arguments they select. Whereas on requires a time span of one day as its internal argument, in selects a time of day like, for example, morning or afternoon, a year, or a season, and at selects a point in time. In each case the preposition selects a time span. In each case something is located temporally, i.e. the role LOCATION is assigned to the internal argument. As is demonstrated by (59 b), on determines a temporally marked proform. Thus these prepositions exhibit lexical properties which differ from those of their spatial equivalents. It is assumed here that this is due to a reanalysis of lexical properties. In the case of on this view is supported by the fact that temporal on takes a YP-complement, which is not possible in the context of spatial on: (60)

On hearing the news Bill left the room.

It is also the case that spatial, but not temporal in and on may be used intransitively. Thus, lexical variants are to be identified. It is easy to see how variants like the above may develop. If it is assumed that primary spatial prepositions exhibit selection properties on the basis of which they select a spatial unit as their internal argument, then it is possible to imagine that deviant marked sequences can be generated by inserting non-spatial complements, thus violating the selection properties and thus inducing a metaphorical interpretation. As Kittay (1981; 1987: 214 ff.) has demonstrated, one of the relevant principles of metaphor is the transfer of structural or organizational properties from one semantic domain to another. It is then obvious why at rather than in was selected to express a point in time, and in rather than at to express the time spans of a time of day, a year or a season. The examples also illustrate that properties defined with respect to spatial units, like 3DIM (x) or 2DIM (x), are selected and transformed in a domain-specific way when transferred to another semantic domain. Whereas area and space are relevant units with respect to the spatial domain, duration is relevant with respect to the temporal domain. While concepts like ABOVE and BEHIND, R I G H T and LEFT yield structural properties for the spatial

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domain, of these only IN F R O N T and B E H I N D are selected and transformed to BEFORE and A F T E R to express relations in the temporal domain. The three dimensions of space contrast with the one-dimensionality of time, which allows only linear sequencing of its units. There are numerous examples of temporal lexical variants of originally spatial prepositions, including derived forms like before ("bi" ( = by, about) + "foran" ( = from the front))·, after ( " a f ' ( = L. ab) + "ter" ( = farther off)); or until ("on" ( = up to) + "till" ( = goal)). Of these, before used as a spatial preposition is rare in Modern English, and after as well as until have completely lost their spatial properties. 13 Changes like these confirm the assumption presented earlier that reanalysis of lexical properties takes place. That these forms constitute lexical heads even in those cases where they take a CP-complement and thus — according to traditional views — represent subordinating conjunctions is evident from the fact that they can be modified by temporal modifiers in either specifier/attribute or adjunct position: (61)

a. Before you came, at about five o'clock, they ... b. Two hours before you came, they ...

(62)

a. After you had arrived, at about five o'clock, they ... b. Soon after you had arrived, they ...

(63)

They stayed right until sunrise. the sun rose.

In additon, theta roles are assigned: the role T H E M E (x) is identified with the role Ε of the matrix verb, while before and after theta mark their complements with the role LOC (x), and until its argument with GOAL (x). Tests related to the other conditions also yield positive results. Obviously, the development from a marked metaphorical use of a form to a lexical variant characterized by reanalyzed lexical properties takes a long time, as is documented by observable intermediate stages. It should also be noted that this process may develop in two divergent directions, which will be discussed in more detail in Sections 3. and 5. In addition to temporal uses of spatial prepositions, there are numerous others, which, in part, have reached a high degree of lexicalization. Interesting cases are those where obviously the metaphorical use has been lexicalized. It is characteristic of these forms that the properties of spatial prepositions are reinterpreted rather than reanalyzed. Since interpretation is a process related to the conceptual level, these variants will here be called "conceptual" variants as opposed to "lexical" variants. These

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include, for example, scalar and sequential uses of spatial prepositions, as illustrated in the following sentences: (64)

a. The temperature is two degree above zero. below b. The temperature is near zero. close to c. Bill is far above average.

(65)

a. In the alphabet a is two letters before c. b. John comes two persons after me. right before

The spatial prepositions in these examples provide properties which specify the kind of relation, i. e., verticality and relative distance in (64), localization on the front-back-axis in (65), and thus provide structural principles according to which other domains may be structured. They do not define properties of their arguments, i. e., they do not provide a domain-specific definition as, for example since or on do in (66) with respect to their respective internal arguments: (66)

a. I haven't seen him since London, b. He arrived on Sunday. *the summer.

In (67) and (68): (67)

Paris is above London.

(68)

Paris comes after London.

the property with respect to which Paris and London are ordered on a scale or in a sequence is not determined. These sentences only express that they are ordered in these ways. This use of prepositions is characterized by the fact that though they may be modified, this again may be done only by way of metaphor, i.e., by using spatial expressions or expressions which may modify spatial prepositions. Identification of the relevant domain is possible only via nominal or verbal expressions, or on the basis of further linguistic or extra-linguistic context. It is also significant that there are no proforms corresponding to spatial and temporal prepositional proforms. Thus it would be inadequate to talk of scalar or sequential prepositions in the same way as of spatial and temporal ones. These variants do not represent lexical prepositions, which

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require a lexical entry of their own, but rather lexicalized conceptual variants dependent on the lexical spatial variant. In addition to spatial and temporal prepositions, some causal and modal forms like because of, on account of, and by means of, in accordance with, exhibit all the properties of lexical prepositions: they define their internal argument as a causal or modal unit, they assign theta roles, they take specifiers/attributes and adjuncts which are domain-specific, and they determine domain-specific proforms: (69)

a. Bill did it just because of Mary on behalf of her father. especially b. Bill did it especially on account of his failures on behalf of his friend. c. Why did he do it? — Because of Mary. — On account of his failures.

(70)

a. Bill did it almost by means of will power by virtue of his firmness. b. Bill did it especially in accordance with almost his instructions by means of his will power. c. How did he do it? — By means of will power. — In accordance with his instructions.

In addition, causal and modal prepositions exhibit a variety of C-selection properties, including the selection of various categories, as is shown in the following examples: (71)

a. Bill did it in order [ CP PRO to win]. *[to [ NP John]], b. Bill did it because [of [ NP Mary]]. (*of) [Cp Mary wanted it].

(72)

a. Bill did it by means of [ NP his strength], (*of) *[CP Mary wanted it], b. Bill did it in accordance with [ NP his decisions], (*with) *[CP he decided].

Examples like (71 b) illustrate what has already been pointed out with respect to deadjectival and denominal spatial prepositions, i. e., that the preposition preceding the NP-complement compensates for the lack of Case assigning properties of the complex preposition, which seems to be inherited from its nominal origin. Since lexical NPs, but not CPs, must

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be Case marked, only in the former context is a prepositional form like of, to, with, etc. needed. These latter are, in general, considered constituents of phrasal prepositions (cf., e.g., Sweet 1892: 134 f.; Poutsma 1926: 715ff.; Kruisinga 1932: 382 f.; Quirk and Mulholland 1964). We will return to this subject at a later stage (Section 4.). All of the causal and modal prepositions discussed so far exhibit all the properties of lexical prepositions. There are others which do not. Some do not determine a proform: (73)

a. Bill did it especially in regard of his exam. *Why did he do it? — In regard of his exam. In regard of what did he do it? — In regard of his exam, b. Bill did it especially in contrast with his friends. *How did he do it? — In contrast with his friends. In contrast with whom did he do it? — In contrast with his friends.

Others neither determine a proform nor take specifiers/attributes or adjuncts: (74)

Bill did it *especially by virtue of his strength * almost by way of fighting *by way of fighting. *How did he do it? — By virtue of his strength. By virtue of what did he do it? — By virtue of his strength.

They share this scale of deviation from complete lexicality with numerous phrasal prepositions, which are rather specific semantically and cannot be included in general classes such as causal or modal. To these belong at the cost of, at the risk of, at the desire of, in favour of, in preference to, in relation to, and many others. Expressions like these are relevant in connexion with the non-lexical prepositions discussed in the next section.

3. Prepositions in fixed phrases A large number of prepositions occur in phrases which constitute syntactically invariant syntagmas. In addition, these constructions often exhibit fixed semantic and/or morphological properties. In the examples under (75) the noun expresses a normal constitutive aspect of a person or thing, in (76) a measure unit:

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(75)

out out out out out out

of of of of of of

shape form order character tune temper

(76)

by the pound by the meter by the dozen

In the examples under (77) and (78) the noun is always deadjectival, in those under (79) and (80) deverbal: (77)

on the quiet on the sly on the cheap

(78)

in in in in

the the the the

(79)

on on on on on on

the the the the the the

(80)

in the know in the swim

clear dark raw open beat hop mend move run trot

In constructions like these the prepositions are not the head of the construction, neither syntactically, nor semantically. They take neither specifiers, which are possible in the context of lexical prepositions, nor attributes or adjuncts: (81)

a. b. c. d. e.

Bill Bill Bill Bill Bill

is (*right) out of shape (*near twenty pounds). bought the coffee (*right) by the pound (*in a bag). had a whisky (*right) on the quiet (*on the sly). is (*right) on the move (*near London). is (*right) in the swim (*in the Thames).

The accompanying NP is fixed, i. e., it cannot be altered:

Lexical and non-lexical prepositions

(82)

a. b. c. d. e.

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Bill is out of (*good) shape. *Bill bought the coffee by two pounds. Bill had a whisky on the (*stealthy) quiet. Bill is on the (*long) move (*to London). *Bill is in good know of the events.

The preposition does not determine a proform, neither syntactically nor semantically. In some cases how may occur, a form which may be substituted for predicative APs and their adverbial variants, as (84) illustrates: (83)

a. How did he buy his coffee? — By the pound. b. How did he drink his whisky? — On the sly. c. How is Bill? — *Out of shape. *On the move. *In the know.

(84)

a. How is she? — Nice. b. How did he do it? — Nicely. c. *How girl is she? — Nice.

We shall see later on that this is significant. Whether prepositions in these constructions have Case properties can only be inferred via analogy, not proved. In English, Case marking is visible only in the case of nominal proforms like him, her, me, etc., which are not allowed here. Since, however, of as part of the owr-o/-constructions is assumed to be a Case assigner (cf. Section 4.), it may be concluded by analogy that in the constructions containing primary prepositions the latter also assign Case to the following NP. The argument structure and theta grid in these constructions cannot be identified in the same way as it can for lexical prepositions. The fact that these constructions never occur as complements in referential positions but rather either as predicates or adjuncts, and the fact that they do not determine deictically used proforms and do not take specifiers/ attributes or adjuncts indicate that no referential role is involved here. On the contrary, it may be concluded that it is the lack of a referential role which explains the observed syntactic properties. An external role and, accordingly, an external argument must be present, however, since, as was pointed out in 2.2.3., adjuncts are licensed only by their external roles. If the expressions are considered as semantically marked, metaphorically interpretable constructions, the external role may be identified as the THEME. On the same basis, then, an internal non-referential role may be identified. In the examples presented it is the role LOCATION.

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Again on the same basis, it may be stated that the preposition determines the kind of relation. From the set of properties of the spatial lexical prepositions those properties are selected which fit the metaphorical use, and they are interpreted accordingly. In the case of in this is the relation INCLUDE (y, x), for out of EXCLUDE (y, x) and in the case of on SUPPORT (y, x). According to the claims and partial results of recent research on metaphors, which also deals with prepositions, cognitive principles can be identified which determine restrictions on the possibility and order of the transfer of spatial properties to non-spatial semantic domains and thus allow predictions about possible arguments of certain prepositions. 14 Applied to the present case, this would imply, provided the principles of order and transfer are known, that the prepositions in these contexts behave as regularly as the conceptual variants discussed in 2.3.2. Of these it was claimed that, as lexicalized metaphorical uses dependent on spatial lexical prepositions, they are represented in the lexical entry for the latter. However, comparing the two types in question leads to the conclusion that the syntactic deviation of the constructions under investigation here also has semantic effects. At the same time it becomes evident that metaphorical use of language may induce different processes of reanalysis, which first result in lexical and finally also syntactic changes (cf. Section 5.). Comparing conceptual variants like scalar and sequential uses of spatial prepositions with the uses of spatial prepositions considered here reveals a significant difference. Whereas the former remain heads of constructions, with the same syntactic properties as their spatial sources and with reinterpreted semantic properties, this is not the case with respect to the latter. As was demonstrated above, they are definitely not syntactic heads of the constructions. Strangely enough, however, in these constructions the accompanying noun is not the head either, as is illustrated by the inadequacy of replacing it by a proform: (85)

a. *Bill had a drink what? - On the quiet. *On what did he have a drink? — On the quiet, b. *Bill is what? — In the know. *In what is Bill? — In the know.

Thus, these constructions are exocentric and therefore marked, i. e., they do not conform to the principles of X-bar-theory. The fact that some of these constructions may be replaced by proforms which may also replace predicative adjectives and their adverbial variants, as was pointed out

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before, as well as the fact that these constructions take the adjectival or adverbial specifier so rather than any prepositional specifier, (86)

a. She is so nice. She did it so nicely. b. Why did you do it so on the quiet? c. Why was she left so in the dark? d. He is always so on the run. e. He is so in the swim nowadays.

the fact that they coordinate with APs or AdvPs rather than with genuine PPs, (87)

a. He had a drink on the quiet and quickly. *in the house. b. Bill is in the clear and innocent. *at his sister's. c. Bill is on the move and happy. *in London. d. Now Mary is in the know and nervous. *in London.

the fact that, like APs and AdvPs, they may function as adjuncts or predicates, and not as complements, like genuine PPs, but sometimes even as attributes, (88)

a. He is an out of work teacher. b. He is good at after dinner speeches. c. He watched an on-line operation.

and, finally, the fact that in Modern English there are many expressions classified as adjectives and/or adverbs which have developed out of [Ρ +NP] constructions, (89)

a. A: awake, aghast, alive, alert, akin b. Adv: again, apart, aloud, aboard, ashore, apace c. A, Adv: alike, ajar, aloof, alone, amiss

all this provides evidence for the claim that what is involved here is a kind of word-formation process on a phrasal basis, which can be explained on semantic as well as syntactic grounds. Obviously there is, first of all, a communicational need to express semantically differentiated properties, circumstances or states as modifications with respect to a given referent for which the language does not

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provide adjectives/adverbs and which are essentially characterized by the semantics of given nouns. NPs, however, cannot function syntactically as adjuncts since there is no way to license them in this position. They do not provide an unsaturated external role which could be identified with the referential role of the head of the construction since the role in question is already saturated inside the N P by theta binding. Semantically, isolated nouns or NPs cannot express properties, circumstances or states as modifications of given referents since, again, this capacity is dependent on a kind of external argument that is lacking for nouns. The relevant syntactic properties that nominal heads need to function as adjuncts and the semantic properties needed to express properties, circumstances or states as modifications can be provided by prepositions which, for their part, lack the capacity to express the required semantic differentiation. Thus the [P + NP]-constructions under consideration can be viewed as a symbiosis of elements of two categories, each one providing properties which are inherited by the new product thus created. The inheriting, syncategorematic, syntactically marked construction X receives the external role and the external argument as well as relational properties from P, and semantic properties from N. 1 5 The internal role of Ρ is, as in compounds or derivations, saturated by the N P inside the construction. The construction X is, however, syntactically as well as morphologically marked. It is neither a phrase conforming to syntactic principles, nor a word conforming to morphological ones. Therefore, expressions like those presented represent one lexical unit. Of these, units exhibiting the same patterns, sharing syntactic, semantic and morphological properties, are related by lexical rules. The symbiotic relation between Ρ and NP leads to both together being considered a unique semantic unit and interpreted accordingly. Deriving the original metaphorical interpretation requires a conscious act of separating the set of features and redistributing them to their respective sources. Since the properties of such Xs — disregarding their position relative to nominal heads — correspond to those of adjectives or adverbs, they may be used like the latter. A recategorization of these marked structures in the direction of adjectives or adverbs, reducing their degree of markedness and finally reintegrating them into the grammar, begins when they start taking adjectival or adverbial specifiers. It may be considered completed when the two constituents merge to form one phonological unit and thus one word, representing an element of one category and exhibiting the properties of this category. On the basis of the properties pointed out here, this type of use of prepositions might be called "adjectivizing" or

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"adverbializing", independently of whether the final step of lexicalization has taken place, since prepositions in this context allow NPs to be used as adjectives or adverbs.

4. Case prepositions A small set of prepositions occurs in [P + NP] constructions strictly subcategorized by verbs, adjectives or nouns, Ρ being lexically required and in this sense governed by these categories: (90)

a. Bill [VP believes in science], b. Bill is [ AP good at tennis], c. Bill is [Np an expert on instruments].

In general, the sequence [P + NP] is described as a PP-complement (e.g., Chomsky 1965: 101 f.; Akmajian, Steele and Wasow 1977; Bresnan 1978: 18 f.; Ο'Grady 1985; Radford 1988: 344 ff.), with the selection of a specific preposition noted as an idiosyncratic lexical property in the following way: (91)

a. believe·. V, [_ [PP in NP]] b. good: A, [_ [ PP at NP]] c. expert: N, [_ [ PP on NP]]

Thus Ρ in this funcion is described as the head of a PP. However, prepositions in these positions do not exhibit syntactic properties of a head. They take neither specifiers/attributes nor adjuncts: (92)

a. Bill [VP believes (*right) in science (*near mathematics)]. b. Bill is [ AP good (*right) at tennis (*across the net)]. c. Bill is [ NP an expert (*right) on instruments (*close to the news)].

N o XP other than NP may follow, indicating that there is no genuine C-selection. Neither semantically nor syntactically is a prepositional proform determined, further evidence for the absence of a referential role: (93)

a. Bill believes in science. *there. *then. therefore. *thus.

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b. Bill is good at tennis. *there. "then. *therefore. *thus. c. Bill is an expert on instruments. * there. *then. ""therefore. *thus. In addition, coordination with other PPs yields ungrammatical results: (94)

a. *Bill believes in science and during his life. b. *Bill is good at tennis and in London. c. *Bill is an expert on instruments and in London.

Case properties, however, are present: (95)

a. Bill believes in Mary. her. b. Bill is good at tennis and cricket. them. c. Bill is an expert on instruments. them.

Semantic properties of heads are absent in the sense that Ρ does not define the type of internal argument. This argument is defined semantically by the governing V, A or Ν: (96)

a. Bill appealed to Mary. *the station. b. Bill is good at tennis. *the station. c. Bill is an expert on instruments. *the station.

However, as with the examples discussed in Section 3., theta properties as well as properties defining the type of relation can be identified, provided a metaphorical interpretation is assumed. Seen in this way the prepositions from, to and in in (97) assigning the role THEME to their external argument and the roles SOURCE, GOAL and LOCATION to the following NP, the domains concerned here not representing spatial

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units but rather units selected by the semantics of the governing V, A or N: (97)

a. The soldier died from his wounds. b. The answers were acceptable to the committee. c. Bill has confidence in his abilities.

Seen in this way, the prepositions on, in, and over in (98 b) to (100 b) define the properties of the relations as do their lexical equivalents in (98a) to (100a), i.e., SUPPORT (y, x), INCLUDE (y, x) and ABOVE (y, x), respectively: (98)

a. Bill sat on a chair, b. Bill lives on rice.

(99)

a. Bill lives in a large house. b. Bill participated in the meeting.

(100) a. The cloth lay over the table. b. This view predominated over all the others. The properties of Ρ in these constructions thus correspond to those identified for Ρ in the constructions in Section 3. However, there is a significant difference with respect to NP since — as has been pointed out — there is a selectional relation between NP and the governing V, A or N, which defines NP as the latter's object. This relation is especially evident when passivization is possible and the NP is the subject of the passive construction: (101) a. Bill appealed to Mary, b. Mary was appealed to. (102) a. Bill talked about John, b. John was talked about. Examples like these illustrate that independently of Ρ there is a relation between — in this case — V and NP, defined via theta role assignment and selection properties of V, which is modified only by P. This is evident in cases where there is an alternative between NP- and [P + NP]-complements: (103) a. Bill believed his friend. b. Bill believed in his friend. (104) a. Bill knew the problem. b. Bill knew about the problem.

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It may be concluded, therefore, that in these constructions Ν is the head. From a semantic perspective, the role of Ρ is comparable to that of case affixes. Ρ differs from case affixes, however, as far as its position and Case assigning properties are concerned. If, then, Ν represents the head of the [Ρ + NP] constructions considered here, what is the category of the construction as a whole? The evidence suggests that it is an NP, its internal structure being the following: (105)

NP / \ Ρ

NP

This structure represents the similarity between Ρ and case affixes in various ways. Instead of an unmarked Case, the governing N, A or Ν lexically assign the semantically and syntactically marked form P. Ρ thus corresponds to inherent Cases in case-marking languages, for example, the accusative in the context of lehren or the genitive in the context of gedenken in German, which are also assigned lexically. The scope of Ρ is — just like that of Case — the whole NP. Another correspondence is that Ρ as well as case affixes are preserved in the context of proforms: (106) a. Bill read Mary's book. b. Whose book did Bill read? (107) a. Bill gave the book to Mary. b. To whom did Bill give the book? Thus, to whom represents a P-marked NP, not a PP. On the basis of this analysis a problem pointed out by O'Grady (1985) can be solved in an elegant way. O'Grady observes that the constructions under consideration, which he describes as PPs, behave like NPs rather than other PPs with respect to control and floated quantifiers. In order to capture these facts, he introduces a new principle TDR (Thematic Dependency Requirement) which provides a basis for distinguishing the two types of PP. One is described as thematically dependent, i. e., it receives a theta role from the verb. In the other case, however, it is the NP within the PP rather than the PP that is thematically dependent. Only in the latter case may the NP within the PP provide an antecedent for control and floated quantifiers: (108) a. He counted on the boysi [PRO, to leave], b. ?The book was brought by Johnj [PRO( to read during the party].

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(109) a. He talked to the girlsj several times each;. b. *She sat near the boySj several times each;. (Compare O'Grady 1985: 170, 172) Analyzing the sequence [P -4- NP] in (108 a) and (109 a) as NP rather than PP, as suggested here, there is no need for a new principle. The constructions under consideration are explained with reference to government, as are other cases of NP-control (cf. Goodluck 1978) and floated quantifiers (cf. Jaeggli 1982). In addition, structure (105) illustrates that the dominant NP is assigned a theta role by the verb, which is then modified by the theta role assigned by Ρ to the dominated NP. Analyzing the [P + NP]-constructions investigated here as NPs with Ρ as a case preposition has further advantages. It should be noted first that the analysis is compatible with the Case Theory of the Theory of Principles and Parameters, according to which each lexical NP has to be Case marked. Assuming that Ρ represents inherent Case lexically assigned by the appropriate governor, the dominant NP in structure (105) is inherently Case marked by P, whereas the dominated NP is assigned Case by P. One problem of Case Theory as presented by Chomsky (1986 b: 192) is the fact that of as a Case marker in the context of adjectives and nouns is considered an exception which needs to be stipulated, (cf. Section 2.1.2.). In the analysis suggested here, the status of an "exception" is unnecessary. When they are case prepositions in structures like (105), prepositions in English may in general assume the function of case affixes, i. e., in the context of V, Ν and A, as is demonstrated by the examples above. In the case of Ν and A, this is the only possible way in which Case can be marked. This assumption also provides an explanation for the phenomenon, so far unexplained, that adjectives as well as nouns in Modern English have lost their Case assigning properties present in Old English. The analysis presented here supports the claim that these properties have not vanished. Instead, the semantically less differentiated case affixes have been replaced by the more differentiated case prepositions. The adequacy of this analysis is confirmed by the fact that in some contexts the semantically neutral case preposition of alternates with the genitive affix, both Case markers occurring on the periphery of an NP rather than on the head of this NP: 16 (110) a. [ NP John]'s book b. [ NP the man in the green shirtj's book (111) a. the book of [ NP John] b. the book of [ NP the man in the green shirt]

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Analyzing governed prepositions as case prepositions also provides an explanation for the second or third elements in transitive phrasal prepositions. These are lexically determined by the preceding noun (e. g., with respect to; in accordance with) or adjective (e. g., near to; next to) and in this sense governed. As case prepositions they serve to Case mark the following NP in a semantically differentiated way. This explains why they do not occur in intransitive uses or with a CP-complement (cf. Section 2.3.2.). Since Chomsky (1965: 106), and especially Hornstein and Weinberg (1981), it has been known that the constructions considered here allow preposition stranding, i. e., the NP may be moved out of the construction and leave Ρ behind: (112) a. About whom is Bill angry? b. Who is Bill angry about? (113) a. What did Bill comment on? b. The book was commented on by everybody. However, movement of NP out of a structure like (105) is excluded by the A-over-A principle. Nevertheless, examples like (112 b) and (113) need not be considered as evidence that (105) is inadequate. They simply indicate that this is an unstable domain in the grammar of English, permitting two analyses for the same sequence of units, in (112) and (113) A + Ρ + NP and V + Ρ +NP, respectively. For V, the first of these is presented in (105), here repeated as (114 a), the second in (114 b): (114) a.

V'

b.

V

V'

NP

Ρ

V

NP

V

NP

Ρ

Thus, in this domain, the present state of English exhibits phenomena which are characterized as two separate processes by diachronic linguists, for whom a specific property of prepositions is the fact that, originating as adverbs, they have migrated either to nouns to specify the semantics of cases or to verbs to specify the semantics of verbs (cf., e. g., Delbrück 1893: 654 ff.; Brugmann 1911: 758 ff.; Wackernagel 1924: 153 ff.). In addition, the examples investigated here illustrate the process described

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by Nichols (1986: 84 ff.) as "headward migration". The form Ρ that marks NP, a constituent dependent on V, migrates from the dependent constituent to its head. A similar process may be observed with respect to socalled phrasal verbs like look up; come o f f , carry on, etc. which, however, will not be considered here. Examples like (112) illustrate that this analysis has been transferred to nonverbal contexts too. It is questionable whether a description of the syntactic ambiguity as a purely syntactic process is justified, as Hornstein and Weinberg (1981) and others assume. The problem seems rather to be a lexical one and is treated accordingly in Rauh (1991 b).

5.

Summary

5.1. Prepositional variants The preceding discussion has provided evidence for the fact that the diverging views on prepositions presented in the introduction are justified to some extent. None of them, however, characterizes the whole set of prepositions, each correlates with a subset only. Thus it has been demonstrated on syntactic grounds that prepositions exhibit properties of lexical heads and are therefore justifiably considered elements of a lexical category by Emonds (1972; 1976); Jackendoff (1973; 1977); Stowell (1983); Fukui and Speas (1986) or Chomsky (1986 b). The relevant properties are summarized in the following: 1. Projection properties: — lexical prepositions may take NP, CP and/or PP complements; they may also be intransitive; — they allow pre- or postmodifying adjuncts; — they allow a specifier (if a distinction between specifier and modifier is made). 2. Case properties: — lexical prepositions in general assign structural Case; — some deadjectival and denominal lexical prepositions, which cannot assign structural Case, assign inherent, lexically determined Case, expressed by "case prepositions". 3. Argument structure: — lexical prepositions are two-place predicates: Ρ (χ, y).

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4. Theta roles: external role: internal role:

referential role:

T H E M E (y) LOCATION (x) SOURCE (x) PATH (x) or GOAL (x) identical to the internal role.

It was pointed out, in addition, that lexical prepositions exhibit selection al and inherent semantic properties, the former defining the properties of potential arguments, the latter defining properties of the relation expressed by the preposition: 5. Selectional semantic properties: — defining the ontological type of the arguments e.g., SPATIAL (x) T E M P O R A L (x) — defining specific properties of the internal argument e. g., 3 DIM (x) TIME SPAN (x) 6. Inherent semantic properties: e.g., CONTACT (x, y) BELOW (x, y) I N C L U D E (x, y) These findings provide evidence for the fact that the special treatment of prepositions as "grammatical heads" presented by Emonds (1985), which diverges from his earlier views, is not justified. It has also been demonstrated that prepositions do not represent lexical heads in all of their uses. In numerous constructions they assume other functions. Because of these, Fillmore's statement quoted in the introduction that "preposition phrase" "is a terminological nuisance" is very appropriate. In a subset of these constructions prepositions have precisely the role which Fillmore identified for them in the framework of his Case Grammar. They represent alternative, semantically specified expressions of case affixes, "analytic cases" as Deutschbein (1917) claims, or "inflectional particles" in the terminology of Curme (1926: 29). Therefore, they are here called "case prepositions". They are not restricted to a few, of, to, for or by, for example, as is sometimes assumed (cf. Poutsma 1926: 761). All primary spatial prepositions and some derived ones may occur in this function. Syntactically they form an N P together with the NP

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which they relate to the V, A or Ν by which they themselves are governed. In these constructions, however, they maintain their prenominal position as well as their Case assigning properties, and they differ from case affixes in this respect. As semantically marked alternatives to those case affixes which are lexically determined by a governor, they correspond to inherent Cases, which are assigned lexically. Thus, case prepositions represent a syntactically definable variant of prepositions and are grammaticalizations of origninally autonomous lexical forms in the sense of Meillet (1912) and Lehmann (1985; 1986/87). Grammaticalization results in a loss of lexical autonomy. The variants do not have lexical entries of their own. They are introduced in the entry for the unit by which they are governed. Their use is thus automatically restricted to complement positions. In these positions prepositions exhibit the following set of properties which, as a reduction and partial reinterpretation of the set of properties of lexical prepositions, provides evidence for the effect of the process of grammaticalization: 1. Projection properties Case prepositions have no projection properties — they always precede NPs; — they allow no pre- or postmodifying adjuncts; — they allow no specifier. 2. Case properties — case prepositions assign structural Case. 3. Argument structure — case prepositions are two-place predicates: Ρ (χ, y). 4. Theta roles — case prepositions do not assign theta roles but the related semantic roles, which have no syntactic relevance; — case prepositions have no referential role. 5. Selectional semantic properties — case prepositions exhibit no selectional properties defining the ontological type of their arguments; — they do exhibit specific properties of their internal argument which are, however, reinterpreted in accordance with the ontological type as determined by the lexically governing category. 6. Inherent semantic properties — case prepositions exhibit inherent semantic properties which, again, are reinterpreted in accordance with the ontological type of the arguments as determined by the lexically governing category.

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Another syntactically definable variant was exemplified by those prepositions which occur in fixed phrases and form a symbiotic, syncategorematic construction with a following NP. The resulting exocentric, marked structure X inherits syntactic and semantic properties from Ρ as well as NP, allowing it to be used as an adjunct. Because of this combination of inherited properties, these constructions are similar to predicative adjectives and adverbs. This explains why in the history of English predicative adjectives or adverbs have developed out of constructions of this type. This may be taken as evidence for the tendency inherent in natural languages to reintegrate marked structures into the grammar. The variants considered here also represent examples of grammaticalization. Originally autonomous lexical units, they have lost their autonomy in a symbiotic construction. Their grammatical properties in this construction are similar to those of case prepositions except that they do not precede full NPs but fixed NP-forms and except that the reinterpretation of selectional and inherent semantic properties occurs not in accordance with the type of argument as determined by a lexically governing category but as determined by the Ν in the construction. The grammatical function of these variants consists in attributing adjectival or adverbial properties to NPs. The loss of autonomy means that prepositions of this type always occur together with their nominal "Siamese sisters" in one entry in the lexicon. In this way the markedness of these constructions is represented.

5.2. Metaphors, lexicalization and lexical units During the course of this presentation it has been pointed out more or less explicitly that the syntactic prepositional variants originate in metaphorical use. In conclusion, therefore, a remark on the relationship between metaphor, lexicalization and lexical units is in place. In connexion with lexical prepositions it was argued that lexical variants may develop out of originally spatial prepositions via the cognitive process of metaphor. Lexical variants represent the end of a process which starts with a marked use, a metaphor, and is finished when the lexical properties of the original form are reanalyzed and the result is lexicalized, when, for example, in addition to a spatial preposition there is finally a temporal one exhibiting its own lexical properties. The subsequent argumentation demonstrated that this is not the only way to derive new lexical units. Various paths may lead from metaphor to lexical unit, yielding different results. In addition to new lexical prepositions, new lexical adjectives and

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adverbs may be derived. This process not only involves reanalysis of individual semantic properties but, in addition, recategorization of a sequence of two elements of two categories to one element of one category. In both cases forms derived from marked constructions are reintegrated into the grammar. As new lexical elements they are autonomous and have lexical entries of their own. Examples of the lexicalization of marked structures were also presented, and here there are differences in the degree of lexicalization. In Section 2.3.2. lexicalized metaphorical uses were presented as conceptual variants of prepositions, referring to scalar and sequential uses as examples. These are syntactically regular but semantically marked. No reanalysis but only the reinterpretation of semantic properties is involved. The parasitic dependency on spatial prepositions is captured by the fact that these uses are indicated within the lexical entries for spatial prepositions, possibly in a way suggested by Bierwisch (1983: 87 ff.) for various uses of the same lexical unit which may be considered the result of conceptual shift. Bierwisch rejects the notion of conceptual shift for his examples, but in the cases discussed here conceptual shift is in fact involved; the spatial use provides the basic meaning which represents the source of the shift. The marked [P + NP]-constructions presented in Section 3. also represent examples of lexicalized units with lexical entries of their own. They are, however, syntactically as well as semantically — and often even morphologically — marked. Since these constructions form recurrent patterns, their lexical representations are related by lexical rules. In addition to such fixed phrases, there are phrasal schemata which are semantically marked only, such as, for example, the use of spatial prepositions to express emotions as in in pain, out of hatred, etc. It may be assumed, therefore, that there are conceptual variants here, too, which in the process of the development of language may, but need not become syntactically marked structures and finally develop into elements of a different lexical category, namely adjective or adverb. Taking into account the fact that the different kinds of lexicalization indicated here as well as their different grammatical consequences are due to the same metaphorical processes, it is evident that the linguistic facts cannot be described simply on the basis of conceptual cognitive principles which define the potential for and restrictions on metaphor. They explain no more — but also no less — than the conceptual cognitive prerequisites for the potential of lexicalization. The linguistic facts themselves, however, can only be described on the basis of grammar.

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Notes 1. The inadequacy of such claims is demonstrated in Rauh (1990). 2. The structural representations of the PPs are as follows: a.

PP I P'

PP I P' I P I down b.

his friends PP I Ρ' r

PP

I down

I P' ρ I to his friends

Thus in (a) to is the head of the construction and down its premodifying adjunct whereas in (b) down is the head and to his friends its postmodifying adjunct. 3. A detailed description of the projection properties of English prepositions is presented in Othmar (1990). 4. It should be pointed out, however, that there is a causal variant of since which takes CP-complements only as, for example, in: He wouldn't come since he knew you were here. 5. If one assumes, following Fukui and Speas (1986); Abney (1987); Olsen (1990) and others, that the determiner is not the specifier of Ν but rather the head of a DP, the semantic relations identified here represent head-to-head relations. This assumption does not alter the fact that these relations — in this case S-selection of D with respect to Ν — exist and are relevant. It does, however, alter the domain of the semantic "projection properties" identified here, which are then restricted to X 1 . Inclusion of the DP-analysis would have involved a lengthy discussion of the consequences for other lexical categories. Given the present state of research, there would have been more confusion than clarification, and this would have been unnecessary since the main arguments presented here are not affected.

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6. It should be noted here too, that applying the DP-analysis would yield different results. According to Olsen (1990: 40), pronouns are intransitive determiners. 7. In contrast to Williams (1981 a), who assumes the theta grid implies the argument structure, which thus need not be stated explicitly, both are here listed separately. Only in this way is it possible to consider theta roles properties which are assigned to arguments. And only in this way is it possible to capture the fact that there is no biunique mapping of theta roles and arguments onto each other, which is an inevitable consequence if referential roles are assumed, as will be seen in the following. 8. Bierwisch (1988) comes to a different conclusion. He assumes that PPs are not referential due to the fact that they do not take specifiers. In the following it will be demonstrated, however, that with respect to P, the referential role is not related to the specifier position as Bierwisch assumes by analogy with the referential role of N. 9. See, for example, the following, as representative of many: Bennett (1975); Brugman (1988); Hawkins (1984); Wunderlich (1981; 1985); Herskovits (1986); Hottenroth (1991); Lang (1991); Schepping (1991). 10. See, for example, Closs-Traugott (1985). 11. This is demonstrated by Clark (1973), for example. 12. For further information on a systematic semantic analysis of prepositions see, for example, Wunderlich (1981; 1985) or Lang (1991). 13. See also Closs-Traugott (1985). 14. See, for example, Brugman (1988); Lindner (1981); Lakoff (1987); Langacker (1987) or Dirven (this volume). 15. On the inheritance of properties inside compounds and derivatives see, for example, Williams (1981 b), Lieber (1980, chapter 2; 1983) and Boase-Beier and Toman (1986). It should be pointed out though that in the examples discussed, it is not the head that provides the features, as is assumed by Williams. 16. This is important because English differs in this respect from case-marking languages like German or Latin. While in these languages elements within a maximal projection of Ν inherit case from the case-marked head, this is not the case in English, where a Case marker is attached to the periphery of the NP, thus exhibiting something like phrasal inflection.

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Wackernagel, Jakob 1924 Vorlesungen über Syntax. Bd. 2. Basel: In Kommissionsverlag von Emil Birkhäuser & Cie. Weinreich, Uriel 1972 Explorations in semantic theory. The Hague; Paris: Mouton. Whitney, William D. 1889 [1969] Sanskrit Grammar. Delhi: Motilal Banarsidass. Williams, Edwin 1981 a "Argument structure and morphology", The Linguistic Review 1: 81-114. 1981 b "On the notions 'lexically related' and 'head of a word'", Linguistic Inquiry 12: 245-274. Wunderlich, Dieter 1981 "Sprache und Raum", Studium Linguistik 12: 1-19; 13: 37-59. 1984 "Zur Syntax der Präpositionalphrasen im Deutschen", Zeitschrift fiir Sprachwissenschaft 3: 65-99. 1985 "Raumkonzepte — Zur Semantik der lokalen Präpositionen", in: Ballmer, Thomas — Roland Posner (eds.). Nach-Chomskysche Linguistik. Berlin, New York: de Gruyter. 340-361.

Prepositions: Patterns of polysemization and strategies of disambiguation John R. Taylor

1. Introduction Much has changed since 1973, when Ray Jackendoff could write that "people seem never to have taken prepositions seriously" (Jackendoff 1973: 345). Not only have prepositions played a significant role in Jackendoff s own subsequent work (Jackendoff 1977, 1983), the last two decades have seen an extraordinary burgeoning of research on this formerly neglected part of speech, by linguists working within a number of different theoretical frameworks. 1 Several factors have contributed to the ennoblement of the humble preposition. Foremost amongst these has been an interest in the relation between cognition and linguistic structure, with spatial cognition, especially, being at the centre of attention. Interest in spatial cognition coincided with the demise of what Lakoff (1987) has called "objectivist semantics". Jackendoff (1983), Langacker (1987), Fauconnier (1985), and many others, have argued that linguistic expressions do not and cannot stand in any simple, direct relation to states of affairs in real or possible worlds; rather, linguistic expressions invoke a speaker's construal, conceptualisation, or mental representation of states of affairs. Lakoff emphasises that a rejection of objectivism need not lead into the cul-de-sac of solipsism. Conceptualisations are ultimately grounded in, and structured by, "pre-propositional" bodily experience. Our bodily sensations, our experience of space, of objects in space, of forces acting on these objects, provide the basic structures which, through analogy, metaphor, and metonymy, enable us to conceptualise ever more abstract cognitive domains. Given such a theoretical orientation, it was inevitable, perhaps, that attention should come to focus on those lexical items whose function is, primarily, to symbolise conceptualisations of spatial relations, and which, through semantic extension, are extensively employed in the construal of relations in more abstract domains. A further factor has been a renewed interest in lexical semantics, which has led, amongst other things, to the recognition of polysemy as the

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normal order of things in a natural language (Langacker 1988: 50), and thereby created a need for linguistic theory to accommodate polysemy as a natural and inevitable phenomenon (Johnson 1987:193). In this climate, it is only natural, again, that attention should have been directed towards those lexical items which are amongst the most highly polysemous, in English and other languages, viz. the prepositions. This paper focuses on some "general" patterns of meaning extension exhibited by the English prepositions. Some meaning extensions are idiosyncratic to individual prepositions. Such, for example, is the extension of on from its basic sense of location within a 2-dimensional plane (There's a book on the table) to its use in connection with conveyance by a scheduled means of transportation (There were some children on the bus). In contrast, other processes of polysemisation are manifested, not only by individual prepositions, but by classes of prepositions. A survey of some general polysemisation processes is the topic of Section 3. The survey is preceded by a brief discussion of some basic concepts in prepositional semantics (Section 2.). Then, in Section 4., I take up the issue of disambiguation. The question is important in so far as the polysemy of prepositions is a potential source of sentence ambiguity. Section 4. surveys some of the strategies available to a listener for the disambiguation of potentially ambiguous prepositional phrases. In order to avoid possible misunderstandings, a few preliminary words are necessary on the approach I shall take in this paper. Some readers may balk at the idea that a preposition may have up to a dozen separate senses; such rampant polysemy, it might be argued, ought to be contained by a search for maximally general meanings, of which specific meanings are contextual variants (Herweg 1989: 106; Wunderlich 1991: 593). As Geeraerts (1992) has argued, the two approaches — i.e., focus on maximally general meanings vs. focus on highly differentiated specific meanings — are complementary, rather than in conflict; and indeed, Langacker's "network model" of category structure explicitly incorporates both aspects. Thus, Langacker (1988: 51-53) envisages two kinds of relation between the senses of a linguistic form, viz. relations of instantiation, or elaboration (the one meaning elaborates, with greater specificity, a more abstract, schematic meaning), and relations of extension (certain specifications of the one meaning are suspended or modified in the extended meaning). Recognition of an array of distinct senses of a linguistic form does not therefore in itself preclude the possibility that the different senses might be compatible with a single more abstract representation. (But at the same time, recognition of a single general meaning does not remove

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the need to identify more specific meanings; see Taylor, 1992.) My motivation for focusing on the more specific senses in this paper, is, precisely, to study the general patterns of semantic differentiation exhibited by the prepositions, as well as to draw attention, when appropriate, to departures from these general patterns.

2. Some basic notions Prepositions denote a relation involving two or more participant entities. The relation is inherently asymmetrical, in that one participant is selected for foregrounding, while the other participant(s) serves as a background, or reference point entity. The expressions in (1): (1)

a. the picture above the sofa b. the sofa below the picture

could well have identical truth-conditions. The expressions differ, however, with respect to foregrounding. In the former, the picture is located relative to the sofa, in the latter, the sofa is located relative to the picutre. Following Langacker (1987), I will refer to the foregrounded entity as the trajector (tr) of the relation, and the reference point entity as the landmark (lm). In their spatial senses — our main concern in this paper — prepositions characterise the spatial disposition of a tr with respect to a lm. The tr may be either a thing, as in (2 a), or a process, 2 as in (2 b). Typically, the lm is a thing, e.g., table in (2a) and (2b). Alternatively, the lm may be a place, as in (2 c), where the lm of from is a place, designated by the prepositional phrase under the table: (2)

a. The book is on the table. b. They were sitting on the table. c. Take the book from under the table.

We may make a broad distinction between three categories of relations expressed by prepositions, viz. place, goal, and path. (A fourth relation, that of source, perhaps also needs to be added to this list; see Section 3.3.) These relations constitute what Johnson (1987) has called "image schemas". Johnson characterises image schemas as recurring patterns of experience involving "human bodily movement, manipulation of objects, and perceptual interactions" (1987: xxxvi). Johnson emphasises the non-

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propositional nature of image schemas, and at the same time their abstractness relative to "rich" visual and kinetic images. It is, he maintains, the very abstractness and generality of image schemas that make it possible for us to structure "indefinitely many perceptions, images, and events" (p. 29). Consider the notion of "place". That things occupy places relative to other things is a basic, recurrent element of our experience. Yet the notion of place is sufficiently abstract as to preclude specification of the precise spatial disposition of one thing with respect to another. Objects not only occupy places, they also move from one place to another place, along a trajectory. Leaving aside the possibility of perpetual motion, any object moving on a trajectory has necessarily started at some place of origin, and will come to rest at a place of destination. Likewise, arrival at a destination necessarily presupposes movement along a trajectory, from some place of origin. Thus the notions of origin, trajectory and destination mutually presuppose one another. However, different linguistic forms can focus on, or "profile", different facets of the objecton-a-trajectory schema. In a path sense, a preposition profiles only the trajectory (or a part of the trajectory) of a tr, without regard for the endpoint or point of origin; conversely, in its goal sense, a preposition profiles only the end-point of a trajectory, both the origin and the trajectory itself being unspecified and out of focus. The notions of place, goal, and path are thus intimately linked, in virtue of the trajectory schema; a goal, for example, is a place at the termination of a path. It is not surprising, therefore, that single lexical items, viz. the prepositions, exhibit considerable polysemy with regard to the three notions. We shall see, however, that further refinements on this three-way distinction will prove to be necessary.

3. Polysemisation processes The following prepositions were take into consideration for the purpose of this study: above, across, along, (a)round,3 at, behind, beside, between, beyond, by, down, from, in, in front of, into, o f f , on, onto, out (of), over, past, through, throughout, to, towards, under, up, via.

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3.1. PLACE With the exception of via, to and its compounds (towards, into, onto), and past (whose idiosyncratic properties will be mentioned in due course), all the prepositions under consideration can designate the place of a tr with respect to a lm. Place is construed as a stative relation, which can persist without change for an unbounded period of time. With respect to their place meanings, the prepositions can be divided into two broad classes. (i) Simplex. The majority of the prepositions belong to this class. The place of the tr is construed as an internally unstructured point, whose location is characterised relative to the lm. The different prepositions locate the tr in different ways relative to the lm. In locates its tr at a place enclosed by a bounded area or volume, out of locates its tr at a point external to a bounded area or volume, and so on. Simplex prepositions may take as their tr not only entities which are "punctual" in a strict geometrical sense, they also permit spatially extended trs (the book on the table) and multiplex trs (the tr, that is, consists of a multiplicity of entities, e. g., the books under the table).4 The tr may also be a process. The process may likewise involve a simplex participant (He was sitting at the table) or a multiplex participant (They were sitting at the table). (ii) Multiplex: Multiplex prepositions include (a)round, along, through, throughout, as well as, in some of their senses, up, down, over and between. The place at which the tr is located is construed as a multiplicity of points which are occupied simultaneously by the tr. There are two possibilities. Either the tr is a spatially extended entity, whose component parts simultaneously occupy the points; or the tr is a multiplex entity, whose component members simultaneously occupy the points: (3)

a. There's a fence round the garden, (extended tr) b. There are trees round the garden, (multiplex tr)

Alternatively, the tr may be a process that is instantiated simultaneously at a multiplicity of points located relative to the lm: (4)

People were talking round the table.

Multiplex prepositions impose on their tr a conceptualisation consistent with the notion of a multipunctual place. While the following sentences could well describe the same scene, the scene is conceptualised in different ways:

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a. There's a row of trees by the river, (simplex place) b. There's a row of trees along the river, (multiplex place)

In (a), the row of trees is conceptualised as a spatially extended entity located at an internally unstructured point. In (b) the row of trees is located at a multiplex place, which is occupied simultaneously by each constituent member of the tr. Semantic oddity results if the tr cannot be conceptualised in a manner consistent with the requirements of the preposition: (6)

* There's a tree along the river. * There's a man sitting round the table.5

A number of multiplex prepositions impose a further requirement on the tr. Compare: (7)

a. There's a row of trees along the river. b. There's a road along the river.

(8)

a. There's a row of trees up the hill. b. There's a road up the hill.

In both sentences in (7), the tr of along occupies a multiplicity of points located relative to the length of the river. In both sentences the tr occupies a multiplex place. In (8 b) the tr likewise occupies a multiplex place; the road, that is, extends from the bottom of the hill, up the side of the hill, to its top. But in (8 a), the tr occupies a simplex place, located at the end of an imaginary path (see 3.5); the trees, that is, are located on the top of the hill. The reason for the difference between (8 a) and (8 b) lies with the nature of the tr. A road, like a row of trees, may be conceptualised as an extended, one-dimensional (1-D) entity. Alternatively, a road typically defines a potential path, which may be followed by an object moving in a certain direction. Other 1-D entities which define a potential path include footpaths, bridges, tunnels, and railway lines. Significantly, (8 a) can acquire a reading analogous to (8 b) through the addition of elements which convey the idea of directed motion along a path: (9)

a. There's a row of trees going up the hill. b. Follow that row of trees up the hill.

Like up, the prepositions down, through, over, and perhaps more marginally, past, can denote the multiplex place of an extended 1-D tr only on condition that the tr can define a potential path. (The asterisked

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sentences in (10) are, of course, acceptable on an end-point of a path reading, to be discussed in Section 3.5.) (10)

a. b. c. d.

There's There's There's There's

(a tunnel/*a vein of ore) through the mountain. (a way I* a row of houses) down the hill. (a footpath)*a fence) over the hill. (?a main road/*a row of trees) past our house.

Again, multiplex readings of the asterisked sentences become possible if some element in the sentence suggests the notion of directed motion: (11)

a. b. c. d.

There's There's There's There's

a vein of ore running through the mountain. a row of houses going down the hill. a fence going over the hill. a main road running past our house.

Between and over profile both simplex and multiplex relations. In (12), the tr occupies a simplex point relative to the lm entity(ies): (12)

a. There's a tree between the two houses b. There's lamp hanging over the table

(13)

a. There's a fence between the two houses b. He wore a pullover over his shirt

In (13) the tr simultaneously occupies a multitude of points located relative to the lm. 6 Note that the two uses of over in the (b) sentences correlate with other, idiosyncratic differences. In (12 b), the tr must be vertical to, but not in contact with the lm. In (13 b), the tr is in contact with the lm, and need not be vertical to it. 7

3.2. Multiplex prepositions: PLACE and PATH As a group, multiplex prepositions permit a range of semantic extensions which are not available for simplex prepositions. (i) As already noted — see (3) — the place denoted by a multiplex preposition may be occupied simultaneously, either by the parts of a single, extended tr, or by the components of a multiplex tr. This relation may be expressed informally as follows: (A) (with multiplex prepositions) Extended Tr Path of Tr Verbs of motion naturally impose a path reading on a following preposition: (14)

a. There are trees along the river, (place) b. We walked along the river, (path)

(15)

a. She wore a necklace round her neck. b. The Earth moves round the Sun.

See — which Jackendoff treats as a verb of motion — also imposes a path reading, as does look:9 (16)

a. There's a bridge across the harbour, (place) b. We can't see across the harbour, (path)

(17)

a. There's a road going up the hill. b. Look up the hill.

A path may be perfective or imperfective. A perfective path terminates upon the tr's arrival at a definite end-point. Perfectivity may be suggested by the use of the adverbials right, all the way, half way, etc. If you walk right round the block, your path terminates upon your arrival at your original point of departure, if you drive all the way through the tunnel the path terminates on your emergence from the tunnel, if you swim half way over the river the path terminates at a midpoint in the river. An imperfective path, in contrast, is of indeterminate extent. Drive through the tunnel, swim over the river, walk across the street, etc. could denote any arbitrary portion of a path. These prepositions can also suggest an iterative path. A jogger may run round {and round) the block an indefinite number of times. An iterative path is a special instance of an imperfective path. In their path senses, over and (a)round have undergone further specialisation, in that the lm with respect to which the path is characterised may be conceptualised as an obstacle that the tr must "get over" or "get round" in order to pursue its journey. Thus (18) may be interpreted in (at least) two ways. It can convey that the tr traces a roughly circularshaped path with respect to the base of the mountain; alternatively, the

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tr makes a semi-circular deviation in its passage from some unspecified starting point to some unspecified destination. (18)

We drove round the mountain.

(iii) A further source of polysemy with multiplex prepositions is the dimensional properties of the configuration of points profiled by the preposition. The points may form a linear, one-dimensional configuration, or they may be distributed in two- or three-dimensional space. (C) (with multiplex prepositions) 1-D Tr Goal of Tr A couple of examples: (26)

a. The lamp is above the table, (place) b. Hang the lamp above the table, (goal)

(27)

a. There's a fence around the garden. b. They erected a fence around the garden.

Not unexpectedly, place-goal polysemy can give rise to ambiguities. In (28 a) the jumping could be located at a place "on the wall"; alternatively, a place "on the wall" could be the goal of the jumping. (28)

a. He jumped on the wall, (place or goal) b. She fell in the water.

Of somewhat unclear status with regard to place-goal polysemy are off out (of) and from. On the one hand, these have been classified as prepositions of source (e.g., Dirven 1989), on the grounds that in sentences like those in (29), the lm entity characterises a place that the tr moves away from: (29)

a. We drove off the main road. b. Mandela came out of prison. c. John has just arrived from America.

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But it can also be argued that these sentences indicate the place that the tr comes to occupy, i. e., the prepositions can be legitimately classified as prepositions of goal. In (a), for example, the tr comes to occupy a place located "not on lm". Consistent with (D), o f f , out (of), and from can also be used merely to indicate place, i. e., a place not on lm, a place not in lm, or a place separated from lm.14 (30)

a. The motel is off the main road. b. Mandela is out of prison. c. John is from America.

Of the prepositions under consideration, to and its compounds (into, onto, and towards) fail to exhibit place-goal polysemy. As already noted, towards is an exclusively path preposition, which can denote neither place nor goal. To serves exclusively as a goal preposition, and conveys that a tr comes to be located at a lm. (31)

a. The children have gone to school. b. The children are now (at/*to) school.

Likewise into and onto convey that the tr comes to be in or on the lm. Given the place-goal polysemy of in and on, into and onto in (32 a) and (33 a) may be replaced by the monomorphemic prepositions in and on. (32)

a. I've put the money (into/in) my pocket. b. The money is now (inl*into) my pocket.

(33)

a. I've put the vase (onto/on) the ground. b. The vase is now (on/*onto) the ground.

In (32 a) the use of into rather than in emphasises the fact that the tr crosses the boundary of the container lm. But into can also convey that a tr penetrates more deeply into the lm, without necessarily first crossing a boundary; in this case, into is not replaceable by in. (34)

We drove deeper (into/*in) the forest.

While at is predominantly a place preposition, it has limited and specialised use as a preposition of goal. In this sense, at means, not that a tr comes to be located "at" a lm, but that a tr is aimed at, and/or forcefully propelled towards a lm. (35)

They threw stones at the police.

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3.4. Simplex prepositions: PLACE and PATH We have seen that multiplex prepositions can designate both a place and a path (3.2.). A small number of simplex prepositions — viz. by, behind, in front of, under and between — can likewise designate both a stative place relation and a path. In the latter case, the prepositions identify a place which a tr passes through or passes by on its trajectory from some unspecified place to another unspecified place. (E) Place of Tr Place on Path of Tr The following sentences are therefore three-ways ambiguous; in addition to the place and goal readings — cf. (25) — the prepositional phrases can also denote the path of the tr: (36)

a. The dog crept under the table. b. The mouse ran behind the curtain. c. The child walked in front of me.

Via is reserved exclusively to denote a place construed as a point on a path. Place as a point on a path is also the predominant meaning of past. Over and through can likewise designate a place on a path: (37)

a. b. c. d.

I went to Cape Town via Bloemfontein. We must have driven past his house. Throw the ball over the wall. He drove through a red light.

The following pairs of prepositions contrast with regard to their ability to designate a place as a point on a path: PLACE and PATH by in front of behind between over

PLACE only next to, beside at the front of at the back of in between above

Compare, for example, the following pairs of sentences (the asterisks denote unacceptability on the intended senses): (38)

a. We drove (byj*next to) the post office, (path) b. We live (by/next to) the post office, (place)

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(39)

a. The car drove right (in front off* at the front o f ) me. (path) b. They were playing (in front of/at the front o f ) the house, (place)

(40)

a. They ran (between)*in between) the two trees, (path) b. They were playing (between/in between) the two houses, (place)

(41)

a. He jumped (over/*above) the wall, (path) b. The lamp hangs (over/above) the table, (place)

In and out have specialised uses as path prepositions, exemplified in (42). (42)

a. The burglar came in the back door. b. The cat jumped out the window.

Here, the lm entities, i. e., the back door and the window, are construed as apertures in the perimeter of an enclosure, through which the tr enters or exits (cf. Hawkins 1986). The use of in and out exemplified in (42) is idiosyncratic to English, and some other Germanic languages (Taylor 1991). While one can say, in German, Die Katze ist aus dem Fenster gesprungen, in French the path function of the lm entity would have to be explicitly encoded by means of the path preposition par. (43)

Le chat a saute (par/*hors de) la fenetre.

In English, also, the path function of the lm may be made more explicit: (44)

a. The burglar came in by the back door. b. The cat jumped out through the window.

Here, by the back door and through the window designate a place on the path of the tr, while in and out are used intransitively, their lm being understood to be the 3-D enclosure in whose perimeter the back door and the window are located.

3.5. PLACE and GOAL as end-point of PATH Prepositions which denote the path of a tr can also locate a tr at a place construed as the end-point of a path that an observer would have to trace in order to reach the tr. (F) Path «-> Place construed as end-point of Path Via, by and towards do not undergo extension (F). Otherwise, as the following examples testify, (F) is extremely productive.

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(45)

a. John drove round the corner, (path) b. The post office is round the comer, (place as end-point of path)

(46)

a. John swam across the river. b. John lives across the river.

(47)

a. They walked under the bridge. b. The railway station is under the bridge.

(48)

a. The dog ran through the kitchen. b. The pantry is through the kitchen.

(49)

a. They ran down the road. b. Their house is down the road.

(50)

a. I swam over the river. b. They live over the river.

(51)

a. Drive past the police station. b. The school is past the police station.

When denoting place as end-point of a path, the prepositions typically have a strongly deictic component, i. e., they imply a path which has its origin at an observer, typically the speaker or hearer. (45 b), for example, conveys: "In order to get to the post office, you have to go round the corner (from here)." The origin of the imaginary path may be explicitly stated: (52)

The post office is round the corner from the police

station.

Most prepositions that denote a place can also denote a goal (section 3.3.). Not surprisingly, therefore, the end-point of a path may be presented either as the place of the tr, or the goal towards which the tr moves. (G) Path of Tr «-• Goal of Tr at end-point of Path If we take into account this second possibility, it will be apparent that the (a) sentences in (45)—(51) are subtly ambiguous. John swam across the river could designate the path which the tr traces as he swims. The sentence could focus also on the goal of the swimming, i. e., a place located "over the river". The expressions over here and over there exemplify an idiomatic extension of the end-point sense of the preposition. The expressions direct attention to a place which is in the perceptual field of both speaker and hearer, and which is construed as the end-point of an imaginary path

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whose origin is located at the addressee. The plane of the imaginary path must approximate to the horizontal (otherwise up here, down there, etc. are used.) The end-point sense also underlies the intransitive use of over and round in (46): (53)

He came round/over to see me.

Here, the lm of the understood to be the the tr's goal, i. e., the the tr traces a path intervening space.

preposition is sub-lexical; it would probably be space separating the initial location of the tr and home of the speaker. In order to reach this goal, of unspecified topology "round", or "over" the

3.6. PLACE as RESULT Closely related to, but distinct from, the end-point focus discussed in 3.5., is the resultative use of prepositions. In the former case, the preposition profiles the end-point of a potential path, in the second case, the preposition profiles a place relation which has resulted from the attainment of a goal. Compare: (54)

a. He lives over the hill. b. The horse is over the fence!

(54 a) locates the tr at a place construed as the end-point of an imaginary path that originates with an observer. The sentence, as we have seen, is strongly deictic; note also that in (a) the tr itself is not involved in motion along a path. (54 b) might be uttered during a commentary on a horserace. The sentence has no deictic component, and locates the tr with respect to a goal at the end-point of a path which the tr itself has traversed. (H) Goal of Tr We have been waiting since three ο 'clock [ — TEMPORAL EXTENSION]

(2) Wir warten seit drei Stunden => We have been waiting for hours

three

[ + T E M P O R A L EXTENSION]

The first sense of seit 'since' relates the beginning of a TEMPORAL EXTENSION with a POINT IN TIME, that is, it requires its second argument to refer to a point in time. In its second sense seit 'for' expresses the relation between a TEMPORALLY EXTENDED activity and the period of time in which this is temporally located, requiring its second argument to refer to a period of time. In examples (1) and (2) the preposition's meaning could be identified by means of the default meaning of the N P arguments. In the next example the selectional restrictions can only unify with the N P argument by considering specific background knowledge: (3) Seit der Wiederaufbauphase bilindustrie entwickelt.

nach dem Krieg hat sich die Automo-

Since the postwar reconstruction period the car industry has been developing. ?For the postwar reconstruction period ...3 In this example the noun Wiederaufbauphase clearly does not refer to a period of time, which would be assumed as its default, if a context like this were missing. Rather, by considering historical knowledge about the temporal location of events, Wiederaufbauphase is associated with an event located in the past and because of its termination is either projected to the beginning or ending point of this event or in case of vagueness of the starting point of the development of car industry within the postwar reconstruction period the whole period is projected to a point. This explains the use of since in English, which mirrors, that the preposition relates a period to a POINT IN TIME.

(2) Possible spatial relations holding between the related entities. In a specific spatial relation the conceptualization of the second argument

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may constrain the conceptualization of the first argument. The semantic inacceptability of ?the tree standing along the river results from the mismatch of river and tree in this relation: the preposition along forces river to be conceptualized as a linear PATH with an EDGE parallel to which a one-dimensional entity must be conceptually located. This is not possible with tree in contrast to its plural form trees in the trees standing along the river which we idealize to the one-dimensional line connecting the individual trees. (3) The relational concept of a preposition may constrain the indexical meaning of trajector and landmark. These are conditions on trajector and landmark which by an implied norm or normality or a contextually rendered orientation resolve vague relational concepts. It may, for example, depend on the proportion between trajector and landmark whether prepositions such as between, right of, in the corner are true or not. (4) Constraints on "metonymic" conceptualizations of objects. This is what Herskovits designates as geometric description functions (cf. Herskovits 1986: 57) which constrain our conceptualization of some real world entity in terms of different geometric idealizations. We may for instance conceptualize only the SURFACE of a cube or some EDGE of it as its salient part in a given context. The above given example ?the tree standing along the river shows, that the tranformation into different geometric entities is not arbitrary. The meaning of tree may not be extended to refer to a straight line, hence the semantic anomaly. Among constraints bearing on the discourse context Herskovits distinguishes the following pragmatic circumstances: (1) Constraints on the entity's location by the purpose of the relational expression. By uttering the sentence The children are going by bus a speaker will probably answer a question like How are the children getting there? In contrast to this the sentence The children are riding on the bus will answer a question like Where are the children now? (2) Constraints on highlighting some background element associated with some part of the spatial scene. Thus the sentence There is a gas station on the road to London will be uttered in a situation in which the event of someone travelling along the road is conceptualized, CONTIGUITY between the boundaries of the gas station and the road is thereby expressed. In contrast to this the sentence There is a gas station at the road to London only indicates the COINCIDENCE of the position of

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the gas station with that of the road, at instantiating the projection of the gas station to a ZERO-DIMENSIONAL point and that of the road to a ONE-DIMENSIONAL line respectively. This sentence will not necessarily be uttered with a travelling event in mind, that is the speaker is not mentally near to the spatial scene.

3.3. Lexicalization patterns It has always been a main concern of lexicology to draw the line between lexical homonymy, polysemy and lexical vagueness. This is the distinction between two types of differing usage patterns of a word: the context may instantiate the intended sense of a word in different ways. Modification may consist in highlighting different parts, aspects or attributes of the respective entity. This process is also called modulation, because the same entity is referred to in each case (cf. Cruse 1986; Taylor 1989: 124); different highlightings of an entity are not necessarily in disjunctive relationship. The context modulates lexically vague dispositions of one and the same sense in different ways. Modification as the selection or generation of one of several polysemous, disjunctively related senses of a lexical unit consists in the exclusion of the other senses, i.e., a polysemy pattern subsumes several mutually exclusive, but related senses, the use of which depends on the respective discourse situation. Theoretically the differentiation of the senses of a word depends on what one assumes to be part of lexical information, i. e., which properties one assumes to be inherently or intrinsically associated with entities in general. The distinction between inherent and non-inherent information is not a strict one in the sense of analytical truth conditions, as, in accordance with cognitive principles, it may be possible to override inherent properties in highly unusual situations. Pragmatically the distinction between what is lexically polysemous and what is lexically vague depends on the conditions imposed on the uses of words in possible discourse situations: certain properties may remain vague or may be modulated, certain properties have to be obligatorily selected both in encoding and decoding utterances. In the cognitive paradigm prepositions are generally considered ideal for the study of lexicalization patterns for the following reasons: (1) prepositions establish a nearly closed class of lexical units, the meaning of which is mentally represented in terms of highly abstract, i.e., simplified properties;

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(2) prepositions originally are spatial predicates and concrete space is better accessible than its abstract derivate; (3) according to the strong hypothesis we defend, all semantic extension at some time has originated from spatial senses and therefore the study of our conceptual means to structure concrete space at the same time supplies us with clues for our mental organization of semantic space in general (cf. Talmy 1983: 226); for instance the distinction into true lexical homonymy, polysemy and vagueness by the cognitive principles driving these meaning relations may be obtained in a relatively clear way with respect to the physical domain; (4) prepositions are highly polysemous with dense patterns of metonymy and metaphor. To a certain degree polysemy patterns are highly productive and the issue is currently being discussed in computational linguistics under the notions of economy and flexibility. This discussion raises the question of whether productivity is high enough to result in significant regularities, which may be accounted for in more general terms than in recurrent identical descriptions, by which the lexicon becomes highly redundant. Different options of representing and processing polysemy patterns are suggested: The schema model claims that lexical information should be as general as possible in abstracting from different contextually instantiated sense specializations. Sowa (1984); Bierwisch — Lang (1989); and Habel — Herweg — Rehkämper (1989) defend different versions of this idea. It is common to all versions of the schema model that a strict distinction is made between linguistic-semantic knowledge encoded in the lexicon and conceptual knowledge induced by the context. The prototype model assumes different polysemes of a word to establish a family resemblance structure, which may be graded in that there is a typical, most representative sense of a word, to which continuously less typical senses are related; Barsalou (1992) assumes that typicality derives from frequency of instantiation. Boguraev and Pustejovsky (1990) assume logical metonymy relations between senses and logically derive metonymies and metaphors from lexically encoded defaults; in the absence of contextual restrictions this may be taken to establish the typical, most representative sense. The commonsense model proceeds from Putnam's (1975) idea of stereotypical knowledge about words. Dahlgren (1988), Hobbs (Hobbs et al. 1987) are defendants of this model. They claim to represent the average everyday knowledge of speakers. In the same way as prototpye semantics they consider semantics to be encyclopedic. A major concern of naive

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semantics is the relation between knowledge about typical properties in specific domains and kind types, which establish very basic classificatory knowledge. Dahlgren assumes a single entry for each words sense, as the typicality patterns of word meanings are domain-dependent, and kind types constrain these in specific ways for each sense. The sense generation model of situation semantics claims different senses of a word to be anchored in real situations and to be generated nonmonotonically in accordance with the respective discourse situation (cf. Franks - Braisby 1990; Myers - Franks - Braisby 1989). The default meaning corresponds to the contextfree lexicalized meaning (cf. Myers 1989: 8). In principle, there is no constraint on defeating a property associated with a word. Cognitive Grammar refrains from accepting any of these suggestions as an exclusive model of language. It rather seems that several types of lexical abstraction have to be considered by a model of the mental lexicon. Both schemata and prototypes are economical mental strategies for abstracting from the vast amount of information offered by reality. The two strategies work in close interrelation. For instance, the exclusive use of schemata has often proved to be insufficient, as schemata are too coarse and not flexible enough for drawing inferences. The reason for this is that similarity relations between polysemes are not necessarily transitive and that one schematic abstraction does not necessarily generalize over all senses of a polysemy pattern of a word. Cognitive Grammarians also emphasize that metonymy relations are not completely regular. Lehrer (1990: 240) concludes on an empirical basis that, although there are many miniregularities, only a few rules are without any exceptions. This implies that the lexicon must also contain redundant information. Although these irregularities may be accounted for by nonmonotonic procedures, the latter are constrained by cognitive priciples, that is, contrary to situation semantics we hold that in a specific pragmatic environment certain semantic properties may not be defeated. It follows that the relations between polysemes determine the degree of lexical redundancy, which has to be somewhere between a pure enumeration of the senses of a word and the association of a word with a regular polysemy pattern as a semantic type. With prepositions the interaction between different types of lexical abstraction is assumed to be the following: a preposition may express a family of senses, the relations between which consist in a generalized schema and an ideal. In contrast to a prototype, which represents the best exemplar of a category by characterizing it in fine detail, an ideal establishes an idealization of typical properties, in terms of a reduction

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or simplification. Ideals are repesented in terms of relatively simple structures, compared to our bodily experience they are derived from. As such, Lakoff calls them image schemata (cf. Lakoff 1987: 267). It is common to all types of lexical abstraction that all senses may be related to it, either by way of specializing some abstract schema, or by different transformations, which relate the ideal meaning to all its metonymical and metaphorical derivations radiating from it in the way modelled by Dirven in this volume. One purpose of modelling polysemy in this way is the interpretation of novel uses (cf. Herskovits 1986: 40). For instance, the preposition in has one ideal meaning, it expresses the relation of INCLUSION, requiring its second argument to refer to a COMPLETELY BOUNDED THREE-DIMENSIONAL entity. Around this, all derived senses center by exploiting and transforming the ideal meaning in different ways. Whereas the PP the fly in the box expresses an ideal inclusion, in the PP Big Ben in London the preposition in is semantically related to the prototypical sense relation: London is idealized to a TWO-DIMENSIONAL AREA and thus can only provide a PARTIAL ENCLOSURE. Yet the relation of INCLUSION holds, although in a less typical way. In the same way as a prototype the ideal meaning does not establish a common core of the category. This may be illustrated with the preposition on. With the lexical pattern of this preposition the notion of a family of senses, which Wittgenstein has set against the core meaning notion, becomes obvious: in its ideal meaning the preposition on seems to express the idea of SUPPORT which implies CONTIGUITY of the parts of the scene related so that the larger part of the scene provides its SURFACE on which the other part is located and thus supported. This ideal meaning is expressed by a vase on the table. There is, however, a meaning of on which lacks the idea of SUPPORT, only implying CONTIGUITY. This concept may be considered to be derived from the ideal meaning. Again this derived concept is exploited in several different ways. Table 1 illustrates the concept of CONTIGUITY, in which the senses are given in order of decreasing typicality (cf. Herskovits 1986: 40 ff.).

Table 1. The concept of CONTIGUITY EXAMPLE

CATEGORY

Two physically extended entities in

CONTIGUITY

relation

a lock on the forehead

Physically extended entity projected to be C O N T I G U O U S with the E D G E of a T W O - D I M E N S I O N A L L Y extended entity

a house on the park

Visually apparent

shadows on the wall

CONTIGUITY

between two entities pro-

j e c t e d t o TWO-DIMENSIONAL AREAS

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4. What do prepositions express? Within the framework of Cognitive Grammar an old assumption of formal semantics has undergone a revival: prepositions are considered as two- or three-place predicates, because they express a relation between two or three speech participants. Hence Langacker classifies prepositions as relational expressions, because they express how the conceptualizer configurates the parts which constitute a spatial scene with respect to each other. Thus prepositions express how the speaker establishes a cognitive link between two or three parts of a spatial scene. This cognitive relation is profiled in accordance with cognitive principles operating on the conventions associated with the respective parts of a spatial scene in the particular cognitive domain. These conventions yield one part as the new part which is standing out as the foreground from an already known part establishing the background, which functions as a location. In this partitioning the foregrounded figure receives prominence, because in a particular cognitive domain it is mobile or more movable in relation to its location which usually is more stationary. Langacker (cf. e.g., 1987: 217 ff.) has introduced the terms of trajector and landmark for these old gestalt-psychological distinctions in order to mark their linguistic function. The foreground is called the trajector and the background the landmark. Both are constrained with respect to the conceptualizations they can undergo (cf. Hawkins this volume). The landmark functions as a reference point with respect to which the trajector's motion, location or orientation is specified. In European languages this location is typically designated by a nounphrase in object position. The trajector may be either an entity designated by a subject N P or a relation, which is typically designated by a verb of motion, position or direction in the spatial domain: (4) (5)

The cat is on the mat. The cat is playing on the mat.

Sentence (4) expresses the spatial relation between two entities, between the cat as the trajector, and the mat as the landmark. Sentence (5) relates the cat's activity of playing, the trajector, to the mat's location, the landmark. These examples show that the conceptual partitioning of the real spatial scene is asymmetrical. We can say that under normal pragmatic conditions the cat in sentence (4) is the more movable entity, as it is MOBILE. Therefore it is focussed as standing out in the profiled relation and hence functions

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as the trajector. In sentence (5) the same holds for the cat's activity of playing. In both sentences the mat as the IMMOBILE entity is less movable and therefore the less prominent backgrounded entity with respect to which the trajector is located. The asymmetrical relation between trajector and landmark becomes most obvious if we try to turn the relationship around as in the following examples: (6) (60

The cat is on the mat. ?The mat is under the cat.

(7) (70

The lid is on the teapot. ?The teapot is under the lid.

(8) (80

Marseille lies on the Mediterranean. *The Mediterranean lies on Marseille.

A speaker would only utter sentence (6'), if, contrary to the normal situation, his focus of attention did not rest on his cat, but on the correct position of the mat. (7') would only be acceptable in an extremely unusual situation in which normal pragmatic conditions do not hold. The normal function of the lid is to cover the teapot, which would be expressed by the preposition on. Without any context from which these conditions may be inferred a normal hearer's assumptions are violated by this sentence. For sentence (8') there seem to be no exceptional conditions at all under which it would be semantically acceptable. Although the Mediterranean may doubtlessly be conceived as lying between Europe and Africa, its extension does not allow for the conception that it lies on Marseille, since the use of the preposition on has to follow the condition that the trajector is smaller than the landmark. Prepositions may basically express two complementary relations: COINCIDENCE and SEPARATION (cf. Langacker 1987: 223 ff.; see also Hawkins, this volume). That is, they express whether some part of the space which trajector and landmark occupy is the same or whether they occupy different spatially discontinuous places. Set-theoretically these basic relations may be expressed in the following way: COINCIDENCE: PLACE ( T R ) SEPARATION: PLACE ( T R ) η

C

PLACE ( L M )

PLACE ( L M ) =

0

These basic relations are logically disjunct, that is, only one of both may apply. They do not depend on the conventional setting of the environment, although they are related to it insofar as the two basic relations are assumed to be generalizations over all language-specific ones. That

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is, the basic relations hold universally across domains and utterance situations, while the language-specific specilizations centre around them. Thus the basic relations constitute the tertium comparationis which may be used for relating the semantic representations of different languages.

5.

Schematization as the process of conceptualizing spatial relations

5.1. The constitution of schematization The main point we want to illustrate with the translation of prepositions is how certain circumstances and purposes of an utterance instantiate important principles of conceptualization. We will particularly consider pragmatic factors resulting from the specific environment of the language user and the utterance situation; we will investigate how these pragmatic factors determine the relevance, salience and typicality of the entities constituting the conceived situation. Moreover, we consider these pragmatic factors, which depend on the culture-specific environment of the language user, to be conceptual motivations of meaning which are perceptually driven, i.e., abstract mental space configurations have originated from physical space configurations. Being conceptually mediated, reality is not expressed directly by language. Rather, language expresses how speakers have mentally implemented the common experience of the specific environment they live in. This implies that the semantic distinctions conforming to our linguistic utterances about our spatial environment do not agree with the real physical extension of the configurated parts, but with their conceptual SCHEMATIZATION. SCHEMATIZATION is the fundamental principle underlying the linguistic expressions of spatial configurations (cf. Talmy 1983: 225): it is the selection of those spatial properties of a scene which in a given domain and situation are essential to how we view it as a whole, while the remaining properties, being non-essential, do not participate in this process. This selection process relies predominantly on geometrical and topological properties. It operates on two preconditions: While prepositions as relational predications are highly polysemous with respect to the possible relations they can express, the entities which they relate are

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lexically vague with respect to the possible spatial properties they may adopt in the respective configurations. Each schematization process results in the conceptualization of a schematization type. We will assume that there exists a limited set of schematization types; these include all and only the properties essential for us in the conceptualization of space. The process of schematization may be characterized in terms of the following complementary strategies (cf. Talmy 1983: 225): (1)

IDEALIZATION

This is the process by which we make entities which in physical reality are highly complex and variegated conform to some associated mental scheme. This process is comparable to the process of prototyping our environment (cf. Rosch 1978) with the difference that, whereas prototypes, as best exemplars of a category, may be mentally represented in fine detail, the representation of ideal meanings is reduced to very abstract geometrical and topological properties. A typical case of idealization is the projection of a three-dimensionally extended object to a one-dimensional line when its designating noun precedes prepositions such as English along as in the trees along the river. Here the trees, which in reality are dicontinuously located, are idealized to a continuously extending one-dimensional line, as required by the ideal meaning relation expressed by along. Thus the boundary conditions of an entity, which constitute the enclosure, may be idealized by what Hottenroth (in this volume) calls Gestaltschließung, so that we conceive of a COMPLETE ENCLOSURE of what in reality is partially bounded, as we do with a bowl, if used in the PP the fruit in the bowl, when some of the fruit is ranging over its edge. Another case of idealizing of the boundary conditions may occur by bounding of a MASS, as with SCALE entities referred to in the idioms within the reach of, at the height of, where the SCALE noun functions as a classifier of some background, by which a certain amount of the per se unbounded MASS is particularized. The same holds for MENTAL or SEMIOTIC CONTAINER entities, which per se are U N B O U N D E D STATES or ACTIVITIES in the temporal domain. Here volitional action or time is presumed as delimiting background for individuation, as in in the conviction/hope that, in the style of the 1950s.4 With raisins in the dough, a nail in the wood, a red thread in the fabric, the delimiting background is the presumed function of the per se unbounded MASS; this function only operates on an individuated part. Moreover, against this background knowledge the individuation of the

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may be easily achieved, by mentally referring to a lexical substitution, such as raisins in the cake, a nail in the board, a red thread in the cloth; in analogy to the COUNT nouns cake, board, cloth reference to an individual part of dough, wood, fabric occurs. In its extreme form, idealization can be compared to spatial relations defined within the mathematical field of topology (cf. Talmy 1983: 261 f.). What the ideal meaning of the preposition requires is satisfied by drifting, adapting, projecting or completing the gestalt of the trajector in dependence of the landmark. For instance the shape and magnitide of the landmark may be irrelevant. What counts is the geometric relation. However, we have seen that idealization can only be achieved within certain limits. An example was the preposition along. It is not only its trajector which must fulfil certain standards, but also its landmark. The latter may not go under a certain treshold of extension as in ?the items along the left margin. So along seems to be inherently restricted with respect to magnitude on behalf of its etymological derivation; originally it denoted a long extension (cf. The Shorter Oxford English Dictionary). MASS

(2)

ABSTRACTION

Abstraction is complementary to the process of idealization and consists in focussing on what is essential in the speaker's view of the spatial scene whilst ignoring the non-essential properties. Thus the idealized relation expressed by the PP the trees along the river can only be interpreted or linguistically encoded, if one abstracts from all details constituting the real spatial extension of the trees, which would prohibit the idealization to a line. The strategies of schematization are driven by several related cognitive principles which by means of specializing, highlighting, excluding or prefering certain parts and aspects of a scene instantiate those spatial properties which are essential in the specific situation (cf. Herskovits 1986: 73 ff.): — The salience principle results in the metonymic relations holding between the parts of an entity or its projections which become functionally salient in alternative spatial configurations. For instance in the conceptualization of the sentence the children are riding on the bus it is not the whole bus, which is THREE-DIMENSIONAL, that is salient, but only its TWODIMENSIONAL floor. This becomes selected by the prototypical functional relation assumed between the landmark entity and the action of riding, which implies the basic location of the trajector with respect to the

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landmark: in this case the relation of COINCIDENCE holds; the trajector is located within the space occupied by the landmark. In this schematization of an entity's salient shape only some of its spatial properties are focussed on, while the rest is neglected, as its function is irrelevant within this configuration. The latter holds, e.g., for the vertical dimension, which might well become salient if the function of the bus as a double-decker were in the foreground. The INTRINSIC ORIENTATION of bus is also irrelevant in this configuration, which one might well move into the foreground in a configuration designated by the bus is going towards London. By uttering the sentence The children are riding on the bus the original native speaker's intention was to refer to a bus established by a platform, which by its normal function of carrying passengers rendered its SURFACE to be its salient shape. This can be explained etymologically: originally busses were platforms in England, and while the concept may not be vivid anymore, because busses have become closed objects in England too, the expression has been kept and relates the action of riding to large vehicles in general, as in ride on a plane, ride on a train, ride on a ship. Another explanation is that the concept of a SURFACE is enforced by the verb, the original and typical meaning of which is that of riding on top of an animal. From this use of the verb the use of passengers being carried by an artificial means of transport has been derived. Thus by the salience principle the cross-linguistic relation of COINCIDENCE, which has been assumed as the prototypical functional relation, is specialized by the relation of SUPPORT in English. — The typicality principle implies the designation of a spatial configuration dependent on the typical relations existing between the entities in normal situations. In our example The children are riding on the bus the discourse situation which is about transport in traffic makes the hearer assume that the default relation corresponding to the typical situation holds, in which the children are located inside of the bus and not on top of it. Likewise the typicality principle constrains the possible figure-ground reversals, and relations as expressed by the following sentence are not schematized: ?The bus is under the children. The typicality principle also makes possible the interpretation of an entity's INTRINSIC orientation as the default case if information to the contrary is lacking. Some entities possess an intrinsic spatial orientation in analogy to the normal orientation of the human body within the gravitational system. For instance human bodies, churches and other

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buildings have an intrinsic frontal orientation and a prominent vertical axis, which the human conceptualizer associates with these objects independently of the surrounding objects and the dimensional grid of the earth, unless the normal position of a human being or church is violated. In this case contextual orientation may override the intrinsic one. — The tolerance principle controls the permitted degree of flexibility in the use of prepositions, i.e., it guarantees that the spatial configuration designated by the preposition is within the range of permitted deviations from the ideal meaning. This is done by constraining the pragmatic conditions under which expressions chosen by the speaker are adequate. The tolerance principle may, for instance, control whether the idealization of trajector and landmark to a point, as it corresponds to the use of the preposition at, is adequate with respect to the specific position of the speaker. The tolerance principle also controls the specific range of PLASTICITY of a relation, PLASTICITY is the general possibility of stretching the boundaries of a spatial schematization type with respect to the range of possible scenes conforming to it. Thus, in dependence of the gestalt, function and magnitude of the related objects in front of may be used even if the located entity is not exactly in front of but also slightly beside another entity. The same holds for the corresponding relation of nearness in the vertical dimension expressed by the preposition over: (9)

?A bird is flying over the house.

(10)

A plane is just flying over the house.

The relations are illustrated in Figure 1. >VN

Figure 1. The plasticity ο the relation expressed by over

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The relation of nearness may only be schematized in dependence of the magnitude of the trajector. Although moving in the same distance from the house as the plane, the bird is too small — it would normally not be perceivable — so that the relation of vertical nearness cannot be stretched as far as to include the bird's position. The same relation, however, may be stretched, to include the plane as the trajector in the respective utterance situation. The significance of the relation as to this configuration can be explained by the plane's magnitude and its perceivable noise. This sentence might for instance be uttered, when the noise of the plane disturbs a telephone conversation. — The relevance principle implies that dependent on the communicative goals the speaker can choose semantically alternate prepositions for one and the same spatial configuration. The communicative goals depend on the speaker's viewpoint, which in turn depends on the utterance situation. The following example may illustrate this principle. Imagine a scene in which Mary is inside the building of a supermarket. If the speaker were far away from the scene he would designate Mary's location by saying Mary is at the supermarket, thus expressing that he idealizes the threedimensional extension of the supermarket to a zero-dimensional point which is associated with the supermarket as an INSTITUTION: by using the preposition at he asserts that Mary's position coincides with that of the supermarket. If the speaker, however, were himself on the premises of the supermarket, he would rather designate Mary's location by the sentence Mary is in the supermarket, thus referring to the three-dimensional extension of the building of the supermarket, which in this relation functions as an ENCLOSURE. This shows that different utterance situations result in disjoint conceptualizations and hence different expressions of the same physical scene. The different spatial conceptualizations of the landmark rest on different implicatures about the rest of the scene which sometimes are not overtly expressed (cf. Talmy 1983: 230). Depending on which background the speaker associates with the scene, he schematizes the spatial configuration into different relations, by selecting different aspects to have communicative relevance. Thus by means of different contextual requirements these principles drive the process of schematizing spatial scenes: the typical function assumed for an entity in a specific configuration enforces its salient shape and at the same time excludes all other shapes. Speaker and hearer make default assumptions about the normal relations between the parts of a

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scene. The indexical meaning of the preposition is controlled by the range of possible proportions between the entities determined by some background scale. The communicative relevance determines which relation is schematized for a specific spatial configuration.

5.2. Schematization and the lexicon Although we associate many individual concrete entities with a canonical representation of the shape which belongs to the whole entity, there are many parts of our environment with which we do not intuitively associate a canonical shape representation. Take the example of a meadow: it is exclusively a matter of the speaker's viewpoint whether a meadow functions as a two-dimensional area the length of the grass and other plants being irrelevant, or as a three-dimensional layer of earth, possibly with trees, air and grass. Yet, this semantic distinction is not part of the denotation of meadow, but is a matter of contextual modulation. This can be shown by using one and the same token in different meaning relations as in the following example, which does not turn out to be semantically anomalous: (11)

She walked through the meadow on which long grass was growing.

In this sentence the meadow is semantically constrained in two different ways: the preposition through enforces a three-dimensional view on meadow, while the modifying relative clause, which is attached by the preposition on, makes us view the meadow as a two-dimensional area covered with grass. As both senses can be activated without any zeugmatic effect, meadow is lexically vague with respect to its dimensional properties. The same holds for cupboard in the flowers on top of the empty cupboard, or for river in the ship on the river which I walk along. This confirms the validity of the principles of schematization: it is the context which specializes an entity's spatial properties: salience, indexicality and relevance have been shown to be contexutally established. As to our ultimate goal of N L P system design it seems that lexical information either guarantees the potential of schematization in being maximally general and inclusive, that it excludes impossible idealizations of an entity, or that it provides the default assumption about an entity or situation. The context then has the function of specializing the generalized lexical information or of relating less typical meanings to the defaults by regular metonymy rules. For instance, the speaker's distri-

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bution of attention, which partitions a scene into foregrounded trajector and backgrounded landmark is lexically constrained by assigning per default typical functions to an entity, as for instance VEHICLE OF TRANSPORT FOR HUMAN BEINGS as the typical function of bus, which as the landmark unifies with the verb ride, which is assigned as one of its senses t h e ACTION BY WHICH HUMAN BEINGS ARE TRANSPORTED IN A VEHICLE. T h e

noun child is inherently H U M A N , which means that this lexical property may not be contextually defeated (these definitions are given in the Oxford Advanced Learner's Dictionary; they have been slightly paraphrased). The assumption of the lexically encoded typical function of the bus also enforces its salient shape and the verb, by its lexically encoded senses provides the discourse situation, which in turn determines the relevant relation of COINCIDENCE, specializing as support in English, to be schematized. What is also lexically significant is the intrinsic orientation of entities, which may only be overridden by contextually violating circumstances which are highly unusual. In terms of types of knowledge and their processing we assume the following lexical encodings: — — — —

the spatial disposition of an entity, such as + its typical function its inherent vz. intrinsic properties constraints on idealization

SHAPE, + DIMENSION

By these properties we can unify those component parts of a given configuration which are in conformity with each other. Thereby a specific schematization is achieved by recursive specialization of the spatial dispositions. In the case of defeating conditions, which contrast with the default assumptions encoded in the lexicon, unification on the basis of the lexically encoded defaults fails. It is by general pragmatic principles, which generalize over unusual situations, that overriding of some of the lexical properties is attempted in dependence of those properties which have to be kept constant.

5.3. The process of schematization and its translation The process of schematization results in the asymmetrical relation between trajector and landmark. The relational concept — the trajector's spatial disposition — is designated by the preposition.

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As indicated in the last section the trajector's site, path or orientation are the result of a complex interaction between the parts of the spatial scene on which the speaker's attention rests. In this section we want to model this complex interaction by applying the strategies and principles which constitute the process of schematization to our example sentence The children are riding on the bus, which translates into German Die Kinder fahren im Bus. On the basis of this constitution we want to model the mutual development of the meaning of the assumed parts of the scene: the parts condition each other by relating information from different semantic resources which control their typicality, salience and relevance. We have chosen this example, as the preposition's meaning becomes relevant in the translation into German. Whereas in German busses provide CONTAINERS for passengers, in English a passenger is conceptually located on the SURFACE of the bus. Our ultimate aim to model the process of translation with this sentence divides into the following steps: (1) to profile the language-specific relation of the source language in analysis; (2) to abstract from the language-specific relation a relation which we assume to be constant across languages; (3) to hand this abstract relation together with the trajector-landmark configuration and the discourse situation over to the target language and to transfer at the same time the lexical units which are semantically constrained by the preposition; (4) to unify the transferred relation with the language-specific meaning of the lexical units taking part in the relation and thereby to specialize the abstract relation into the specific one of the target language; (5) to generate the target language expression out of the relation obtained in (4). The model to be achieved via these subgoals should be the precondition for its implementation in a translation system. In Figure 2 we represent how these goals are achieved in the process of translating one schematization type into another. We start with the source language sentence as input, the language-specific relation of which is decoded first according to the principles of schematization, which become active in the assumed situation. The analysis of the English input sentence starts with the lexically encoded information: (1) The lexical unit child is associated with the semantic categories (lexsemcat) HUMAN and MOBILE; the first category is inherent, which means

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that, according to cognitive constraints, this information may not be defeated. (2) The lexical unit ride denotes the action by which human beings are transported by something or someone; so human beings are required as the subject in the selectional restrictions of the verb and the means of transport as the object. (3) The preposition on predicates the relation of SUPPORT implying CONTIGUITY.

(4) The noun bus denotes a movable, but immobile entity; it typically refers to its function as a LARGE VEHICLE for HUMANS; typical properties establish the default, which applies in typical situations; properties applying in other situations may be derived. For instance another lexical property of bus is its intrinsic front, from which all localizations determined by it may be derived. We assume the schematization process to operate on this lexical information in the following way: (5) The lexical information of the verb — TRANSPORT of someone by someone or something — is assumed to provide the discourse situation. (6) The speaker's distribution of attention is constrained syntactically and semantically; the children as HUMANS and MOBILE entities are in subject position and hence interpreted as the trajector to be localized with respect to the bus, which as IMMOBILE ARTEFACT is in object position and is interpreted as the landmark. (7) On the basis of the lexically encoded typical function of the bus and in dependence of the discourse situation, the shape of a SURFACE which is salient and the floor as the part which is relevant in this situation are idealized. (8) The subject is unified with the verb's selectional restrictions. (9) The verb is unified with the bus' idealized two-dimensional floor as SURFACE and the relational meaning of SUPPORT is generated, which unifies with the ideal meaning of on. SUPPORT is defined as that idealized relation in which the trajector is contiguous with a LINE or SURFACE of the landmark and the landmark supports the trajector, formally represented as: CONTIGUOUS ( L M , T R ) & SUPPORT (SURFACE ( L M ) ,

TR)

(10) The English concept of SUPPORT is subsumed by the relation of COINCIDENCE, which is the cross-language relation (C) to be transferred to the target language. The discourse situation is transferred as part of

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the sentence meaning. The trajector-landmark configuration is also transferred by default. In Figure 2 the transfer of these "interlingually constant" properties is represented by a broken line. (11) By lexical transfer all "referential" lexical units are transferred into the target language by unifying the semantic features: child translates into Kind, ride into fahren; bus into Bus. Now the schematization process operates on the language-specific lexical and compositional rules as well as on the transferred information in order to generate the correct target language expression: (12) In contrast to English in German the salient shape of Bus idealized from its prototypical function and the discourse situation provided by the verb is CONTAINER and the surroundings of the whole entity are relevant in this situation. (13) The transferred COINCIDENCE relation is unified with the CONTAINER concept of bus to specialize as the INCLUSION relation, which unifies with the ideal meaning of the lexical unit in. By outlining the schematization process with the interpretation of the English source sentence it should have become clear that by idealizing the salient shape of the landmark entity to pertain to its relevant part, all other schematizations are excluded from being possible. Another schematization, though unusual, would, for instance, be that in which the children are sitting on top of the bus; this relation would not unify with the relevant part. Yet another schematization would be that in which the children are conceptualized as being enclosed by the bus; this would be the relation of inclusion, which again would unify neither with the salient shape nor with the relevant part of bus in this situation, but rather with the shape of a taxi, of which all enclosing sides become salient to establish a CONTAINER, and in is used, as in the customer in the taxi.

6. Spatial metaphor In German spatial metaphor is most frequently realized with prepositions (cf. Wunderlich 1985: 76). Thus prepositional metaphor may be taken to offer a model for metaphorical processes in general. The basic idea is that physical entities are directly meaningful as the basic building-blocks of our life and of any conceptualization related to it. The process of

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profiling a relation between trajector and landmark takes place with the perception of concrete spatial scenes and with the conception of abstract scenes, which in analogy to the model of concrete space are schematized in mental space. That is, we assume abstract mental space configurations in the domain of time, causation and reason, circumstance, manner, means etc. (see Dirven in this volume) to be semantic extensions of spatial configurations relying on physical properties. This implies the hypothesis that the configurations expressed by prepositions always rely on physical properties either directly or by meaning extension of one or more physical properties into some abstract domain. Such an extension may result from metonymy, metaphor or other function as they are given in detail, e. g., by Lipka (1988); Allan (1981); Nunberg (1978); Norrick (1981); Dirven (in this volume). Applications in Computational Linguistics are reported, e.g., in Wilensky (1990). Among the most frequently occurring meaning extensions in abstract text types are INSTITUTIONS and SEMIOTIC contents or INSTRUMENTS: by semantic extension CONCRETE objects such as buildings and manifestitations of SEMIOTIC contents function, among others, as CONTAINERS in an ABSTRACT sense when configurating as a landmark in a relation expressed by the preposition in. Metonymy and metaphor are productive processes operating on the lexicon. It is central to the theory of Cognitive Grammar that these processes are treated only as one case and thus in accordance with the general phenomenon of semantic extension resulting in polysemy. Semantic extension to new literal meanings and to metaphorical meanings only differs in the degree of semantic distance between old and new sense. If a certain semantic distance is exceeded, especially if a domain shift occurs, the semantic extension is considered as metaphorical. It is the characteristic trait of metonymic and metaphorical extensions to denote semantic domains which are distinct from the domain of the respective source sense. The transfer of meaning from one domain to another is most productive with spatial expressions because of their expressive force: our most basic experience is spatial, therefore spatial expressions are ideal for improving our experience and imagination of less basic information. Prepositions are one example of meaning extension from concrete into increasingly abstract domains. The productiveness of this process clearly shows its linguistic motivation and communicative function: metaphors are created in order to understand one thing in terms of another. The less-known is understood and communicated in terms of the well-known. In particular, the creation of metaphors involves a

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mapping between clearly distinct domains. This mapping is effected by creating an analogy between the structure of source and target domain. In analogy to the schematization of concrete entities we schematize abstract entities in the domain of human behaviour and conventions. We use the structure of our spatial knowledge about entities in physical source domains for the conceptualization of entities in abstract target domains (cf. Lakoff — Johnson 1980: 81). The reason is the knowledge transfer from concrete source domains into abstract target domains in order to interpret the latter in terms of the former. Lakoff and Johnson (1980) see the essential motivation for the creation of metaphors in the fact that we understand abstract things which seem difficult for us to interpret in terms of concrete things for which we have simple, obvious and perceivable interpretations. "... we typically conceptualize the nonphysical in terms of the physical — that is we conceptualize the less clearly delineated in terms of the more clearly delineated" (Lakoff — Johnson 1987: 59). Thus we can draw inferences which we could not draw on a literal basis (cf. Hobbs 1983). This means that metaphorical processes are constitutive of our understanding of the world and that we have to interpret them in this respect. Metaphorical extensions are not totally unpredictable (cf. Lakoff — Johnson 1980: 30 ff.). There exist well-established regular metaphorical mapping relations by which concrete schematization types of the spatial source domain transfer some of their properties to abstract target domains (cf. Lakoff — Johnson 1980: 30). This is defined as "limited inheritance between concepts" by Martin (1988: 397) rendered by a certain "view relation". "An adequate account of metaphor must allow that the primary or original meanings of words remain active in their metaphorical setting" (Davidson 1978: 34). The relations of analogy, similarity and coincidence and distance, which constitute the metaphorical mapping relations between different knowledge domains, have to be specified so that the interpretation of new metaphors becomes possible. In terms of a computationally viable interpretation of new metaphors this would raise the following tasks: — Our knowledge about specific source domains has to be organized in gestalt structures as proposed by Lakoff — Johnson (1980), which represent types of experience about situations. — The adaptation of these "well-understood" structures to the respective "ill-structured" (Carbonell 1980: 424) target domains into which knowledge transfer has taken place, the deduction of the conventionalized associations and their resulting use in the target domain, the definition in terms of knowledge transferring functions.

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— The generation of novel metaphorical senses by letting the knowledge transferring functions operate on the gestalt structure of the source domain. The investigation of the relations holding between source and target domain also implies the question as to which properties a metaphorical expression provides that a literal expression lacks (cf. Carbonell 1980: 424). The degree of regularity pertaining to the patterns of metaphorical extension is vital for a dynamic interpretation of non-lexicalized metaphors in a computational environment. Dirven's paper in this volume illustrates that, though different prepositions show up meanings in the same domains to an astonishingly high degree, there are also semantic gaps, that is certain prepositions do not fully exhaust the general semantic pattern. This shows that predictability is possible, though within certain limits. The conventionalized associations existing between source and target domain have to be known for this purpose; these are exactly the properties which become salient in the schematization types. It is our assumption that a semantic representation which attempts to guarantee a successful synthesis and to have explanatory value at the same time, cannot evade the generalization over the semantic structure of source and target concept. Still, a major question raises the problem of efficiency as to the adaptation of the human process of knowledge transfer to the computational process of knowledge transfer. Following our basic hypothesis about perceptually driven conceptualization it seems reasonable to proceed from an analysis of the concrete spatial relations of the source domain, both because the perceivable properties of physical space are better accessible to linguistic analysis (cf. Lakoff — Johnson 1980: 56), and because as directly meaningful properties they can be considered as axioms. The abstract schematization types of the target domains may then be derived from the source types in a second step. Let us illustrate and thus corroborate this procedure with a concrete example. In the following examples the NPs refer to the same concrete source domain: (12)

Die Frau im Mantel, die Frau im roten Kleid 'the woman in a coat, the woman in a red dress'

The interpretations of these expressions result in the following schematization type, which implies the semantic categories by which the prepositional predicate constrains trajector and landmark:

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mod cat = pp

predicate cat = prep PLACE = CONTAINS (TR, LM)

trajector

landmark

cat = np

cat = np

ABSTRACTION = CONCRETE

ABSTRACTION = CONCRETE

IDEALIZATION = 3 - D BOUNDEDNESS = COUNT

IDEALIZATION =

3-D

BOUNDEDNESS = COUNT SHAPE = {ENCLOSURE = ENVELOPE}

Figure 3. Schematization type of the woman in a coat

The enveloping property of the landmark implies how something is represented physically. This is typically transferred to semiotic arguments as in the following examples: (13)

das Programm in Prolog 'the programme in prologue'

(14)

die Implementierung in ALEP 'the implementation in ALEP'

(15)

Der Brief ist in Kursivschrift geschrieben. 'The letter is written in italics.'

These examples refer to the abstract domain of semiotic conventions. This domain is related to the concrete source domain of clothing conventions by the salient shape properties of the schematization type. The following schematization type represents the properties which get salient in the target domain of semiotic conventions: mod cat = pp

predicate

landmark

trajector

cat = prep

cat = np

cat = np

PLACE =

ABSTRACTION =

ABSTRACTION =

CONTAINS (TR, LM)

{ABSTRACT = SEMIOTIC}

{ABSTRACT = SEMIOTIC}

BOUNDEDNESS = COUNT

SHAPE = {ENCLOSURE = ENVELOPE}

Figure 4. Schematization type of the programme in prologue

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The metaphorical meaning which this target schematization type represents is implied in the prepositional predicate which is used metaphorically. In the concrete spatial domain it can be considered to function as the vehicle in being instantiated by a landmark whose salient shape is an ENVELOPING ENCLOSURE. We have seen that its source domain is clearly distinct from the target domain, although the semantic analogy which is obligatory for metaphor interpretation also exists. The domain, over which the metaphorized relation is predicated — in this case the semiotic domain — provides the topic (traditionally called the tenor since introduced as such by Richards 1936), which adopts the SHAPE properties. The ground, which is the relation of analogy on which the agreement between topic and vehicle rests and which is necessarry for the interpretation, is rendered by the knowledge transferring functions existing between the original and transferred properties. The metaphorical transfer consists of the transaction of the properties which figure out as salient in the vehicle's schematization types in the source domain to the domain of the topic. In our example the preposition in with its landmark can be said to function as vehicle in that it provides its concrete spatial meaning and thus transfers it to the topic, the SEMIOTIC landmark, which then is interpreted as the bearer of the SHAPE property which has figured out as salient in the schematization type of the spatial source domain. If we consider our own interpetations of these examples, however, a common trait of the interpretation of established metaphors becomes evident: often the metaphorical relation is no longer relevant; the interpretation of the abstract term is no longer dependent on the meaning of its concrete mediator of spatial meaning. 5 Many or — from a radical perspective — all abstract meanings have originated as metaphors. With many established metaphors the metaphoricity is no longer vivid, because the metaphor is frozen or even dead. Their cultural motivation is no longer relevant for their interpretation, because their meaning is directly associated with them. The computational quintessence though is this: Whereas today the language user understands the abstract relational concept without referring to the concrete source concept (cf. Gibbs 1984), originally analogical reasoning was to help us to conceptualize more clearly the function of the abstract relational concept; this reasoning process has to be traced back by the computational linguist in order to construe target schematization types, in terms of which semantically abstract uses of prepositions may be interpreted. In machine translation the correct schematization type, implying the

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relational concept, will then unify with the semantic relation encoded by the preposition to be used. This clearly is a case in which the computational interpretation is different from the human one.

7. Conclusion We have proceeded from the claim that Machine Translation needs to be conceptually constrained in order to interpret and generate different usage patterns in different languages. The considereration of the conceptual constraints, which have been suggested by different Cognitive Grammarians, has led us to a model of the semantic lexicon in which the distinction of lexical vagueness and lexical ambiguity is given special importance. All polysemes of a preposition are represented in this lexicon as departing from an ideal meaning. We have shown how the selection, specialization and modulation of the lexical meaning of an entity comes about by the degree of relevance, salience and typicality attributed to the parts of a scene on which the speaker's attention lies in a specific environment of the language and the utterance situation. The translational context has given rise to the possiblity and necessity of distinguishing beside languagespecific relations more abstract relations, which have cross-language validity. In translating a simple example sentence containing a prepositional phrase from German to English we have shown the complex interdepencies existing between the cognitive principles during the process of translation. The example of this schematization type has to be corroborated by testing the range of its generalization. Only having touched on the use of prepositions in abstract domains, the very beginnings of its formalization are still an untackled problem. Complex as the bus example given may be, it is far from being representative of how the meaning of prepositions is constituted in general. While in this example the discourse situation is provided intrasententially by the action of riding, it will very often only be revealed in complex textual structures. This opens an area for future research which will comprise among other things interaction with a knowledge base and the search for an adequate formalism with which these complex relations may be expressed.

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Notes 1. I wish to thank Johann Haller, Wiebke Ramm, Randall Sharp and Jörg Schütz as well as many other colleagues for having discussed with me earlier versions of this paper. Thanks are also due to Angelika and Johannes Müller for their patience in drawing the graphics as well as to David Horton who has given the finishing touches to my English. 2. Yet we know that this is a rather crude idea of the process of translation, as many concepts with cultural significance in the source language have to be transferred directly into the target language or adapted to the knowledge of the target language users. In this paper, however, we are not concerned with this problem. 3. This is a slightly altered example taken from the EC ESPRIT programme. 4. Cf. Zelinsky-Wibbelt (1991 and 1992) as well as Zelinsky-Wibbelt (forthcoming) for a detailed discussion of the conceptual bounding and unbounding of masses. 5. According to psycholinguistic evidence (cf. Pollio et al. 1984, Gibbs 1984, Verbrugge 1977) the human interpretation of established metaphors does not proceed from the source meaning in a two phase interpretation but is rather contextually resolved directly. That is, under the respective contextual conditions the hearer/reader has direct access to the metaphorical meaning and does need any regress to the source meaning.

References Allan, Keith 1981 "Interpreting from context". Lingua 53: 151-173. Annick, Peter — James Pustejovsky 1990 "An application of lexical semantics to knowledge acquisition from corpora". in: Proceedings from the 13th International Conference on Computational Linguistics, Helsinki 1990. Vol. 2: 7-12. Barsalou, Lawrence W. 1982 "Context-independent and context-dependent information in concepts". Memory and Cognition 10 (1). Bierwisch, Manfred — Ewald Lang (eds.) 1989 Dimensional adjectives. Grammatical structure and conceptual interpretation. Berlin: Springer. Boguraev, Branimir — James Pustejovsky 1990 "Lexical ambiguity and the role of knowledge representation in lexicon design", in: Proceedings from the 13th International Conference on Computational Linguistics, Helsinki. Vol. 2: 36-41. Briscoe, Ted — Ann Copestake — Branimir Boguraev 1990 "Lexical semantics via lexicology", in: Proceedings from the 13 th International Conference on Computational Linguistics, Helsinki 1990. Vol. 2: 42-47. Carbonell, Jaimes G. 1980 "Metaphor: an inescapable phenomenon in natural language comprehension". in: Proceedings of the 18th Meeting of Computational Linguistics: 415434. Cruse, D. Alan 1986 Lexical semantics. Cambridge: Cambridge University Press.

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Dahlgren, Kathleen 1988 Naive semantics for natural language understanding. Amsterdam: Kluwer Academic Publishers. Dahlgren, Kathleen — Joyce McDowell — Edward P. Stabler 1989 "Knowledge representation for common sense reasoning". Computational Linguistics 15 (3): 149-170. Davidson, Donald 1978 "What metaphors mean". Critical Inquiry 5: 31^4-7. Franks, Bradley — Nicholas Braisby 1990 Sense generation or how to make the mental lexicon flexible. [Research Paper EUCCS/RP-39. Centre for Cognitive Science, University of Edinburgh.] Frege, Gottlob 1892 "Über Sinn und Bedeutung", Zeitschrift für Philosophie und philosophische Kritik N F 100: 25-50. Geiger, Richard A. (ed.) 1994 Reference in Multidisciplinary Perspective: Philosophical Object, Cognitive Subject, Intersubjective Process. Hildesheim: Georg Olms Verlag. Gibbs, Raymond 1984 "Literal meaning and psychological theory", Cognitive Science 8: 275-304. Gunderson, Keith (ed.) 1975 Language, Mind, and Knowledge. Minneapolis: University of Minnesota Press. Habel, Christopher — Michael Herweg — Klaus Rehkämper 1989 Raumkonzepte in Verstehensprozessen. Tübingen: Max Niemeyer Verlag. Hawkins, Bruce W. 1985 The semantics of English spatial prepositions. [Doctoral Dissertation.] L. A. U. T. Paper 142. (Linguistic Agency of the University of Trier.) Herskovits, Annette 1986 Language and spatial cognition. Cambridge: Cambridge University Press. Hobbs, Jerry R. 1983 "Metaphor interpretation as selective inferencing. Cognitive processes in understanding metaphor." Part 1 and 2. Empirical Studies of the Arts 1 (1 and 2). Hobbs, Jerry R. — William Croft — Tedd Davies — Douglas Edwards — Kenneth Laws 1987 "Commonsense metaphysics and lexical semantics", Computational Linguistics 13: 241-250. Hüllen, Werner — Rainer Schulze (eds.) 1988 Understanding the lexicon. Meaning, sense and world knowledge in lexical semantics. Tübingen: Niemeyer. Jackendoff, Ray 1987 Consciousness and the computational mind. Cambridge, Mass.: MIT Press. Lakoff, George 1982 Categories and cognitive models. L. A. U. D. Linguistic Agency of the university of Duisburg. Duisburg. 1987 Women, fire, and dangerous things. What categories reveal about the mind. Chicago, London: University of Chicago Press. Lakoff, George — Mark Johnson 1980 Metaphors we live by. Chicago: Chicago University Press.

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Langacker, Ronald 1987 Foundations of Cognitive Grammar. Vol. 1. Theoretical Prerequisites. Stanford: University Press. Lehrer, Adrianne 1990 "Polysemy, conventionality, and the structure of the lexicon", Cognitive Linguistics 1: 207-246. Lipka, Leonhard 1988 "A rose is a rose is a rose: On simple and dual categorization in natural languages", in: Hüllen, Werner — Rainer Schulze (eds.), 355-366. Martin, James H. 1988 "Representing regularities in the metaphoric lexicon", in: Proceedings of the 12th International Conference on Computational Linguistics, Budapest 1988: 396-401. Miller, George A. — Philip N. Johnson-Laird 1976 Language and perception. London: Cambridge University Press. Moens, Marc — Jo Calder — Ewan Klein — Mike Reape — Henk Zeevat 1989 "Expressing generalizations in unification based formalisms", in: Proceedings of the 3rd European Conference of the Association for Computational Linguistics, Manchester 1989: 174-181. Myers, Terry — Bradley-Franks — Nicholas R. Braisby 1989 "Partiality and coherence in concept combination", in: Dunbar, George — Bradley Franks — Terry Myers (eds.) Papers from the 1989 Edinburgh Round Table on the Mental Lexicon. 1-19 (Edinburgh Working Papers in Cognitive Science.) Edinburgh: Centre for Cognitive Science. Nirenburg, Sergei — Victor Raskin — Allen Tucker 1985 "Interlingua design in TRANSLATOR", in: Nirenburg, Sergei (ed.) Proceedings of the Conference on Theoretical and Methodological Issues in Machine Translation, 1985, New York: Hamilton. Norrick, Neal 1981 Semiotic principles in semantic theory. Amsterdam: John Benjamins. Nunberg, Geoffrey 1978 The pragmatics of reference. Bloomington: Indiana University Linguistics Club. The Oxford Advanced Learner's Dictionary of Current English 1948 (4th edition) Oxford: Oxford University Press. [1989] Pick, Herbert — Lind Acredolo (eds.) 1983 Spatial orientation: Theory, research and application. New York: Plenum Press. Pollio, Howard — Michael Fabrizi — Abigail Sills — Michael Smith 1984 "Need metaphoric comprehension take longer than literal comprehension?" Journal of Psycholinguistic Research 13: 195-214. Pustejovsky, James 1989 "Current issues in computational lexical semantics", in: Proceedings of the 3rd European Conference of the Association for Computational Linguistics, Manchester 1989: xvii-xxiii. Pustejovsky, James (ed.) 1992 Semantics in the lexicon. Amsterdam: Kluwer Academic Publishers.

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Putnam, Hilary 1975 "The meaning of meaning", in: Gunderson, Keith (ed.) Richards, Ivor Armstrong 1936 The philosophy of rhetoric. Oxford: Oxford University Press. Schweizer,Harro (ed.) 1985 Sprache und Raum. Ein Arbeitsbuch für das Lehren von Forschung. Stuttgart: Metzlersche Verlagsbuchhandlung. The Shorter Oxford English Dictionary 1933 (3rd edition) Oxford: Oxford Clarendon Press. [1974] Sowa, John F. 1984 Conceptual Structures Information Processing in Mind and Machine. London, Addison — Wesley. Steiner, Erich — Paul Schmidt — Cornelia Zelinsky-Wibbelt (eds.) 1988 From syntax to semantics. Insights from machine translation. London: Frances Pinter. Talmy, Leonard 1983 "How language structures space", in: Pick, Herbert — Lind Acredolo (eds.), 225-282. Taylor, John 1989 Linguistic categorization: Prototypes in linguistic theory. Oxford: Clarendon Press. Vendler, Zeno 1967 Linguistics in philosophy. London: Cornell University Press. Verbrugge, Robert 1977 "Metaphoric comprehension: Studies in reminding and resembling", Cognitive Psychology 9: 494-533. Wilensky, Robert 1990 "Extending the lexicon by exploiting subregularities", in: Proceedings of the 13th International Conference on Computational Linguistics, Helsinki 1990: Vol. 2: 407-412. Wittgenstein, Ludwig 1953 Philosophical investigations. Oxford: Blackwell. Wunderlich, Dieter 1985 "Raum, Zeit und das Lexikon", in: Schweizer, Harro (ed.), 66-89. Zelinsky-Wibbelt, Cornelia 1988 "From Cognitive Grammar to the generation of semantic interpretation in machine translation", in: Steiner, Erich — Paul Schmidt — Cornelia ZelinskyWibbelt (eds.), 105-132. 1990 a Machine translation based on Cognitive Linguistics: What lexical semantics contributes to the semantic unity of a sentence. Eurotra-D Working Paper 16. 1990 b "The semantic representation of spatial configurations: A conceptual motivation for generation in machine translation", in: Proceedings of the 13th International Conference on Computational Linguistics, Helsinki 1990. 299303. 1991 "Token reference vs. type reference: implications for machine translation", Machine Translation, Eurotra Special Issue 2. 183-192.

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Cornelia Zelinsky-Wibbelt "Exploiting linguistic iconism for article selection in machine translation", in: Proceedings of the 15th International Conference on Computational Linguistics, Nantes 1992. Vol. 792-797. "Reference as a universal cognitive process: a contrastive study of article use", in: Geiger, Richard (ed.). (Now available as E U R O T R A - D Working Paper 21.)

4. Image understanding and prepositions

A three-level approach to the semantics of space Michel Aurnague — Laure Vieu

1. Introduction The aim of our work is to elaborate some formal tools in order to represent the semantic content of Natural Language (henceforth NL) expressions referring to space, in the framework of French text analysis. Many NL markers allow us to describe space but, usually, it is possible to classify them in two main groups: spatial referents (nouns and adjectives), and spatial relations (prepositions, verbs of movement). We give some examples below: (1) referents

a. Le haut de la tour est en ruine. 'The top of the tower is in ruins.' b. L'arbre est haut de 5 metres. 'The tree is 5 meters high'.

(2) relations

a. Le restaurant est situe entre la banque et le bureau de poste. 'The restaurant is situated between the bank and the post office.' b. Le bateau s'eloigne de la cöte. 'The boat is going away from the coast.'

It can be observed that whereas referents (sentences (1 a) and (1 b)) identify a portion of an object, relations (sentences (2 a) and 2 b)) situate a localized object (called trajector) with respect to a reference object (called landmark). We take as source data discourses containing sentences like those above and try to represent their semantic content with the formal tools we build. The elaboration of these representations follows a methodology based on two main points. First, the study is based on a detailed and systematic linguistic analysis which must highlight and classify the different meanings of each lexeme, in particular (in the field of spatial expressions) the distinct spatial configurations it refers to. This survey of the different meanings has to be as detailed and systematic as possible so as to formalize the semantics of the spatial expressions covering all their pos-

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sible uses. Since we are interested in the expression of space in NL, we naturally set aside all the uses of the lexemes studied which are not purely spatial or not about concrete objects like, for instance, metaphorical uses. The second point of our methodology concerns the elaborated formalisms which, beyond the representation of the semantic content, should have adequate inferential properties. This means that we want to use the formalisms to make deductions whose results must be similar to the reasoning made by a human being. We consider that a "complete" semantics must aim not only at encoding the content of the lexemes studied, but also at reproducing the human reasoning involving those lexemes. Moreover, such a comparison between the results of inferences and reasoning constitutes a real way to validate the semantics elaborated. A direct consequence of this inferential constraint is the choice of logic as an appropriate framework to build our formal tools. The representation system of spatial entities and relations whose main lines we explain here has been used to give a formal definition to the prepositions dans 'in' and sur 'on' and to some Internal Localization Nouns (henceforth ILN) such as haut 'top', bas 'bottom', devant 'front extremity', dessus 'top extremity', interieur 'inside', bord 'edge', angle 'corner', etc., which are all lexical elements pointing out the different portions of an object (Borillo, A. 1988). The two prepositions sur 'on' and dans 'in' and the ILNs have been studied in the following syntactic structure which corresponds to a static localization process: Ntraj etre prep [ILN de] Nland 'Ntraj to be prep [ILN of] Nland' Some examples of sentences constructed according to this structure are: (3)

a. Les armoiries sont sur le devant de la maison. 'The coat of arms is on the front (extremity) of the house.' b. Le livre est dans I'armoire. 'The book is in the cupboard.'

In this paper we look closely into the semantics of sur 'on' and dans 'in' showing that a three-level approach (geometrical, functional, pragmatic) enables us to appropriately formalize their spatial uses.

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2. An analysis on three levels Throughout this paper, we try to illustrate our approach to the semantic analysis of spatial expressions, namely that we advocate distinguishing between several types of elements which make up their meaning. There are two main reasons for this. First of all, these elements clearly belong to different qualitative categories: separate treatment is therefore more efficient. Second, studying what is going on within each category and between them forces us to go deeper into the analysis of the semantics at stake than if we adopt a global approach. As a result, we progress towards one of the principal goals of our work, that is, obtaining adequacy between the inferences which can be drawn from the representation system and the deductions acknowledged by common sense. The observation on which the first reason is based is founded to a large extent on the linguistic analysis of the spatial prepositions in two important works: Herskovits (1982) and Vandeloise (1986). Nonetheless, we should note that their authors do not conclude as we do and stick mainly to a global approach.

2.1. Definition of the three levels Contrary to Leech (1969) and to a certain extent Miller — JohnsonLaird (1976), Vandeloise (1986) showed that a purely geometrical representation of the semantics of spatial prepositions is not appropriate. For instance, if sur 'on' were represented only with the relation of contact, we could not make the difference between the sentences (4 a) and (4 b): (4)

a. L'affiche est sur le mur. 'The poster is on the wall.' b. L'armoire est contre le mur. 'The cupboard is against the wall.'

In the same way, if the inclusion of the trajector in the convex hull of the landmark fully described the preposition dans 'in' (which is described this way or simply by inclusion in most of the literature), we would not explain why in the situation depicted by Figure 1, sentence (5) cannot be asserted (this last example is taken from Herskovits 1982). (5)

La mouche est dans le verre. 'The fly is in the glass.'

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In these examples, the geometrical approach does not take into account the functional components of the semantics of the prepositions sur 'on' and dans 'in': for the first one, the notion of support is essential, and for the second, containment is very important. More generally, the functional aspects of the relations and entities they describe play a major part in the semantics of spatial markers. These functional aspects may belong to the "naive physics group" (as defined in Hayes 1985), as do the relations of support and containment; or they may belong to the "orientation group", as do the functionality of a cupboard which makes it possible to speak of the front part of the cupboard; finally, they may belong to the "structure group", as do the characteristic of being considered as discrete or continuous and all the aspects concerning the composition of the entities. As in any field of NL, pragmatic phenomena influence the semantics of the spatial markers, as can be seen in the following example. (6)

a. La voiture est dans le garage. 'The car is in the garage.' b. Le moteur de la voiture est dans le garage. 'The car's engine is in the garage.' c. Le moteur de la voiture η 'est pas dans le garage. 'The car's engine is not in the garage.'

From sentence (6 a) the semantics of dans 'in' should enable us to infer sentence (6 b). Indeed, if (6 a) is true, then (6 b) is also true or at least it cannot be denied: clearly, here (6 c) is false. Nevertheless, knowing (6 a), we would not utter (6 b) alone because it somehow "implies" that the engine is separated from the car, lying somewhere in the garage.

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Several pragmatic principles can be isolated, as for instance the "principle of maximum trajector" involved in the last example: "do not localize a part if you can localize the whole, unless you have good reasons to do so" and its corollary "generally, the entity localized is not a part of a bigger entity being in the same situation". These principles or conventions are in fact instances of more general ones that rule any kind of discourse or dialogue, as Grice's principle of cooperativity which is composed of four maxims (Grice 1975) (the principle of maximum trajector is just a particular case of the maxim of quantity), and the search for the highest degree of typicality. Of course, these principles generate implicatures (as the above corallary), not inferences. Consequently, these will have to be represented within a non-monotonic logic. We should also stress that they need more information than is contained in the text being analysed, that is, they often rely on world knowledge (here we used the knowledge that a car has an engine) and extralinguistic context (here we have assumed a "normal" context, not one, for instance, in which the car engine has just exploded and someone is asking where it occurred). To sum up, we have identified three types of elements involved in the "meaning" of the spatial markers we studied. First, there are of course the geometrical properties of the entities and the geometrical relations, which cannot be put aside. 1 Second, we have seen that the functional properties and relations also play an important part. Third, we have seen that pragmatic principles together with a representation of (some) world knowledge and (part of) the context can significantly modify what is obtained from the elements of the first two types only. Consequently, the representation system we have built to formalize the semantics of the spatial markers consists of three parts.

2.2. Organization of the levels Before we stark looking into each one of the three parts which make up the representation system, we must say a word on how these parts are organized. The geometrical level is at the root of this system. It constitutes a formal structure where we represent the objective, purely spatial data present in the text analysed. This data is said to be objective not only because it does not take into account context and discourse conventions, but also because it is independent from the function and internal structure of the entities, which is often induced by the particular point of view the

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τι

cFb

Τ

ibl

icFb

Fb

st

ßL - ί Figure 2. Partial description of a c u p b o a r d (topology)

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Figure 2 (following) entity or spatial referent

symbol

amoire face a face a' corps-face a interieur-corps-face a bord 1 interieur-bord 1 face b face b' corps-face b interieur-corps-face b

ar fa fa' cfa icfa bl ibl fb f'b cfb icfb

autour interieur-autour

aut iaut

c(-,-)

ar*

Fa*

Fa

ρ (cfa*, fa*) p(bl*, fa*) p(cfb*,fb*) p(bl*, fb*) p(fa*, ar*) p(fb*,ar*)

cFa* icFa

ar*

+

Fa*

+

+

Fa

+

+

+

cFa*

+

+

+

+

icFa

+

+

+

+

bl*

+

+

+

ibl

+

+

Fb*

+

+

F'b

+

+

cFb*

bl*

ibl

Fb*

comp-ass(cfa, fa) comp-ass(bl, fa) comp-ass(cfb, fb) comp-ass(bl, fb) comp-ass(fa, ar) comp-ass(fb, ar)

Fb

cFb* icFb

+

+

+

+

+

+

+

+

+

+

+

+

icFb

+

+

+

+

aut*

+

+

+

+

iaut

+

+

iaut

+

+

+

aut*

+

+

+

+

+

+

note: the addition of * to an entity X (notation X*) means that we consider the spatial referent of that entity X (that is, X* = sref(X)).

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locutor has chosen when naming the entities. For instance, sentences (7 a) and (7 b) describe the same geometrical relation (contact and relative position on the vertical axis) between the same concrete "objects", although the two entities they localize are different, for the first may be new while the second may be old. (7)

a. La bague est sur la table. 'The ring is on the table.' b. Le morceau d'or est sur la table. 'The piece of gold is on the table.'

This difference is not taken into account on the geometrical level, but on the functional level where all the properties of the entities are represented. As a consequence, and to emphasize the difference between these two levels, we look upon the elements handled on the geometrical level as different from the entities handled on the functional level: we call them the "spatial referents" of the entities. Formally, it is just a trick to say that all the entities describing the same concrete object, and thus the same "space portion", make up an equivalence class with respect to the geometrical relations. The functional level is of course based on the geometrical level, since the spatial properties are part of the properties of the entities, and many functional relations imply geometrical ones (e.g., containment implies inclusion in the interior). It is at this level that we represent the "crude" semantics of the spatial markers we have studied. Here and on the geometrical level, all the information, including the inferred information, is certain; that is, this information is not defeasible, although some pragmatic principles may act later as a filter and eliminate "what is not false but cannot be said" when using the system in a generation mode (for instance, answering a question). The pragmatic level relies heavily on functional properties as will be seen in the fifth section. In addition, it needs two different structures to represent context and world knowledge, but these will not be dealt with in this paper, as much work remains to be done on them. The specific knowledge that the pragmatic level embodies is procedural: either it works as a filter as we just mentioned, or it produces defeasible information. It is also here that an occurrence of a spatial expression is interpreted as an instance of a particular case 2 of this expression. These processes are not completely formalized at the moment, so in Section 5. we will simply present in an informal way what in the meaning of the studied spatial markers we feel belongs to this level, and we will try to justify it. Even

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though we know that the separation between semantics and pragmatics is highly controversial, we feel we could use the term semantics to designate the first two levels and the term pragmatics for the third. We hope the reader is kind enough not to take offence at this, in case s/he uses these two terms in a different manner.

3. The geometrical level As it has been underlined, on the geometrical level we handle the spatial referents of the entities, that is the space portion determined by their matter at a given time. At this level we deal with the topological notions of inclusion, contact, boundary, etc., and with concepts related to projective geometry such as straight line, distance, order on a straight line, etc. The actual use of prepositions like sur 'on' and dans 'in' which allows us to situate a trajector with respect to a landmark shows the relational nature of the structures handled in the language as opposed to the absolute spaces used in robotics (where entities are localized by means of coordinates). This property of space in N L has also been emphasized in various works related to psychology and linguistics like those of G. Miller - P. Johnson-Laird (1976), L. Talmy (1983), A. Herskovits (1982) or C. Vandeloise (1986). In addition, researchers like P. Hayes (1976) who, in the field of naive physics, try to formalize commonsense reasoning, make a similar assumption. Moreover, two properties of these absolute spaces seem to contradict the structures of space in NL. Whereas, in a coordinate system, the positions of every entity need to be known exactly, the spatial information expressed in a text is often partial and imprecise. Another problem arises from the fact that the variable granularity of space in N L (for instance in N L the same entity can be considered at one time as a point and later as a volume) is not compatible with the discrete structure characterizing an implementable coordinate system, where the minimum units are defined a priori. So, knowledge representation on the geometrical level will be done within a relational structure and not within a coordinate system. As a consequence, the spatial referent of the entities will be taken as primitive elements and not, for instance, as sets of points of an Euclidian space. Space is therefore built from the text and not assumed beforehand (this is similar to the construction of time proposed in Kamp 1979).

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It must be stressed that, contrary to an absolute space in which all geometrical concepts can be expressed by using classical theories of mathematics (for instance, Euclidian geometry), relational structures imply formalizing topology and projective geometry in two independent modules. We already showed in Aurnague (1991) and Vieu (1991) that, up to now, every attempt to express those two types within only one qualitative formalism has failed. Consequently, the geometrical level of the system is made up of two distinct modules, one dealing with topological information and the other with projective geometry.

3.1. Mereology and Topology In order to fulfil the relational requirement mentioned above, we formalize the topological information using the individual calculus based on connection proposed by B. L. Clarke (1981 and 1985). In fact, we use an extended version of this theory because we modified and completed it so as to take into account some important spatial concepts in language. Following this work and the mereological 3 tradition derived from Leonard — Goodman (1940), we call the spatial referents of the entities "individuals". This calculus is based on the sole relation of connection between two individuals (noted c (X, Y)) to which B. L. Clarke does not give any precise interpretation. However, in order to provide help in reading the axioms, definitions and theorems, B. L. Clarke suggests (according to A. N. Whitehead) considering variables as spatio-temporal individuals, which is the case in our use of this theory, and stating that two individuals are connected if they "share at least one point" (which has no real meaning here since we do not interpret the spatial referents as sets of points). This primitive connection is used to define some mereological operators as well as Boolean and topological ones. It is characterized by two axioms, the first stating reflexivity and symmetry and the latter being a kind of "extensionality axiom" based on a second primitive, the identity relation = s : • VX c (Χ, Χ) Λ VX VY (c (X, Y) => c (Υ, X)) • VX VY (VZ (c (Ζ, X) ^ c (Ζ, Y)) ^ X = s Y). As regards mereology, the disconnection (X is disconnected from Y: de (X, Y)) between two individuals and the configurations of inclusion (X is included in Υ: ρ (Χ, Y)) and overlapping (X overlaps Υ: ο (Χ, Y))

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are introduced. The inclusion, for instance, is defined stating that X is included in Y if every Ζ connected with X is also connected with Y: • ρ (Χ, Y) = d e f VZ (c (Ζ, X) => c (Ζ, Y)) Then, the notion of a proper part (strict inclusion) X of an individual Y can be expressed as: • pp (X, Y) = d e f ρ (Χ, Υ) Λ ~ ι ρ (Υ, X) It must be noted that the part-whole relations (also called meronomies) used in the language (e.g.: cette roue est une partie de ma voiture, 'this wheel is a part of my car') are much more complex than the mere geometrical inclusion because they involve many functional factors depending directly on the entity (and not only on its spatial referent). Consequently, we define this type of relation on the functional level of the system. Two individuals X and Y are overlapping each other if they share a common individual Z: • ο (Χ, Y) = d e f 3Z (ρ (Ζ, Χ) Λ ρ (Ζ, Υ)) Bringing something new to classical mereology (Lesniewski 1927-1931 and Leonard — Goodman 1940), the distinction between connection and overlapping allows B. L. Clarke to define the situation in which two elements are externally connected: • ec (X, Y) = def c (Χ, Υ)

Λ

ίο (Χ, Υ)

A portion X of an individual Y is called a tangential part of Y if there exists an individual Ζ externally connected to both X and Y (the notion of non-tangential part is defined in the same way). In the Boolean part of the calculus, the operators sum ( + ), product (prod) and complement ( —) are defined. We assume here and in the following that the reader is familiar with lattice structures and Boolean algebra. This part of the theory is called pseudo-Boolean because of the lack of a null element which follows from a philosophical postulate of S. Lesniewski (1927-1931) taken up by A. N. Whitehead (1929) and B. L. Clarke. According to this postulate, all the individuals handled in the calculus must have a concrete existence, which is not the case of the null element. The third, and last, part of this calculus covers the topological aspects themselves; it consists in defining the interior of an individual, its closure as well as the properties of being closed and open. For this definition as

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well as for the Boolean part, Β. L. Clarke introduces the fusion operator f between an individual X and a set of individuals α stating that X constitutes the fusion of α if, for every Y connected to X, there exists an element Ζ of α which is also connected to Y: • X = s f (a) = d e f VY (c (Υ, Χ) 3Z (Ze α Λ c (Υ, Z))). Furthermore, an axiom ensures, for any set a, the existence of an individual X corresponding to its fusion (A being the empty set): • Va

ι (a = A) => 3X X = s f (a)).

Then the interior of an individual X can be defined as the fusion of its non-tangential parts: • i ( X ) = def f ({Υ : N T P (Υ, X)}). The closure of X is calculated by fusing all the individuals which are not connected to the interior of its complement: • c(X) =

deff({Y:^c(Y,i(-(X)))})

4

.

Here too it must be underlined that the topological interior of an individual does not correspond to what we usually call interior in the language. For example, when people refer to the natural interior of the glass, they are usually pointing out the portion of space enclosed between its sides (where one can put water) and not to the very interior of those sides which contains only glass and actually corresponds to the topological interior. As the functional aspects play a great part in determining the natural interior of an entity, we introduce this notion on the functional level of the system. From the topological operators "interior" and "closure", open and closed individuals can be characterized in the following way: • op (X) = d e f X = s i ( X ) • cl (X) = d e f X = s c (X) This topological part of the calculus is called pseudo because of the impossibility of handling boundary elements present in classical topology. The principal reasons behind this are the lack of a null element and the distinction between external connection and overlap configurations. Finally, B. L. Clarke introduces an axiom which states that every individual has an interior (i.e., it has a non-tangential part) and constrains the product between two open elements to be itself open:

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• VX [3Z ntp (Ζ, Χ) Λ VY [VZ [(c (Ζ, X) => ο (Ζ, X)) A (C (Ζ, Y) => ο (Ζ, Υ))] => VZ [c (Z, prod (Χ, Υ)) => ο (Ζ, prod (Χ, Y))]]]. The individual calculus based on connection, whose main lines we have just set out, is not sufficient as it is to deal with problems related to the semantics of space in language. Consequently, we have extended this theory in order to express some fundamental spatial notions in the language, such as limit, contact, etc. We noted that one of the main spatial concepts handled in language, limit, could not be directly taken into account by B. L. Clarke's calculus. In order to make up for this lack, we introduce the notion of empty individual and regard a limit as a tangential part having an empty interior. The principal reason why limits can be considered as individuals comes from the fact that we work in a finite domain. If we had added a nonatomicity condition, it would not have been possible to define them in this way since they would have corresponded to the classical notion of limit in mathematics. Moreover, we can characterize the limits in terms of empty individuals because the spatial referents of the objects we handle are closed and not open. An individual is empty if each of its portions are open: • vide (X) = d e f VY [ρ (Υ, X) => op (Y)]. Using this property, we build three types of limits (lim 1, lim 2, lim 3) through which surfaces, lines and points can be differentiated. A portion X of Y is a limit 1 if it is a tangential part of Y having an empty interior and if any tangential part of X is also a tangential part of Y (which means that everything inside the limit is flush with it): • lim 1 (Χ, Y) = d e f vide (i (Χ)) Λ tp (Χ, Υ) A VZ [tp (Ζ, X) => tp (Ζ, Y)]. The enveloppe X of an individual Y is the maximum limit 1 of Y: enveloppe (X, Y) = d e f tp (Χ, Υ) A VZ [lim 1 (Ζ, Υ) ο tp (Ζ, Χ)]. The notion of limit 1 being thus defined, we can now state that a limit 2 is a "boundary" between two individuals which are themselves of the limit 1 type: • lim 2 (Χ, Y) = d e f 3Z [lim 1 (Υ, Z) A enveloppe (Υ, Z) A vide (i (X)) A tp (X, Y) A VT [tp (Τ, X) => 3W [lim 1 (W, Z) A ec (W, T) A ec (W, Y)]]].

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Similarly we regard a limit 3 as a "boundary" between two individuals of the limit 2 category. In short, surfaces, lines and points satisfy the conditions of a limit 1, lines and points those of a limit 2 whereas individuals of the limit 3 category are exclusively points. On the basis of this information it is possible to determine the nature of the spatial referents handled in the system (the predicate con "is connected" is defined elsewhere in the theory): • surface (X, Y) = d e f c o n (Χ) Λ lim 1 (Χ, Υ) A ~i3Z lim2 (Χ, Ζ) • ligne (Χ, Υ) = d e f con (Χ) Λ lim 2 (Χ, Υ) Λ —13Ζ lim 3 (Χ, Ζ) • point (Χ, Υ) ^ d e f con (Χ) Λ lim 3 (Χ, Υ). These limit concepts play a great part in the formalization of ILNs like dessus 'top extremity'; bord 'edge'; angle 'corner', etc. Contact seems to be another fundamental notion for the processing of space in language. In fact, the notion of contact gives rise to two different interpretations. The first one called "strong contact" covers cases in which the two entities in contact are assumed to "share some boundary points" (not the points we just introduced, which are in fact individuals). This type of contact corresponds exactly to the situations described by the predicate of external connection (ec): scont (X, Y) = d e f ec (X, Y). A second category of contact (also called "weak contact") which appears very often in the language, includes all the configurations for which the entities are supposed not to have point in common although they are touching together. As it has been stated in (Vieu 1991), this weak contact is only compatible with a non-classical distance in which two points situated at a null distance from each other are not necessarily identical. An entity X is considered to be in contact with an entity Y if the closure of any open element containing X is connected to Y (a* denotes the universal individual): • cont (X, Y) = d e f - i c (Χ, Υ) Λ VZ [[-ι (Z = s a*) Λ op (Z) A ρ (Χ, Ζ)] => c (c (Ζ), Y)]. Although we used this intuition to describe some predicates, the individuals handled in B. L. Clarke's calculus are not interpreted as sets of points, as we argued for in the introduction of this section. On the contrary, the author indicates in Clarke (1985) a way to introduce points in its system as sets of individuals. This definition based on the filter technique consists in characterizing points through the individuals (connected two by two) "containing them". We proved in Vieu (1991) that the definition in terms of filters worked correctly for interior points, but

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was not right for boundary ones. Actually, its application to boundary points entails that when two individuals are externally connected, any individual is also connected to them (which is a serious restriction on the nature of the modelled worlds). We therefore proposed an alternative definition for boundary points which enables us to represent the limit concept from those boundary points. Whereas, under the atomicity condition, interior points (whose definition is identical to that introduced by B. L. Clarke) each correspond to an atom (which generates the whole set of individuals including it), this is not the case for boundary points. However, the notion of base of a boundary point is defined as the minimal set of individuals generating the whole set defining the point. The definition of a boundary Γ of an individual X (a set of X's boundary points) and that of the base of Γ restricted to X associated with various constraints of minimal thickness are then used to formalize the various limits. The definition of a limit in terms of individuals introduced above and this definition based on points provide identical results. As already mentioned, on the geometrical level of our system we do not only take into account topological data but we also integrate some important concepts of projective geometry.

3.2. Projective geometry In this module we deal with very important notions such as straight line, oriented straight line, position of a point on a straight line, etc. We have above all to make it clear that an important assumption of our study is based on the delimitation of the universe of spatial entities we describe and process (essentially with respect to their shape). So, at least for the analysis of ILNs, we restrict the research field to solid, undeformable and connected objects that also have a normal usefulness. Here we deal with a class of objects whose shape is roughly parallelepipedic, cylindrical or spherical. We associate a system of orthogonal axes (x, y, z) with the spatial referent of every entity having the object status according to its dimensionality and shape. For example, three orthogonal axes are associated with a parallelepiped or a sphere but, whereas in the case of the parallelepiped these axes are each parallel to a pair of sides, in the case of the sphere their position is not exactly determined with respect to the whole object. 5 As every axis is attached to an entity, it will be identified by means of a pair (X, Axe) specifying the entity and the axis's name. In

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this notation, brackets play the part of a function associating the spatial referent of the axis with an entity and an axis's name. We must underline that, from the same axis, it is possible to define two oriented straight lines or directions. Because they depend on the axis, oriented straight lines are noted with the triplet (X, Axe, Dir) in which the variable Dir denotes a direction name. Directions handled on the geometrical level are called abstract because they do not call for any concrete orientation like top, bottom, left, etc. In fact, the assignment of a concrete orientation to an abstract direction is a completely functional process that we model at the functional level of the system. The sorted variable Dir introduced in the notation above in order to designate an abstract direction takes its values in the set {p, op}, whereas the constants + and — point out the concrete orientations appearing at the functional level. In the same way, the variable Axe representing an abstract direction is instantiated by the values {x, y, z} as opposed to 1, 2 and 3 which denote the vertical, frontal and lateral concrete axes, respectively. So, these two sorted variables do not take their values in the entity set. In our representation we project the spatial referent of an entity Y (noted sref (Y)) on the axes generated by an entity X of which Y is a part, and we specify with an interval Int, the axis portion filled by that projection. All this information is integrated in the predicate proj (sref (Υ), (X, Axe), Int). The variable Int represents the interval [Exta, Extb] of (X, Axe) resulting from the projection of sref (Y) on the axis (X, Axe). The spatial referent of an entity is projected on the axes of the entities which immediately contain it 6 and not on every axis system of the entities of which it is a part. We already said that, for the same abstract axis (X, Axe), it was possible to define two abstract directions (X, Axe, Dir) that we distinguish with the values ρ or op of the variable Dir. From an abstract direction (X, Axe, Dir) of an axis (X, Axe), we can build the relation " i n f ' on the set of projection points expressing that a point precedes another in a direction. A and Β being two projection points on an axis, they verify one of the three following configurations (where eg (A, B) means that A equals B): • (inf (A, B), Dir) • (inf (B, A), Dir) • eg (A, B). We use these relations to situate the projection points present on an axis with respect to each other. We specify the relative locations of the

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projection points on an axis by means of the predicate rel ((X, Axe), List) in which the variable List denotes a list of relations like the one we defined. Thanks to these order relations, some operators between intervals that are very similar to those introduced by. J. Allen (Allen 1984) for time can be defined (Aurnague 1991). For example we succeed in calculating that an interval [Exta 1, Extb 1] is more advanced in one direction (noted as plus dir ([Extal, Extbl], [Exta 2, Extb 2], (X, Axe, Dir))) or included (inclus ([Extal, Extbl], [Exta2, Extb2], (X, Axe, Dir))) in another interval [Exta 2, Extb 2]. This system of axes and projections is fundamental in stating the semantic definition of ILNs as haut 'top', bas 'bottom', dessus 'top extremity', dessous 'bottom extremity', etc. (we will give them on the functional level). Another aspect of projective geometry consists in specifying the notions of straight lines, oriented straight lines, etc., through definitions based on the primitive relation "A is situated between Β and C" between points (see View 1991). An important aim now is to specify the system of axes associated with the spatial referent of an entity in terms of this straight line definition. As the determination of these axes relies mostly on the shape of the objects, we would want to deal with the information linked to shape in a qualitative way (as we do for the other types of data), which seems to be very difficult. The last point we deal with in geometry is the notion of distance that we introduce by means of the primitive relation "B is closer to A than C is". As we pointed out it before, the formalization of the intuitive contact implies that this distance should be a non-classical one for which two points situated at a null distance from each other can be considered as distinct (in case of weak contact). We can conclude the presentation of this level by saying that we obtained a complete relational naive geometry. In fact, the information processed at this level is not restricted to the spatial domain since the individuals handled here are really spatio-temporal referents of the entities. Consequently, we introduce purely temporal relations which are similar to those we defined up to now for the space-time structure and we also express the links between these two data types. Figure 2 provides a partial description of a cupboard which uses most of the geometrical tools we have shown up to now. The first table of Figure 2 provides the various elements appearing in the description and the symbols by which we refer to them. Some elements (noted in standard characters) are really entities (and more precisely objects), which means

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that a speaker can individualize them. Other elements are simply spatial referents whose presence is needed for the topological consistency of the spatial structure. The second table shows the connections between the different spatial referents (note that all the information is encoded with the primitive of connection). These connections allow us to calculate, by means of the definitions and axioms of the theory, the inclusions and the external connections between spatial referents. Later, on the functional level, the system deduces part-whole relations 7 for the entities having the object status. Lastly, the system determines (by using the limit definitions) the nature of some spatial referents (surfaces, lines or points). As we showed in the second section, geometrical properties are insufficient to grasp the semantics of spatial expressions and, consequently, we need to take into account on a second level the functional characteristics of the entities.

4. The functional level At this level we deal with the orientation process, plural structures as well as some concepts of naive physics such as stabilization or containment. As all these properties directly concern the entities themselves, we handle variables which represent entities and not simple portions of space (as is the case on the geometrical level). These are designated through the "function" sref. It is also at this level that we introduce the "crude" semantic definitions of the spatial expressions we study.

4.1. Orientations We already mentioned that only abstract directions are handled in the geometrical module. The orientation process consists in mapping an abstract orientation on a concrete one. Since the assignment of a concrete orientation depends on properties of the object itself or of its context, it must be formalized on the functional level. This phenomenon appears very clearly in intrinsic orientation configurations for which the functions of the different parts of an entity give it a canonical position in space (with respect to the vertical axis, the user, etc.), entailing the intrinsic orientation. For instance, the intrinsic front of a computer is derived directly from the usual position of its screen. Therefore, we represent the

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orientation by means of the predicate orient ((X, Axe, Dir), (A, D), V) which specifies the coincidence between the abstract direction (X, Axe, Dir) of X (e. g.: the direction (ar, x, p) of the cupboard in Figure 2) and the concrete orientation (A, D) (e.g.: (1, + ) which denotes the top or the upper orientation). 8 The third term of the predicate points out the entity responsible for this mapping process, which can be the entity X itself (in this case variables V and X are identical and the orientation is intrinsic) or another entity in the context (V and X denote distinct entities and the orientation is deictic). 9 This predicate is used to elaborate various rules for the calculation and processing of orientations. For example, we can deduce an intrinsic orientation of an entity X from the fixedness of one of its parts Y or state that every vertical deictic orientation is induced by gravity. This last property is expressed with the following rule (in which the contextual entity g symbolizes gravity): • VX VAxe VDir VV [[orient ((X, Axe, Dir), (1, D), V) λ (X = V)] => orient ((X, Axe, Dir), (1, D), g)]. Because we restricted the type of entity processed by the system, we introduce, again for the analysis of ILNs, some conditions on orientations. First, the texts studied are "instantaneous" in the sense that the entities described as well as the locutor do not change in position with respect to one another. Moreover, we make the hypothesis that an entity is oriented at one moment by a unique locutor. The result of the instantaneous constraint (which induces the immobility of both the entity and the orientor) can be stated by means of the two following postulates: • VX VAxe 1 VDir 1 VAxe 2 VDir 2 VV VA VD - ι [orient (X, Axe 1, Dir 1), (A, D), V) Λ orient (X, Axe 2, Dir 2), (A, D), V) Λ [-1 (Axe 1 = Axe 2) ν - | ( D i r l = Dir 2)]] • VX VAxe VDir VV VA 1 VD 1 VA 2 VD 2 —ι [orient (X, Axe, Dir), ( A l , D l ) , V) Λ orient ((Χ, Axe, Dir), (A2, D2), V) Λ [ - | ( Α 1 = Α 2) ν ι (D 1 = D 2)]]. The first constraint states that the same concrete orientation cannot be assigned to two different abstract directions whereas the second one prevents the same abstract direction from coinciding with two distinct concrete orientations. In both cases, those multiple orientations can be the result of a movement of the entity or of the orientor-speaker. Another aspect related to orientation which we deal with on this functional level consists in determining the central interval of an axis. As it is shown in Vandeloise (1986), such a determination does not only

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depend on geometrical properties of symmetry because it is greatly conditioned by functional features. After identifying this central interval, we can define two poles surrounding it, each in one of the two directions associated with the axis. All these orientational tools are used in the semantic definitions of ILNs as haut 'top'; bas 'bottom'; devant 'front extremity'; etc., expounded in Aurnague (1991) and allow us to model the component of the semantics of sur 'on' relative to the position of the entities on the vertical axis. For instance, we represent the semantic content of the ILN haut 'top' with the following formula: • VX VAxe VDir VV VN [orient ((X, Axe, Dir), (1, + ) , V) Λ natur_or ((X, Axe, Dir), (1, + ) , V, Ν)] => haut (Υ, Χ, Ν) = d e f ds pole (Υ, (Χ, Axe, Dir)) Λ VZ [ds_pole (Ζ, (X, Axe, Dir)) => part (Ζ, Υ)]. This definition states that when the abstract direction (X, Axe, Dir) of an entity X receives a deictic or intrinsic (variable N) upper orientation, the maximum entity Y situated in the pole whose abstract direction is (X, Axe, Dir) constitutes the top of X. In this definition, it is clear that functional aspects such as orientation directly arise in the semantics of spatial expressions. This observation confirms the assertion of E. Lang who, in his work about dimensional adjectives (Lang 1990) in which the same functional aspects of orientation appear, writes that "the semantic analysis of these linguistic items has to be justified in terms of nonlinguistic conceptual structure formation."

4.2. The structure of the entities On the geometrical level, there is only one relation to link a part to a whole, namely the spatial inclusion (noted p). As a result, it is impossible to describe a spatial referent as having a specific internal structure. However, we often give a particular structure to the entities, sometimes just by choosing the noun phrase used to refer to an object. For instance, the rice is conceived as a continuous entity whereas the rice grains is definitely a discrete one (i. e., a collection). At the same time, there exist several part-whole relations (also called meronomies) between the entities: "member-collection" (e. g., Texas is a member of the USA), "componentassembly" (e. g., this wheel is a part of this car), etc. This diversity alone precludes their direct identification with spatial inclusion. Besides, mer-

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onomies cannot be represented on the geometrical level, because they rely on functional aspects of the entities. In particular, the relation "member-collection" cannot be reduced to a mere inclusion as, among other things, it is not transitive (The USA are a member of U N O whereas Texas is not). We felt that dealing with the internal structures of the entities was part of our work for several reasons. Firstly, ILNs designate parts of a whole, i.e., they describe a kind of meronomy; in addition, we will see in the next section that the preposition dans 'in' can be used to describe meronomies. Secondly, structural relations help explain what the links are between the different entities used to refer to the same physical object. We wanted to be able to differentiate these entities; at the same time, it is desirable to express how they are related. At last, we can mention that on the geometrical level, any sum of individuals is a new individual whereas few of these sums correspond to actual entities. This can be explained by the fact that we conceptualize as entity only what has some kind of internal structure; the knowledge of these structures then takes on another sort of importance.

4.2.1. The plural structure The notion of collection is important in NL: most 1 0 plural noun phrases (e.g., Jean et Marie 'John and Mary'; les arbres 'the trees') refer to a collection, and many singular noun phrases, too (e. g., le couple Dupont 'the couple Dupont'; la foret 'the forest'). Two types of relations are associated with this notion: the relation "member-collection" (e. g., between one tree and the forest) and the relation "subcollection-collection" (e. g., between a smaller group of trees and the forest). To represent them, we have taken up the lattice structure introduced by G. Link in his "Logic of Plurals and Mass Terms" (Link 1983: 311-316). In this structure, also called the "plural" lattice, the entities denoted by singular noun phrases in the discourse analysed are represented as atoms, whereas the entities denoted by plural noun phrases are nonatomic elements. The latter are put in relation to their members and to their sub-collections by the ordering relation (noted 3Y ((obj (Υ) Ν loc (Υ)) Λ det (Υ, X))) • VX VY VT VU ((mor-tt (Χ, Υ) Λ sp-port (Χ) Λ det (Τ, Χ) Λ det (U, Υ)) => (T = U ν part (T, U))

4.3.

The semantic definition of the prepositions: some naive physics concepts

4.3.1. The preposition sur As mentioned in Section 4.1., the position of the entities on the vertical axis is a very important distinction criterion between the different cases of sur 'on' according to the kind of configuration they refer to. If the trajector is placed higher than the landmark (as in sentence (8 a)), this situation is referred to as sur 1 ' o n l ' . The case in which the trajector is on the same level as the landmark (as in (8 b)) is called sur 2 'on 2'. Sur 3 'on 3' applies when the trajector is placed lower than the landmark (as in (8 c)). (8)

a. sur 1 'on 1' Le livre est sur la table. 'The book is on the table.' b. sur 2 'on 2' L'affiche est sur le mur. 'The poster is on the wall.' c. sur 3 'on 3' La mouche est sur le plafond. 'The fly is on the ceiling.'

On the geometrical level, these various configurations give rise to three types of contact between individuals (cont 1, cont 2 and cont 3 respec-

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tively). For instance, cont 1 corresponds to the situation where a piece Ζ 1 of X is in contact with a piece Ζ 2 of Υ, Ζ 1 being higher than Ζ 2. This set of conditions is expressed by the following rule in which the predicate zonecont (Ζ 1, X, Y) denotes the contact area Ζ 1 between two elements X and Y: 17 • cont 1 (X, Y) = d e f cont (Χ, Υ) Λ 3Z 13Z2 [zonecont (Ζ 1, Χ, Υ) Λ zonecont (Z2, Υ, Χ) Λ plus haut ( Z I , Ζ2)]. Thus comparing the relative positions of the two contact areas between the spatial referents of the entities (and not directly the relative position of those spatial referents), all sur 'on' configurations will correspond to one of the three cases mentioned above. Apart from the geometrical characteristics of the relative position of the contact area, two important functional aspects arise in the semantics of sur 'on', namely the notions of "comparable categories" and "stabilization". Two entities X and Y belong to comparable categories if they have similar dimensions; this is noted as catcomp (X, Y). This property is calculated by comparing the projections of the spatial referents of X and Y on each axis of the triaxial system associated with an including entity Ζ (we create here a partial order relation on the projections). The projection on a particular axis can be more relevant than on the others, depending on the configuration of the entities involved. For example, in the case of a sur 1 'on 1' (sentence (9 a)) the respective sizes of the trajector and the landmark according to the vertical axis are relatively little constrained, whereas for usages of the type sur 3 'on 3' it is more difficult to admit an extension of the trajector along this dimension (sentence (9 b)). Thus, we use three different "catcomp" predicates (catcomp 1, catcomp 2, catcomp 3) corresponding to the three configurations of sur 'on'. Furthermore, functional properties and nature of the entities must be taken into account in the definition of "comparable categories". (9)

a. Le vase est sur la nappe. 'The vase in on the table-cloth.' b. *Le lustre est sur le plafond. *'The hanging light is on the ceiling.'

Stabilization (sometimes referred to as support) is another functional concept which actually plays a major part in the semantics of the preposition sur 'on'. In our system, the predicate stabilise (X, Y) indicates that an entity X stabilizes an entity Y and the following postulate shows that, contrary to the contact relation, stabilization is transitive:

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• VX VY VZ [stabilise (Χ, Υ) Λ stabilise (Υ, Z)] => stabilise (X, Z). Any entity stable in essence (e.g.: ground) is called intrinsic stabilizer and every entity which does not belong to that category has to be stabilized by another element in contact with it: • VX ~ι stabilisateur intrinseque (X) => 3 Υ ι (Υ = Χ) λ stabilise (Υ, Χ) Λ cont (sref (Y), sref (X))]. Specific postulates are also introduced in order to account for the interaction between the part-whole relation and the stabilization process. For example, if a piece Ζ of an entity Y stabilizes an entity X, then Y stabilizes X: • VX VY VZ [part (Ζ, Υ) Λ ^ p a r t (Χ, Υ) Λ stabilise (Ζ, X)] => stabilise (Υ, X). The concept of total stabilization is defined by saying that an entity Y totally stabilizes another entity X if, obviously, Y stabilizes X and if, furthermore, every entity Ζ disjoint from Y and directly stabilizing X is itself totally stabilized by Y. These various conditions are expressed by the following definition: • s t a b j o t (Υ, Χ) Ξ def [stabilise (Υ, Χ) Λ VZ [[cont (sref (Z), sref (X)) Λ stabilise (Ζ, Χ) Λ ~ i o (sref (Z), sref (Y)] => s t a b j o t (Υ, Z)]]. All these geometrical and functional tools enable us to state the following definition of the sur I configuration: • sur 1 (Χ, Υ) Ξ d e f c a t c o m p 1 (Χ, Υ) Λ c o n t i (sref (X), sref (Υ)) Λ stabilise (Υ, Χ). This definition shows that if X and Y have comparable categories, if the contact area of X (with Y) is higher than the contact area of Y (with X), and furthermore if Y stabilizes X, we can then deduce that X est sur Υ 'X is on Y \ This is the case of a person sitting on a chair or a glass standing on a table. The configuration sur 2 'on 2' where the trajector is on the same level as the landmark, is represented by a similar definition, the only differences to be found in the kind of contact (cont 2), in comparable categories (catcomp 2) and in stabilization, which, in this case must be total: • sur 2 (Χ, Υ) ξ

def

catcomp 2 (Χ, Υ) λ cont 2 (sref (X), sref (Υ)) λ s t a b j o t (Υ, X).

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It must be reminded here that a total stabilization of X by Y implies that every entity Ζ disjoint from Y and directly stabilizing X is itself stabilized by Y. This way, a TV set on a shelf which is fixed on a wall can be said to be on the wall. On the other hand, if the shelf has legs and is resting (at least partially) on the floor, the wall does not act as a total stabilizer (of the TV) and the TV can only be described as being on the shelf (the shelf being against the wall). The definition associated with the sur3 'on 3' configuration differs from that associated with sur2 'on 2' in the kind of contact between the entities involved and in the predicate catcomp3 (which is the most restrictive of the various "catcomp" predicates, particularly along the vertical axis): • sur 3 (X, Y) = DEF catcomp 3 (Χ, Υ) Λ cont3 (sref (X), sref (Υ)) Λ stab tot (Υ, Χ).

4.3.2. The preposition dans The preposition dans 'in', used in the given syntactic structure and in a concrete spatial sense, can refer to three different configurations between trajector and landmark. In the first configuration, probably the main case, dans links a trajector which is completely included in the interior of the landmark, as in the following examples. These cases are called "total dans". (10)

a. L'eau est dans la verre. 'The water is in the glass.' b. La ville est dans le brouillard. 'The city is in the fog.' c. Paul est dans I'ile.18 'Paul is in the island.' d. II y a un trou dans ce morceau de fromage. 'There is a hole in this piece of cheese.' e. L'ile est dans la mer. 'The island is in the sea.'

In the second one, the trajector is only partially included in the interior of the landmark. We refer to these cases as "partial dans". (11)

a. La rose est dans le vase. 'The rose is in the vase.'

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b. L'arbre est dans une petite cour. 'The tree is in a small yard.' Finally, dans can be used to describe cases of meronomy; the trajector is then a part of the landmark. These cases are called "dans part-of". (12)

a. Μ on cerveau est dans ma tete. 'My brain is in my head.' b. La Bretagne est en France. 'Brittany is in France.' c. Paul est dans le jury. 'Paul is in the jury.'

a. "total dans", "partial dans" and the "interior" function The first two configurations involve the notion of interior in addition to geometrical relations (inclusion and overlap). The interior of an entity must be distinguished: the entity and its interior must not be considered as a whole, since we want to differentiate between "total dans" and "dans part-of'. It is worth noting that the interior, being a space portion, behaves in a very different way from the object: an object included in the interior is not a part of this interior since it can be removed without altering the interior's identity and shape, whereas a (connected) object included in another is a part of it, fully contributing to its nature. However, the interior of an entity is completely determined by this entity, and we always perceive one with the other. This fact has led many authors (including us in an earlier work Borillo — Vieu 1989) to consider the interior as being a part of the entity and then to formalize dans or in as the mere inclusion or overlap between the spatial referents of the trajector and the landmark. The interior of an object can be of two types, depending on its ability to contain another object. If the object is a "container" (solid, offering resistance to gravity and lateral movements), 19 then its interior is defined by functional properties, in addition to geometrical ones. Otherwise, the interior can only be defined geometrically. The sentences (10 a) and (11 a) are examples of the "container" case. As Herskovits and Vandeloise have shown, the "place" of the interior of the glass (the space taken by the interior) cannot be defined only by removing the "place" of the glass in the convex hull of the "place" of the glass, which is a geometrical function. Indeed, we have already seen in Section 2. the situation of a fly and a glass that illustrates it (Figure 1). Restricting the scope of the convex hull to the containing

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parts of the object (as Vandeloise does) is not satisfactory either because in Figure 1, the fly would remain in the glass. We need to take each of the object's concavities into account and either "close" it or not, depending on its containing capability. In the second case, the object is not a "container"; this occurs with collections: la foule 'the crowd', with non-solid objects: I'eau 'water'; le brouillard 'fog' as in (10 b), and with solid objects occupying a volume evenly without filling it: I'arbre 'the tree' (as in I'oiseau est dans I'arbre 'the bird is in the tree'). In these cases, the spatial referent of the interior is determined by an "outline" function. It should be noted that here too, this function is not simply the convex hull. To begin with, the outline clings closer to the sides of the object than the convex hull does. What is more, a sizeable "hole" may be excluded; for instance, if a crowd forms a circle, what is situated dans le cercle 'in the circle' is not situated dans la foule 'in the crowd', i. e. the interior of this circle is not a part of the interior of the crowd. 20 There are also a few cases where the landmark is not a container, yet it is solid and it is not a collection. For instance, in la boite est dans le papier-cadeau 'the box is in the wrapping paper', the paper is not a container but is actually supported by the box. In these cases, the landmark completely surrounds its interior: the spatial referent of the interior is a connected part of the complement of the spatial referent of the landmark. The interior of an object is used to locate other objects as in sentences (10 a), (10 b) and (11a). It is also used to locate space portions as in (10 d). The interpretation of such a sentence is that the space portion (here the hole) is a part of the interior of the object (here the piece of cheese), the meronomy being a "piece-whole" case. It is not just an inclusion, for the hole is "attached" to the object just as the interior is, i. e., both are determined by the object. The interior of a location, as expressed in sentences (10 c) and (11 b), is determined by the location's boundaries and the vertical axis: it is the space portion situated above the ground portion considered. But its exact thickness is not determined. We cannot go too high: a plane flying over a town is not situated dans la ville 'in the town'. We cannot stay too low: a bird can be flying dans la plaine 'in the plain'. When the same noun phrase describes both an object and a location (a town, a forest) the interior of the location includes the interior of the object. It should be clear by now that the "interior" function does not embody a unique concept. However, we will not represent it in such detail because our perspective is not to generate discourses from perception and world

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knowledge, e. g., to decide what is the interior of a given object. Rather, we need to understand how the function interior behaves deductively. For this purpose, examining in detail what is conceived as an interior was helpful. We were led to the conclusion that for a first step, considering the interior as a whole was possible, as its deductive behaviour is almost homogeneous. We must admit that we are leaving some cases aside,21 but we hope that in the future we can model the various notions of interior more precisely. In addition to such cases, there are occurrences of "total dans" or "partial dans" that do not call for the use of an interior. The localization of an object in a space portion (e.g., la chouette est dans le creux de l'arbre 'the owl is in the tree's hollow') is just explained by the inclusion ("total dans") or overlap ("partial dans") of the object's spatial referent with the space portion's spatial referent. The localization of a location in another location, without any part-whole relation between the two is slightly more complicated. Sentence (10 e) is an example of such localization; Berlin-ouest etait en RDA 'West-Berlin was in D D R ' is another one. In these (few) cases, the landmark totally and tightly surrounds the trajector. Another type of location's interior for situating locations could be defined, but its interest would be limited because not every location situated in such an interior would be dans the first location. For instance, a field in the island is not in the sea. A location is "total dans" ("partial dans" is not possible) another location if all the boundaries of the trajector are also boundaries of the landmark. An important fact to note is that even though it is impossible to deal with the function "interior" on the geometrical level (containment and classification of entities are involved in its definition), the preposition dans cannot be reduced to the relation of containment. There are many examples without any containment between the landmark and the trajector: in la mouche est dans la vollere 'the fly is in the aviary', the cage does not prevent the fly from getting out of it, in any direction whatsoever; in (10 b), the city is unable to move anyway, but the fog does not even support it. The definition obtained for "total dans" is: • dst (X, Y) = d e f ((obj (Χ) Λ (obj (Υ) Ν loc (Υ)) Λ ρ (i (sref (X)), sref (int (y)))) ν (sp-port (Χ) λ obj (Υ) λ (mor-tt (X, int (Υ)) ν X = int (Υ))) ν (obj (Χ) λ sp-port (Υ) Λ ρ (i (sref (Χ)), sref (Υ))) Ν (loc (Χ) Λ loc (Υ) Λ front (Γ, sref (Χ), sref (Υ)) Λ front (Γ, sref (Χ), c (sref (ground)-sref (Χ)))))

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The definition for "partial dans" is: • dsp (X, Y) = d e f ((obj (Χ) Λ (obj (Υ) ν loc (Υ)) Λ ο (i (sref (X)), sref (int (y)))) ν (obj (Χ) Λ sp-port (Υ) Λ ο (i (sref (X)), sref (Y))) These definitions are accompanied by the following postulates describing the function "interior": • VX VY (Y = int (X) => ((obj (Χ) ν loc (Χ)) Λ sp-port (Υ) Λ det (Χ, Υ) Λ VZ (Z = int (X) => Υ = Ζ) Λ de (sref (X), sref (Y)) Λ (obj (X) => ρ (i (sref (Y)), preint (sref (X)))))) • VX VY VT VU VR ((T = int (Χ) Λ U = int (Υ) Λ part (Χ, Υ) Λ rest (Υ, X, R)) => ρ (sref (T), sref (U) + sref (R))) • VX VY VT VU VR ((T = int (Χ) Λ U = int (Υ) Λ ρ (i (sref (X)), sref (U)) => ρ (sref (T), sref (U) + sref (Y))) With the geometrical function "preint" designating the convex hull of an individual minus this individual, and the relation rest (Υ, X, R) expressing that R is the rest of the whole, Y, once its part, X, has been taken out. b. "dans p a r t - o f ' The preposition dans cannot be used to describe any meronomy. Vandeloise showed that we cannot say *mon nez est dans ma tete 'my nose is in my head'. We think that this fact is better accounted for by a "contrast principle" than by the explanation he gives (the trajector and the landmark should not share any boundary). This principle expresses that when someone uses a spatial expression to describe a meronomy, he (as well as the hearer) conceives the parts as detached from the whole and situates this part with respect to the rest of its whole. In the case of sentence (12 a), we can see that detaching the brain from the head creates an interior where we situate the brain. Detaching the nose from the head does not create such an interior: the nose cannot be in the head. With this principle, we can even explain why in sentences like l'escargot/la noix est dans sa coquille 'the snail/the nut is in its shell', the whole is described as being in one of its parts! Note that only "total dans" is then possible between the part and the rest of the whole. The same principle can be found in many sentences corresponding to the syntactic structure Ntraj est sur ILN de Nland, such as la poignee est sur le devant de l'armoire 'the handle is on the front of the

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cupboard'. The relation etre sur (here, "sur2") really links the handle and the front of the cupboard without its handle. However, this principle is only required for a "dans part-of" describing the meronomies "component-assembly" and "piece-whole", and only between objects. In all other cases every occurrence of a meronomy can be described by the preposition dans (as in sentences (12 b) and (12 c)). The definition of "dans part-of' is then: • dpt (X, Y) = d e f part (Χ, Υ) Λ ((obj (Χ) Λ (comp-ass (Χ, Υ) Ν mor-tt (Χ, Υ))) => 3Z (rest (Υ, Χ, Ζ) Λ dst (X, Z)))

4.4. Validation: Adequate inferences In the introduction, we presented our methodology: we wished to obtain a semantics allowing the same deductions as those accepted by human beings. The validation phase, i. e., the control of the adequacy between the two kinds of inferences, can now be done. We verify here the inferences a definition leads to by itself as well as some of the inferences obtained by combining the definitions of several markers or cases of the same marker. 4.4.1. Transitivity of the meronomies We have distinguished several meronomies on the grounds that we felt they were describing different situations. It is important to verify that these meronomies are really different in our system, i. e. that they behave in a different way. The part-whole relation has classically been taken as a unique relation and its transitivity assumed. But this has been proved wrong in Winston — Chaffin — Hermann (1987). The relation "member-collection" is not transitive in our system, and it is consistent with its behaviour in NL as we have already seen: Le Texas fait partie des USA. and Les USA font partie de l'ONU. =f> 'Texas is part of the USA.' 'The USA are part of UNO.' *Le Texas fait partie de l'ONU. *'Texas is part of UNO.' This relation can be combined with the relation "subcollection-collection": • VX VY VZ ((el-coll (Χ, Υ) Λ scoll-coll (Υ, Z)) => el-coll (X, Z))

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This is verified in NL. For instance, we have: La Belgique fait partie du Benelux, and Le Benelux fait partie de la CEE. => 'Belgium is part of Benelux.' 'Benelux is part of the EEC." La Belgique fait partie de la CEE. 'Belgium is part of the ECC." The relation "subcollection-collection" is itself transitive, as are the relations "component-assembly" and "piece-whole". We can even combine the relations "piece-whole" and "component-assembly" (in this order only), the result being another relation "piece-whole". But not every mixed combination is valid. As shown by Winston — Chaffin — Hermann, we cannot mix "component-assembly" and "member-collection". This is also the case in the system: Le bras de Jean fait partie de Jean.and Jean fait partie du jury. =t> 'John's arm is part of John.' 'John is a member of the jury.' *Le bras de Jean fait partie du jury. ""John's arm is part of the jury.' Note that in this case, we do not even have a "component-assembly" or "piece-whole" relation between John's arm and the jury, since the jury is a collective entity. The study of the various combinations and their validity can be found in Vieu (1991: 293-296). 4.4.2. The ILNs and sur The definitions given for several ILNs and for the preposition sur 'on' under the constraints of "instantaneity" and "unique locutor", result in the two following inferences: • VX VY VZ VN ((dessus (Ζ, Υ, Ν) Λ sur 1 (Χ, Ζ)) => 3U (haut (U, Υ, Ν) Λ sur 1 (X, U))) For instance, as common sense requires: La boite est sur le dessus de l'armoire. => 'The box is on the top extremity of the cupboard'. La boite est sur le haut de l'armoire. 'The box is on the top of the cupboard.' • VX VY VZ VU VN ((devant (Ζ, Υ, Ν) Λ sur 2 (Χ, Ζ) Λ derriere (U, Υ, N)) => ~ i s u r 2 (X, U))

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For instance: L^tiquette est sur le devant de la boite. => 'The label is on the front (extremity) of the box.' L'etiquette n'est pas sur le derriere de la boite. 'The label is not on the back (extremity) of the box.' The demonstrations of the theorems, along with several others of the same type are rather complex, in particular due to the comparison of contact areas in the semantics of sur. They are fully described in Aurnague (1991: 247-259).

4.4.3. The transitivities of dans First of all, studying the transitivities of dans shows that it was necessary to distinguish three cases: "total dans" is (in some cases) transitive, "partial dans" is not and the transitivity of "dans part-of" depends on the transitivity of the underlying meronomies. For instance: • "total dans" is transitive (between two objects and a location): Paul est dans la maison. and La maison est dans I'ile. => 'Paul is in the house.' 'The house is in the island.' Paul est dans I'ile. 'Paul is in the island.' • "partial dans" is not transitive; moreover, the combination of a "total dans" and a "partial dans" is not valid: L'abeille est dans la rose. and La rose est dans le vase. Φ· 'The bee is in the rose.' 'The rose is in the vase.' *L'abeille est dans le vase. *'The bee is in the vase.' Apart from the distinction in three cases, we have taken into account the class of each argument in the definitions of dans. This was important, as the transitivity of "total dans" depends on its arguments belonging to one or another class. The combination of a "total dans" between an object and a location with a "total dans" between two locations is not valid: Paul est dans I'ile. and L'ile est dans la mer. =t> 'Paul is in the island.' 'The island is in the sea.' *Paul est dans la mer. *'Paul is in the sea.'

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The combination of a "total dans' between a space portion and an object with a "total dans" between two objects is not valid, due to the presence of a meronomy ("piece-whole") in the first relation: II y a un trou dans le drap. and Le drap est dans le tiroir. Φ· 'There is a hole in the sheet.' 'The sheet is in the drawer.' *// y a un trou dans le tiroir. *'There is a hole in the drawer.' The complete study of all the possible combinations (about thirty) can be found in Vieu (1991: 307-313), along with the study of combinations between dans and meronomies (not only those expressed by dans). As it has just been seen, there are many combinations which are not valid, even though many authors have until now taken the transitivity of dans (or in) for granted, defining it only by the relation of inclusion.

5. The pragmatic level We have just seen that the adequacy was rather good between what the system is able to infer, and the deductions a human can make. However, this adequacy is not perfect, because up to now we have only taken into account the semantic aspects of the spatial expressions and, as seen in Section 2., pragmatic phenomena have quite an important influence on their meaning.

5.1. Restrictions on inferences and additional information For instance, let us go back to example (6) from Section 2. The system (made up of the geometrical and functional levels) states that the car's engine is in the garage, whereas a human would not. Therefore, we have to introduce in the system the underlying pragmatic principles people use, in order to filter out the relations inferred "wrongly" (they are not wrong but cannot be said). At the same time, the same principles can be used to deduce (by implicatures) more information than there actually is in the discourse. We will now explore the pragmatic principles involved in the meaning of spatial expressions, although we do not claim to be exhaustive. These principles are not really formalized here, as this part of the work is not completed at the moment.

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5.1.1. The "fixation principle" This principle, first introduced in Vandeloise (1986), expresses that the typical use of an object "fixes" some of its characteristics. For instance, the front and the back of a car are "fixed" by the usual direction of its motion: the front of the car remains the same even when the car is going backwards. We have seen in Section 4.1. that many intrinsic orientations are determined in this way. This principle is also at work when talking about the interior of an object. The interior of a bottle stays the same even when the bottle is handled upside down so that it cannot hold any liquid. Moreover, some of the containing concavities of an object can be rejected as part of its interior on the grounds that there exists another concavity which corresponds to the "fixed" interior. For instance, even if we accept sentence (13 a) to describe the situation where an upside-down bottle has liquid which remains in the hollow of its underside, we will not accept (13 b). (13)

a. II y α de l'eau dans le dessous de la bouteille. 'There is water in the underside of the bottle.' b. II α de l'eau dans la bouteille. 'There is water in the bottle.'

In fact, the inference from (13 a) to (13 b) is valid in the system since the interior of any part of an object is a part of the object's interior. Therefore, for the application of dans, we must check whether, in the world-knowledge base a "fixed" interior is specified for the landmark and whether the trajector is included in this fixed interior. However, nothing is certain here: a "marked" context may accept the use of (13 b); that is why we could not take into account the "fixed" interiors earlier on the functional level. The same actually occurs for any phenomenon belonging to the pragmatic level: we can always find a particular context where the effects of a principle are contradicted. Here is another (extreme) example of the effects of the fixation principle. The following transitivity, correct on the functional level, must be ruled out here: Le crayon est dans la main. and La main est dans le gant. => 'The pencil is in the hand.' 'The hand is in the glove.' ?Le crayon est dans le gant. ?'The pencil is in the glove.' A phenomenon related to this principle must be mentioned. Some objects are not conceived as containers, so they are not usually used as

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a landmark for a dans expression. For instance, a table is not a container although it may have a drawer: the sentence the knife is in the table is difficult to accept in a non-marked context. Certain restrictions with some locations are also difficult to explain: one cannot say *dans la plage 'in the beach', *dans le terrain de football 'in the football field' ... All of the preceding concerned the restrictive aspect of the fixation principle. As a matter of fact, it can also generate some additional information. If sentence (13 b) is present in the analysed discourse, we will have to assume, in the case of a "normal" context, that the water is in the fixed interior of the bottle. The same occurs for the sentence the pencil is in the glove, and indeed for many expressions, we even "choose" the most suitable part of the interior of an object: Mary is in the car strongly suggests that she is sitting in the passenger space and not in the boot. It must be reminded here that this kind of non-certain information has to be handled by a non-monotonic logic. 5.1.2. The principle of maximum trajector This principle, a particular case of H. P. Grice's maxim of quantity (Grice 1975), has already been introduced in Section 2. The object localized by a spatial expression is usually the biggest object we can localize using the same expression. This principle must be used to restrict the results of the following inference rule, which is obviously true on the functional level: • VX VY VZ (dst (Χ, Υ) Λ obj (Χ) Λ part (Ζ, X)) => dst (Ζ, Y)) As we already said, the "principle of maximum trajector" can also be used to add information, stating that in a normal context, for every object localized by a spatial expression, any object it is a part of is not localized the same way. A word must be said about the application of this principle to spatial expressions involving a "partial dans". In fact, the contrary should almost be stated, since the relevance of these expressions decreases as the portion of the trajector totally included in the landmark gets smaller (in proportion). Several rules governing the acceptability of a "partial dans" must be taken into account, since, on the functional level, any partial inclusion between an object and the interior of another is described as a "partial dans". One of these rules states that if there is a typical function between two objects, the object that is situated in the other being also a part of a third one, we cannot express that this third object is "partial dans" the second. For instance, le doigt est dans le de 'the finger is in the thimble'

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implies on the functional level, la main est dans le άέ 'the hand is in the thimble', which is clearly not acceptable and discarded by this rule. We can then see that the pragmatic level has to apply several rules, which are contradictory in some situations. For the moment, it is quite difficult to establish priorities; as said before, the pragmatic level is still in the process of being studied.

5.1.3. The principle of minimum landmark As the general purpose of a spatial expression is to help the hearer in finding the object localized by the expression, the maxim of quantity requires the use of the best localizing landmark. We could conclude that the smaller the landmark, the easier the finding (the hearer knowing where it is). For instance, if Peter has a key in his pocket and Peter is in the kitchen, it is clear that the key is in Peter's pocket is much better than the key is in the kitchen.12 This principle would actually suggest that modelling any kind of transitivity is helpless. What really occurs here is that the last sentence is misleading because Peter (then, Peter's pocket) is not more likely to be in the kitchen than in another room, and someone looking for the key in the kitchen would not think about looking in Peter's pocket. It must be noticed that, if instead of Peter's pocket, the key was in a drawer or a dish, or anything that does not move around by itself, the key is in the kitchen would be totally acceptable. Moreover, such a principle is not desirable because there are some cases where the position of the smallest landmark is determined by the trajector itself. For instance, the gift is in the wrapping paper is not a "good" sentence to help locate the gift. So, this principle is not exactly what is needed here, although we must admit that, in general, if the system is to answer a question like where is X?, it should give the smallest known location. We can then see that Grice's maxims cannot directly be applied. Each of them must be examined for the particular domain of spatial expressions.

5.1.4. Relevance Relevance is a vague concept, which could also cover the preceding principles. We want to consider several phenomena governing the acceptability of a spatial relation describing a situation with respect to

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another relation (up to now, the principles described were about the choice of the arguments of a given relation, not the relation itself). Several relations may compete. For instance, in the case of a bowl turned upside down over an apple, the prepositions dans 'in' and sous 'under' could both describe the situation. However, sous is choosen because the apple and the bowl are not in the situation typically described when using dans, one in which the bowl contains the apple. Containment is not a necessary condition for the use of dans, but it obviously makes it more relevant. Similarly, one is likely to assume that the sentence la pomme est dans le bol 'the apple is in the bowl' describes a situation where the bowl contains the apple. However, containment is not assumed when the typical situation does not involve containment: la main est dans le gant does not suggest that the glove controls the hand's movements. Here again, we need world knowledge about typical situations. It must be noted that typicality and relevance are both concepts that rely heavily on the function of the objects: the function of a bowl is to contain, whereas the function of a glove is to surround a hand in order to protect it. Therefore, the existence of the functional level is crucial for the pragmatic one.

5.2. Additional inferences A spatial expression can be used to describe a situation where in fact its semantics is not totally verified. For instance, a book is usually said to be "on the table" even though the book is on another book, thus not in contact with the table. The loosened definition of " s u r l " , by dropping the contact, gives rise to a kind of "inference", namely the transitivity of "surl". These inferences are not real ones and could not be included on the functional level. Because the relation between the two books is not relevant, one can "forget" about it and put the top book directly in relation to the table. A. Herskovits shows in Herskovits (1982) that, if instead of two books one on top of the other, it was a lid on a tea-pot, it would be impossible to "infer" that the lid is on the table. In this case, being on the tea-pot, the lid fulfils its function with respect to the teapot, so it is relevant for a lid to be on a tea-pot. Consequently, this fact cannot be "forgotten". The underlying pragmatic principles involved in this example are the maxims of relevance and of quantity. If a fact is relevant (in this case the lid is on the pot), to express a less precise fact

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(in this case the lid is on the table) somehow implies that the precise fact is not verified in the given situation. We must mention that it was impossible to deal similarly with "partial dans", that is considering that loosening an inclusion into an overlap is a pragmatic phenomenon, because a "partial dans" is not always used to focus on the part of the trajector which is entirely contained in the landmark. For instance, in la rose est dans le vase 'the rose is in the vase', the part of the rose which is out of the vase cannot be "forgotten" for it is the main part of it! Even though the separation of pragmatics from semantics is not universally agreed on, we hope to have shown how and why separation is needed in our system. We are convinced that without getting into such detail, it would be almost impossible to formalize the meaning of spatial expressions, i. e. to model the deductions allowed by common sense.

6. Conclusion Formal semantics of NL expressions referring to space must integrate the different aspects which underlie their semantics. As shown with the analysis of dans 'in' and sur 'on', mere geometrical data is insufficient to express the semantics of such lexemes, and functional or pragmatic aspects must be also taken into account. These observations have led us to build a three-level system (geometrical, functional and pragmatic) with which we can represent the meaning of spatial expressions and make deductions. This modular construction thus permits us to come closer to the natural reasoning expressed in the discourse and, from this point of view, constitutes a real cognitive approach. Beyond simple comparison between deductions made and reasonings of the speaker, we contemplate now validating our system (in collaboration with psychologists) by verifying through various experiments the psycholinguistic anchorage of the concepts and primitives introduced (M. Borillo 1991). It must be stressed that the class of lexemes for which we gave a formal definition (namely the prepositions dans 'in' and sur 'on' and ten ILNs) seems to be wide enough to encompass the principal concepts underlying the expression of space in NL. Consequently, we think that the semantic content of most spatial expressions can be represented within the framework of this threelevel system, perhaps with modifications or additions. Another interest of this modular approach lies in the fact that the geometrical module

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which is specially suited to N L processing is really independent of it because the individuals handled there have only spatio-temporal properties. The characteristics of this geometrical structure make it very useful for other fields of Artificial Intelligence than NL. Indeed, a similar approach is used in Randell — Cohn (1989) to model naive physics processes such as phagocytosis and the behaviour of a "force pump".

Acknowledgements The authors would like to thank Mario Borillo for his continuing guidance. They are also very grateful to Andree Borillo for her judicious advice. This work was carried out at IRIT, within the framework of two Ph. D. theses, under the direction of Mario Borillo.

Notes 1. Here we are in opposition to Vandeloise's position who takes an all-functional point of view. But looking closer at his proposition, purely geometrical aspects are included in the description of some of his "family resemblances". 2. By particular cases, we mean the different definitions given for each expression in Section 4. For instance, "total dans", "partial dans" or " d a n s / p a r t - o f ' for the expression Ntraj etre dans Nland. 3. Mereology was introduced by S. Lesniewski (1927-1931) and taken up by various researchers among whom H. Leonard — N. G o o d m a n . However, people often directly refer to Leonard — Goodman (1940), probably for reasons of accessibility and readability. 4. It must be noted that it is not possible to define the closure of the universal individual a*, because the complement of a*, which should be the null element, does not exist in this theory. 5. Associating a system of three orthogonal axes to a sphere reveals its three-dimensional nature and means that, interacting with it, a person can define a three-dimensional system. However, because of the regularity of its shape, the exact position of the system of axes with respect to this sphere cannot be determined. 6. An entity X immediately contains an entity Y if pp (sref (Y), sref (X)) and there is no Ζ such that pp (sref (Y), sref (Z)) and pp (sref (Z), sref (X)). 7. As we already said, part-whole relations cannot be reduced to the spatial inclusion and require various functional notions to be taken into account. We will explain further (in Section 4.2.2.) how we define, on the functional level, various categories of part-whole relations that allow us, for example, to distinguish functionally and geometrically well "delimited" components of an entity (comp-ass (X, Y)) from arbitrary pieces of it (mor-tt (X, Y)). The relation part (X, Y) covers all the cases.

A three-level approach to the semantics of space 8.

9.

10.

11. 12.

13.

14.

15. 16.

17,

18.

19.

20.

21,

22.

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In fact, another orientation predicate noted "orient 1" exists in our system. It is intended to deal with the relations between abstract directions like those occurring between the systems of axes associated with the different parts of the same object. With this predicate, we can model the inheritance process of a deictic orientation between an object and one of its parts. Consequently, the nature of the orientation denoted by the predicate natur or ((X, Axe, Dir), (A, D), V, N) can be computed by simply comparing the oriented entity X and the orientor entity V in the predicate orient. There are few exceptions: les arenes 'the amphiteatre' refers only to a single object. In this structure, it is then impossible to make the difference between a singleton and its unique member. We could not find any evidence of NL's behaving otherwise. Only the join operator is useful with respect to mass term properties. This semi-lattice is non-atomic in G. Link's theory: he assumes that there are no minimum portions of a given substance. To fully understand this logic, the reader is strongly invited to read Link (1983). As for mass terms' behaviour, the reader may refer to Pelletier — Schubert (1989), a good synthesis of the abundant literature on this topic. This is not the case for any mass term. For example, it is impossible to determine what is an elementary particle of "dirt", "mud", "milk shake". However, the "set approach" has been taken by a number of authors such as Laycock (1972). Actually, there are two more classes of entity: portions of matter and substances. They are needed to represent mass terms and the two meronomies we have set aside. The space portions could be considered as being of the same type as spatial referents, that is, as being no entity, since their spatial referent as well as all of their properties derive from those of objects or locations. This position was not chosen because we can talk about space portions on the same level as for other entities, and we can even state some of their properties, e. g., the cave is dark and humid. The position on the vertical axis of an element X with respect to an element Y is calculated by comparing the projection intervals of X and Y on an axis (Z, Axe) (of an entity Z) deictically oriented as a vertical axis. With nouns referring to types of location like countries or regions, the use of dans is impossible and en 'in' has to be used (e. g., Paul est en France 'Paul is in France'). Because this fact cannot be explained on semantic grounds, we will deal with these cases as well. This property is actually complex and goes deeply into several "clusters" of naive physics. For example, friction is involved in the situation of a bulb contained by a socket. Here again, to be able to distinguish between several entities having the same spatial referent can be useful. Note that the circle is not linked to the plural entity which the crowd is linked to, so it is not a collection. For instance, from la ville est dans I'enceinte 'the city is in the (surrounding) wall' and ienceinte est dans les arbres 'the wall is in the trees', the sentence la ville est dans les arbres 'the city is in the trees' does not follow, and yet our model does infer this fact. The characterisation of an interior we give actually covers quite well all cases except the case of an "outline" function applied to a landmark having a "hole" (in this example, it is the case for the trees). This example was provided by E. Audureau.

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References Allen, James 1984 "Towards a general theory of action and time", Artificial Intelligence 23, 2: 123-154. Aurnague, Michel 1991 Contribution a I etude de la semantique formelle de l'espace et du raisonnement spatial: la localisation interne en frangais, simantique et structures inferentielles. [Unpublished Ph. D. dissertation, Toulouse: Universite Paul Sabatier.] Bach, Emmon 1986 "The algebra of events", Linguistics and Philosophy 9: 5-16. Bäuerle, Rainer — Urs Egli — Arnim von Stechow (eds.) 1979 Semantics from different points of view. Berlin: Springer. Bäuerle, Rainer — Christof Schwarze — Arnim von Stechow (eds.) 1983 Meaning, use and interpretation of language. Berlin: de Gruyter. Borillo, Andree 1988 "Le lexique de l'espace: les noms et les adjectifs de localisation interne", Cahiers de Grammaire 13: 1-22, Toulouse: UTM. Borillo, Mario 1991 "Semantique de l'espace et raisonnement spatial", in: Proceedings of the Colloque Sciences de la Cognition. Paris: MRT. Borillo, Mario — Laure Vieu 1989 "Elements pour la formalisation du raisonnement spatio-temporel naturel", in: Proceedings of the 7th Congres RFIA. 695-709, Paris: AFCET. Bunt, Harry 1985 Mass terms and model-theoretic semantics. Cambridge: Cambridge University Press. Clarke, Bowman 1981 "A calculus of individuals based on 'connection'", Notre Dame Journal of Formal Logic 22, 3: 204-218. 1985 "Individuals and points", Notre Dame Journal of Formal Logic 26, 1: 61-75. Cole, Peter — Jerry Morgan (eds.) 1975 Syntax and Semantics 3: Speech Acts. New York: Academic Press. Gabbay, Dov — Franz Guenthner (eds.) 1989 Handbook of philosophical logic. Vol. 4. Dordrecht: Reidel. Grice, Paul H. 1975 "Logic and conversation", in: P. Cole — J. L. Morgan (eds.), 41-58. Hayes, Patrick 1985 "The second naive physics manifesto", in: Hobbs, J. R. — Moore, R. C. (eds.), 1-36. Herskovits, Annette 1982 Space and the prepositions in English: Regularities and irregularities in a complex domain. [Ph. D. dissertation, Stanford University.] 1985 Published at Cambridge: Cambridge University Press. Hobbs, Jerry — Robert Moore (eds.) 1985 Formal theories of the commonsense world. Norwood, NJ: Ablex.

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Kamp, Hans 1979 "Events, instants and temporal reference", in: Rainer Bäuerle — Urs Egli — Arnim von Stechow (eds.), 376-417. Lang, Ewald 1990 "Primary perceptual space and inherent proportion schema: two interacting categorization grids underlying the conceptualization of spatial objects", Journal of Semantics 7: 121-141. Laycock, Henry 1972 "Some questions of ontology", Philosophical review 81: 3—42. Leech, Geoffrey 1969 Towards a semantic description of English. London: Longman. Leonard, Henry — Nelson Goodman 1940 "The calculus of individuals and its uses", The Journal of Symbolic Logic 2, 2: 45-55. Lesniewski, Stanislaw 1927-1931 "Ο podstawach matematyki" [On the foundations of mathematics], Przeglad Filosoficzny [Philosophical Review]. Vols. 30-34. Link, Godehard 1983 "The logical analysis of plurals and mass terms: A lattice theoretical approach", in: Rainer Bäuerle — Christoph Schwarze — Arnim von Stechow (eds.), 302-323. Miller, Georges — Phillip Johnson-Laird 1976 Language and perception. Cambridge, MA: Belknap Press of Harvard University Press. Pelletier, Francis — Lenhart Schubert 1989 "Mass expressions", in: D. Gabbay - F. Guenthner (eds.), 327 407. Pick, Herbert — Linda Acredolo (eds.) 1983 Spatial orientation: Theory, research and application. New York: Plenum. Quine, Willard 1960 Word and object. Cambridge, MA: MIT Press. Randell, David — Anthony Cohn 1989 "Modelling topological and metrical properties in physical processes", in: Brachman — Lesveque — Reiter (eds.), Proceedings of the first international conference on principles of knowledge representation and reasoning, 357-368. Talmy, Leonard 1983 "How language structures space", in: H. L. Pick — L. P. Acredolo (eds.), 225-282. Vandeloise, Claude 1986 L'espace en franfais: semantique des prepositions spatiales. Paris: Seuil — Travaux en Linguistique. Vieu, Laure 1991 Semantique des relations spatiales et inferences spatio-temporelles: une contribution ά l'etude des structures formelles de l'espace en langage naturel. [Unpublished Ph. D. dissertation. Toulouse: Universite Paul Sabatier.] Whitehead, Alfred 1929 Process and reality. New York: MacMillan. Winston, Morton — Roger Chaffin — Douglas Herrmann 1987 "A taxonomy of part-whole relations", Cognitive Science 11: 417—444.

Computing the meaning of localization expressions involving prepositions: The role of concepts and spatial context Simone

Pribbenow

1. Introduction: Localization expressions One open problem in the area of Artificial Intelligence is the formalization of a commonsense theory of space (cf. Hobbs — Moore 1985; Davis 1990). What is needed is a theory of spatial reasoning that describes how people solve spatial problems like orientation and pathfinding or manipulation of objects in everyday contexts, and how people cope with the spatial attributes of objects like form and location. This spatial reasoning is of special interest because it forms the intersection of different tasks such as vision, the use of cognitive or geographical maps, physical reasoning, and — last but not least — natural language processing. A commonsense theory of space must provide the representation and processing of the basic concepts that are needed for reasoning. Natural language expressions concerning spatial aspects give us good access to the concepts which underly the human dealing with space. Thus theories for the processing of spatial expressions can be used as building blocks for a commonsense theory of space. Therefore, it is expected that the spatial concepts and principles developed in this paper can not only be used for natural language processing but also for other tasks involving space. This paper is concerned with one aspect of spatial reasoning, the location of objects. It presents a computational theory of German natural language expressions that describe the location of objects by stating the spatial relations between them. In the following, I call these expressions localization expressions thus focussing on their function and abstracting from their different linguistic manifestations. In their simplest form, localization expressions look like the expression in (1). (1)

das Pferd auf der Rennbahn 'the horse' 'on' 'the race track' LE REL RO

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The first object, the horse, is the entity to be located or LE for short. 1 This object is located with respect to the second object, the reference object or RO, in example (1) the race track. The spatial relation REL between the two entities LE and RO corresponds to the preposition on. The following three examples (2)-(4) show the whole range of localization expressions by giving typical examples for the different classes of localization. (2)

Die Konstanzer Universität liegt am Bodensee. 'The university of Konstanz is located by the Bodensee.'

(3)

Die Protestkundgebung der Studenten fand vor dem Hauptgebäude statt. 'The student demonstration took place in front of the main building.'

(4)

Anschließend zogen die Studenten zum Rathaus. 'Afterwards, the students marched to the city hall.'

The first example (2) describes the localization of an object — here the university of Konstanz — and the second (3) that of a situation, the demonstration. 2 The sentence (4) provides information about the motion of the students by localizing the end of their march at the city hall. The first two cases (2) and (3) describe static localization, because the entities involved as LE are not moving, or their motion is not relevant in the current context. A localization expression is called a dynamic localization if it localizes the source, goal (as in (4)), route or direction of a path. In most cases the path is induced by a passive or active motion. But it is worth mentioning that objects of a special elongated form such as streets and rivers (see (4 b)) or a collection of objects forming a line (see (4 c)) can also induce a path. (4)

b. Die Straße führt zum Stadtzentrum. 'The street leads to the city center.'

(4)

c. Der Zug der Demonstranten reicht von einem Ende des Campus bis zum anderen. 'The line of demonstrators reached from one end of the campus to the other.'

In general, a localization expression describes the position of an entity, which can be an object, a situation or a path. This is normally done with

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respect to another object, the reference object. It is also possible but in everyday contexts only seldom practable to use coordinates as in (5). (5)

Unser Schiff liegt auf 38°49' nördlicher Breite, 15° 17' östlicher Länge. O u r ship is located at 38°49' north, 15° 17' east.'

Up to now, a preposition is used in all examples to indicate the spatial relation between LE and RO. Although prepositions are likely to be the most important way to denote spatial relations, adverbs provide another way of describing localization (see (6 a) and (6 b)). Deictic expressions, in German hier, da, dort 'here', 'there', are one category of adverbs. They can be used to describe static localizations (see (6 a)), or dynamic ones if the affix hin '-ward' is added. (6)

a. Hier fand der Protestmarsch statt. 'The demonstration took place here.'

Other alternatives are adverbs which denote directions as in sentence (6 b), or correspond to prepositions, such as vorne, vor 'in front', 'in front of. (6)

b. Die Studenten zogen stadteinwärts. 'The students marched toward the city.'

In localization expressions using adverbs as (6), the reference object is not given explicitly but must be inferred from the — textual or situational — context. On the grammatical level, prepositions and adverbs are conflated by the classification of adverbs as intransitive prepositions. Intransitive prepositional phrases are phrases without explicit internal argument, in the case of local phrases without explicitly mentioned reference object. The missing internal argument — the RO of the localization expression — must be inferred from the context. Assuming that it is in the processed phrases possible to infer the RO, I will not make any distinction between localizations described by means of prepositions and those involving adverbs in the remainder of this paper. In the following sections, I will present the computational interpretation of localization expressions. The processing is embedded in a text understanding system with the additional ability to answer questions. The task of the processing is to build up an internal model of the text which is similar to a "mental model" in the sense of Johnson-Laird (1983). Localization expressions determine that part of the model that deals with the spatial relations between objects. The internal model is used for

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further problem solving, in our case for answering questions. Other spatial tasks for which localization facts could be useful are pathfinding or the generation of spatial descriptions. In this paper, I will concentrate on the representation and the construction of the internal model. The question answering is only described briefly; for more details see Pribbenow (1990). I assume a two-level semantics consisting of a linguistic level concerned with language-specific features and a conceptual level based on a language-independent set of (spatial) concepts. This paper concentrates on the conceptual processing of localization expressions which uses a combination of propositional and picture-like formalisms. I will not discuss semantic aspects in detail; examinations which focus on that subject or on the relation between semantic and conceptual representation can be found for example in Bierwisch (1988), Wunderlich - Herweg (1991), or Klein (1990). The next section discusses the basic assumptions which leads to the design of a system adequate for processing spatial aspects and the spatial concepts underlying the interpretation of localization expressions. The third section describes the phenomenon of localization and its formalization in terms of localization areas. Each localization expression is interpreted by an area which consists of a primary area characterized by spatial concepts and priorizations, which rely on expectations where the LE can most probably be found. The fourth section presents the conceptual interpretation of localization expressions based on those areas. My goal is to show how textual and situational context influences the interpretation of localization expressions and how this contextual influence can be integrated in the computation of the (conceptual) meaning of localization expressions.

2.

Design and conceptual basis of the system

2.1. Basic assumptions The design of a system that computes the meaning of localization expressions is guided by the following three assumptions from linguistics and psychology: A. a two-level meaning representation consisting of a semantic and a conceptual level;

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B. the existence of a set of language-independent spatial concepts on the conceptual level; and C. dual (hybrid) processing on the conceptual level. The first assumption A. is based on the work of Bierwisch (1983) and Bierwisch — Lang (1987) who present a general paradigm for the processing of natural language, not only for spatial expressions. The theory assumes two levels of meaning representation: a semantic level that focuses on the language itself and a conceptual level which is based on language-independent general concepts. On the semantic level, underdetermined abstract representations are constructed which normally involve variables. A transformation function translates these semantic representations into conceptual meaning representations, e.g., by instantiating the variables and interpreting the abstract semantic labels by concepts. This makes it possible in a two-level semantics to establish a unique representation for each lexical item (on the semantic level) as well as a fully specified meaning representation that reflects contextual influences (on the conceptual level). For my work, the theory of Bierwisch — Lang has the advantage of allowing me to concentrate on the conceptual level and ignore the semantic level. Thus I can work out the processing relevant for a commonsense theory of space without having to worry much about language-specific features. Another advantage of the two-level approach is that it reflects the — assumed — modularity of cognitive behavior. According to the thesis of modularity, the linguistic system (to which the semantic level is assigned) exists independently of but in interaction with the conceptual system (to which the conceptual level is assigned). While the linguistic system focuses only on the features of language, the conceptual system forms the interface between various subsystems of human cognitive behavior, e.g., the different perceptual systems, the motor system, the linguistic system, and so on. To be able to function as an interface, the conceptual system must include for each domain a set of concepts which is used by the relevant subsystems but which is independent of each specific subsystem. Assumption B. specifies this observation for the spatial domain: there exists a set of spatial concepts which is accessed by subsystems with spatial tasks, e. g., by the linguistic system for processing spatial expressions, but which is independent of each single subsystem as the linguistic one. Therefore the spatial concepts can be characterized as language-independent even so they guide the processing of natural language expressions concerning spatial aspects. The most important concepts for localization are presented in the next section (2.2.).

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Concerning the processing of space, the relevant subsystems besides the linguistic system are the vision and the motor system. All these subsystems are seen as independent modules which interact with each other via the conceptual system by using overlapping sets of spatial concepts. This interaction between the subsystems via common concepts can explain why we are able to speak about our motions, describe the relations between objects we see, or carry out commands concerning spatial tasks. The last assumption C. is concerned with the representation and processing of spatial knowledge, e. g., the spatial concepts. To allow for effective and cognitively adequate processing, a representation formalism suitable for space is needed. By now it is generally agreed that for solving certain problems, especially in the spatial domain, mental pictures are used by humans. Following the dual-coding theory (Paivio 1983), there exist at least two independent formalisms for representation and problem solving, one propositional and one picture-like. In the terminology of Artificial Intelligence, systems consisting of more than one formalism are called "hybrid" (Brachman — Gilbert — Levesque 1985). The picture-like formalism used for representing space should have properties of mental pictures, e.g., it should be sketchy. One possible realization are depictorial representations (Kosslyn 1980) which could be used as a cognitively adequate representation of space (Habel 1987). The relevant advantage of picture-like and therefore also of depictorial formalisms is that they "simulate" space. Picture-like formalisms automatically ensure topological and geometrical properties of space and each picture is complete with respect to the spatial relations between all objects in the picture once it is created. The last aspect makes the computation of non-explicit relations very efficient using pictures, whereas a lot of inferences are sometimes necessary to do the same in a propositional system (see Lindsay 1988 for more details). Figure 1 shows the design of a system for text understanding and question answering that respects the three assumptions A.-C. This system consists of linguistic and conceptual processing, realizing the semantic and the conceptual level. The interface to the user is given by the input/ output modules. The linguistic subsystem includes the syntactic and the semantic processing and uses mainly linguistic knowledge such as grammar rules or lexical entries and in some cases also world knowledge, e. g., terminological information. The conceptual system consists of a propositional and a depictorial subsystem and uses only the world knowledge. This knowledge consists of terminological knowledge in particular in-

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eluding knowledge about object categories, different types of situations, and (spatial) concepts, knowledge about individual entities, and (procedural) knowledge about the processing. input

output

linguistic processing (syntactic and semantic)

conceptual processing prepositional subsystem

world knowledge

Η

(terminological individual procedural)

depictorial subsystem

τ

Τ L ι — I II

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perceptual system

. JI

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motor system

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Figure 1. A system for processing localization expressions

The assumption A. of a two-level meaning representation is reflected in the separation of linguistic and conceptual processing. The world knowledge includes the language-independent concepts (assumption B.). If necessary, the conceptual module can serve as an interface to other subsystems which are illustrated in Figure 1 by dotted blocks and arrows. According to C., conceptual processing works on different subsystems: one propositional, e. g., realized by a logical formalism, and one depictorial, e.g., realized by cell matrices. One possible implementation of such a system is the LEU/2-system, a prototype developed by the IBM in co-operation with five universities (see Herzog — Rollinger 1991 for a description of the system and its underlying theories). The work presented in this paper is integrated in the LEU/2-system.

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2.2. Basic concepts for localization The concepts concerning localization form only a part of the conceptual basis for processing space. They interact with other spatial and nonspatial, e. g., functional, concepts. It should be noticed that the following set of concepts is most likely not the only possible base for localization. 3 But it is one that is sufficient for computing the meaning of localization expressions. The concepts under consideration form two classes: — general localization principles which control the process of localization itself and — localization concepts which are used to describe concrete localizations.

General localization principles The most important principles are those of the different roles of RO and LE and of the influence of the situational context. As stated in the introduction, a localization expression involves two entities, the reference object RO and the entity to be located LE. For the process of localization the different roles of LE and RO lead to different views on RO and LE (see Talmy 1983; Herskovits 1986).4 The reference object forms the basis of the localization and must therefore be able to function as a landmark. 5 A localization process can only be successful if the position of the RO is known in advance or can easily be detected. For that reason, the reference object is normally more relevant and perceptually conspicious, e.g., bigger, than the LE. Often, special parts of the RO such as one side are focussed to narrow the space under consideration. This is done using conceptualizations of the reference object (see the explanation of object concepts above). In contrast, the LE is typically a less salient, smaller object without further conceptualization. The different roles of the two objects reflect that in general a localization expression cannot be inverted by simply exchanging RO and LE, as example (7) shows. (7)

a. die Straßenlaterne beim Park 'the lamp near the park' b. ?der Park bei der Straßenlaterne ?'the park near the lamp'

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In a situation as described in (7), the lamp can be located relative to the park. But it does not seem to make sense, even if it is grammatically correct, to describe the position of the whole park by relating it to a lamp. This is only possible for parts of the park, e. g., a piece of the wall surrounding the park. The second general localization principle concerns the influence of the situational context on the localization process. According to this principle a localization expression can only be interpreted or generated by taking into account the concrete situation. Sometimes the contextual knowledge is obligatory, for example if adverbs or extrinsic expressions (expressions needing a "secondary reference object" (cf. Talmy 1983: 245) for their interpretation) are involved. As stated in the introduction, localization expressions involving adverbs have no explicit RO; it must be inferred from the context. For the analysis of extrinsic expressions the relevant secondary RO, e.g., the spatial origo in deictic cases, must be provided by the spatial situation under consideration. The following section about localization concepts provides examples of various secondary ROs extrinsic expressions could refer to. In other cases the situational context as far as it is known influences the interpretation process. Examples are objects which restrict the possible location of the LE by functioning as barriers or competing objects (a definition is given in Section 4.2. C).

Localization concepts For the description of a concrete localization, e. g., given by a localization expression, two different classes of concepts are needed: object and distance concepts. The object concepts allow for different views on a (perhaps complex) object, which are in the following called object conceptualizations. The distance concepts describe the (qualitative) distance between two objects. Some of the object concepts describe requirements on an object concerning its form, dimensionality or plurality. Certain spatial relations like entlang 'along' or um 'around' assume that the LE can be conceptualized as a line with a special relation to the RO. The dimensionality of the reference object restricts the choice of the spatial relation. If the RO is viewed as a two-dimensional object like a field a motion from one end of the RO to the other is described with über 'across', whereas if the RO is seen as a three-dimensional object like a house durch 'through' must

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be used. Although natural objects are always three-dimensional, most objects allow for different conceptualizations of their dimensionality according to the context. The concept of plurality is only important for a small number of relations which need a complex RO, such as zwischen 'between' or inmitten 'amongst'. More important than the concepts for describing requirements are those object concepts that provide conceptualizations which focus on parts of an object. The focussing could be done by using the concept of relevance of parts or the concept of orientation via reference systems. The conceptualization of an object with respect to the relevance of parts is controlled by functional concepts such as containment, different kinds of support or part-of relations. These functional concepts are involved if certain prepositions like in 'in', an 'at', 'on' or auf 'on', 'upon' are used, which in some cases express not only spatial aspects but also functional ones. In these cases, the RO and the LE must be restricted to those parts which can provide the relevant function. One well-known example of a conceptualization following the concept of relevant parts of an object is given by (8). (8)

a. das Wasser in der Vase 'the water in the vase' b. der Sprung in der Vase 'the crack in the vase'

As Figure 2 a shows, the water is located between the sides of the vase, and the RO is conceptualized only as its hollow space. The crack, however, must be located in the material parts of the vase (Figure 2 b); it seems to be more a part of the vase itself than an independent object.

a: the water in the vase Figure 2. Conceptualizations of the RO

b: the crack in the vase

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deictic point DP

back

right

L Jl.X.i right -

•ieS rvvv

front

north

* ' front

left

west

back

a: intrinsic

left b: deixis

east

south c: geosystem

Figure 3. Different reference systems

The conceptualization of relevant parts can be also used for the LE. The localization expression (8 c) describes a situation where normally only a part of the flowers is located inside the hollow space of the RO and thus only a partial localization of the LE is provided. (8)

c. die Blumen in der Vase 'the flowers in the vase'

According to the functionality of containment, the part of the flowers inside the vase must be long enough to prevent the flowers from falling out. According to pragmatic expectations, the part inside the vase belongs to the stems and not to the blossoms. Notice that the localization expression (8 c) would not turn out to be wrong, if these expectations are not fulfilled, e. g., the whole flowers including the blossoms felt into the vase. Another way to focus on parts of an object is given by the concept of orientation via reference systems. This concept is only used with objects serving as the RO of a localization expression. A reference system or reference frame is projected on the object, so that different parts of the object belong to different directions of the frame and can be selected with respect to the applied direction. Figure 3 shows a house which is oriented by different reference systems. There are two classes of reference systems, the intrinsic and the extrinsic ones. 6 In intrinsic cases, the RO itself establishes the frame of reference. The house in Figure 3 a establishes a reference system with six orientations, which form three pairs of opposite directions. The entrance provides the front side, and opposite the back. The right and left side are induced orthogonally. The upper and the lower side are given by the gravitation; they are omitted in the picture. Reference systems with less than six orientations are possible, for example, a tower provides only upper and

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lower side. There exist also objects, e. g., balls, which are not able to establish any orientation at all by themselves. The most complete list of how different classes of objects induce intrinsic systems is presented by Miller - Johnson-Laird (1976: 403). To establish extrinsic reference systems, a secondary reference object is needed. If this secondary RO is the origo of the spatial deixis, e. g., the location of the speaker or listener, than the frame is called a deictic reference system. Figure 3 b shows how the orientation of the deictic point DP is induced on the primary RO in a mirror-like way. The part of the RO focussing the deictic point becomes the front, its opposite the back and the part focussing the right or left side of the DP becomes the right or left part of the primary reference object. The vertical axis with upper and lower sides remains unchanged. Another kind of orientation is induced by the geographical system, which forms another class of extrinsic reference systems. In that case, the two reference objects are not disjoint, but the primary RO is included in the secondary RO (the Earth) and inherits its four orientations from it (Figure 3 c). Other ways of inducing extrinsic orientations can be found in Wunderlich — Herweg (1991). The object concepts can only be used for each object independent from the other involved in the localization. To describe the relation between two objects, distance concepts are used. 7 For the processing of localization expressions, it turns out to be suitable to choose four basic distances: inclusion, contact/direct nearness, nearness and remoteness. The concept of inclusion, referred to by prepositions like in 'in' or durch 'through', says that the LE is included in the space occupied by or assigned to the RO. Inclusion is normally related to the functional concept of containment which is supplied for the LE by the RO or of the partwhole relation between them. To be in a contact/direct nearness relation to the RO, e.g., as induced by an 'at', 'on' or auf 'on', 'upon', the LE must be near enough to the RO so that an underlying functional relation like support or an intentional relation like waiting at a cash point can be possible. If no functional relation is involved in the situation under consideration, the two objects must touch each other. The concept of nearness underlying the majority of prepositions, e. g., bei 'near' or vor 'in front o f , does not have any underlying functional aspects. The LE is near the RO if it is in the vicinity of the RO and the RO can serve as a landmark for the LE. Sometimes the space of possible near-locations of the LE is called the "region of interaction" (Miller — Johnson-Laird 1976) of the reference object with respect to the LE. If

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the LE is outside of this region, the two objects stand in a remoteness relation to each other as denoted by jenseits 'beyond'. For a coarser classification, the first three concepts inclusion, contact/ direct nearness and nearness are generalized to the concept of proximity in contrast to the concept of distality which is provided by remoteness. The validity of the concepts proximity/distality is not restricted to the spatial domain. The same pair can be found for example in connection with events (Herweg 1990). As the following investigations will show in more detail, each localization can be described by a combination of object and distance concepts. The LE normally has a neutral (that means no) conceptualization, whereas the RO is conceptualized according to the object concepts of relevance of parts, orientation via reference systems or also in a neutral way. Then the adequate distance concept is applied to the conceptualizations of RO and LE. If necessary the other object concepts (form, dimensionality and plurality) can be used to describe requirements on both objects.

3.

A first view on the processing of localization expressions

3.1. The phenomenon of localization and its formalization The processing of localization expressions is guided by the features which are assigned to the phenomenon of localization. The theory described in this paper is based on two characteristic features of the localization process: — localization as segmentation and — localization as search. According to the first characterization, the localization of an entity involves the segmentation of the space under consideration. Under that view, a localization corresponds to the delimitation and description of the part of space that contains the LE. The selected part of space is called a localization area or, more specifically, primary (localization) area. The segmentation of the space under consideration can be induced by coordinate systems or by the objects contained in the space. Sentence (5) in the introduction gives an example for the use of a coordinate system.

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R R = (R -

O)

R N = R F U RRS U RΒ

^ RLS

Figure 4. Segmentation of a space

But as stated there, the normal way to localize objects is to relate them to other objects. Therefore, it is more interesting to see how the delimitation and description is done with respect to an object included in the space under consideration. The localization concepts presented in 2.2. are used to segment a space with respect to an object O. Figure 4 shows that an object divides a space under consideration into the space Ο occupied by the object itself — in the following also described by place (O) — and the surrounding space R. If the distance concept of nearness is applied, the space R can be split up into the nearness-area R N and the remoteness-area R r . If the object Ο is conceptualized with respect to a reference system, the orientation of Ο can be inherited to the surrounding nearness-area R N . In Figure 4 an intrinsic or deictic reference system is used to split R N into four possibly overlapping parts: R F corresponds to the part of R N related to the — intrinsic or deictic — front of the object, R r s to that related to the right side, R B to the back and R LS to the left side. The second characterization of the phenomenon of localization as search emphasizes its procedural aspect. According to that characterization, the selected part of space serves as a "search domain" 8 for the LE. In order to get a suitable search domain, the selected part of space, the primary area, is combined with expectations about the probable locations of the LE. These expectations about locations lead to priorizations. Positive priorizations are parts of the space that are good candidates for

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places to find the LE within, e.g., the typical locations of the entity to be located. Thus these pieces of space are preferred in contrast to the rest, and are the first to be searched for the object to be located. There is also the possibility of negative priorizations, which exclude parts of the space from the parts to be searched. The result of all available positive and negative priorizations is the delimitation of a part of the primary area. In the following, such a fully specified localization area is called a search domain. While the primary localization area contains all possible locations of the LE, a fully specified search domain contains only the likely ones. So the last kind of localization area can better serve as a basis for search than the primary selected space. In situations where no priorizations are available, the primary area and the search domain turn out to be the same. For all other cases it should be noted that priorizations are based on expectations and not on certain knowledge. So it must always be possible to withdraw its results if an expectation turn out to be wrong after new knowledge is added or after an unsuccessful search. This is not the case with the primary area, which should be consistent with the given localization expressions. The two characteristic features of localization lead to the formalization of the phenomenon given by definition (9). (9)

LOK ([relevant_parts](LE), G s ) with a. Gg = G ° Gpi ° Gp2 ° ... ° Gpn b. R 2 G, c. G 2 place ([relevant_parts](LE)]

The definition of localization given in (9) is based on the concept of the search domain. The predicate LOK relates the LE to the relevant search domain G s . If functional aspects are involved, only the relevant parts of the LE with respect to the underlying functional relation between LE and RO are considered. An example is provided by expression (8 a) in Section 2.2., which describes the partial localization of flowers in a vase where the stems provide the relevant parts that are located inside the RO. As indicated by the squares, this conceptualization of the LE with respect to relevant parts is optional. If there is no functional relation involved in the situation, that demands such conceptualization, the whole, that means neutral conceptualized, LE is considered. The first condition a. describes that the search domain G s consists of the primary localization area G modified by the priorizations G Pj . The area G is the result of the segmentation process. Condition b. ensures that all areas are really a part of the space R under consideration. The

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area G is considered as the set of all possible locations of the LE according to the known (localization) facts. This implies that the space occupied by the LE or its relevant parts respectively is included in G. This fact is expressed by the last condition, where place (LE) or place (relevant_parts (LE)) refer to the space occupied by the LE or its relevant parts. It should be noted that no condition requires the LE to be included in the search domain G s . As explained above, the priorizations represent only default knowledge which could be withdrawn. We only suppose to find the LE inside the search domain, but can never be sure of it.

3.2. An overview of the interpretation process Now the question arises, how these localization areas are computed as to localization expressions. This section gives an overview of the whole interpretation process. One part of it, the conceptual processing, will be specified in the following section. According to the basic assumption A. given in Section 2.1., the interpretation process consists of two levels, the linguistic and the conceptual one. The conceptual level involves propositional and depictorial processing as stated in assumption C. Figure 5 shows the steps of the process by the predicates resulting from each processing step. The linguistic analysis computes static and dynamic localization facts from the natural language input. 10 Static localization facts are induced by expressions describing the location of objects or situations (see examples (2) and (3) in the introduction). These facts are represented by the predicate Lok sem which indicates the localization of an object Ο or a situation S with respect to the spatial region SR. A spatial region is an abstract entity that is defined by the reference object RO and the spatial relation REL extracted from the input or, if necessary, from the textual or situational context. Dynamic localization facts are computed from dynamic localization expressions which describe the motion of an object (see example (3 a)) or the course of an elongated object like streets or plural objects (see (3 b) and (3 c)). They are given by an instantiation of the predicate Move (O, PR) which describes the motion or the course of Ο along the path-region PR. Path-regions are internally structured regions consisting of a sequence of simple spatial regions. Before the computation of localization areas can start, the semantic facts must be transformed into a canonical form. The transformation is

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c

localization expression

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457

natural language input

s y n t a c t i c and s e m a n t i c analysis ioksem (0,SR) Loksem ( S , S R ) Move (0, P R ) t r a n s f o r m a t i o n of static

linguistic level

t r a n s f o r m a t i o n of

localizations

dynamic

of s i t u a t i o n s

localizations

M o v e (0, P R )

Loksem ( S . S R ) Loksem (0, S R ) LOKsem (Patn, 5 R )

area c o n s t i t u t i n g process

LOK ( O / P a t h , 6 s ) Depiction

conceptual level

Figure

5.

Interpretation process for localization expressions9

done by abstracting from dynamical and situation-specific features so that only the static localization of objects must be analyzed by the area constituting process. This restriction makes it possible to use a static depictorial formalism with single pictures for the conceptual processing and to ignore temporal aspects on the propositional level. As the examples (10) and (11) will show, this is achieved by abstracting from all temporal aspects in dynamic localization and by abstracting from situations in static localization involving situations. The abstraction process is carried out by the conceptual pre-processing which computes a canonical form for all localization facts.

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For static localization facts involving objects, no further work has to be done. The localization of situations is reduced to the (static) localization of certain objects involved in the considered situation. The first step is to compute the objects involved in the current situation with the help of world knowledge about the relevant type of situation (compare Figure 1 and its explanations). As example (10) shows, which of these objects are located depends on the given spatial region. (10)

a. Babette führt im Labor Experimente durch. 'Babette is carrying out experiments in the laboratory.' b. Babette führt unter dem Abzug Experimente durch. 'Babette is carrying out experiments under the flue.'

In both sentences, the situation "Babette is carrying out experiments" is located, but with respect to different regions. The world knowledge about making experiments contains the information that a concrete situation of that type normally involves person(s) performing the experiments, the instruments needed and the objects or material examined. In example (10 a) all these entities can be assumed to be inside the laboratory and therefore inside the spatial region. The localization of the situation is transformed to the localization of all involved entities. For (10 b) this is not possible because a flue is to small to cover whole persons. In that case, only some of the instruments and the objects examined are located inside the spatial region, but not the woman making the experiments. So the localization of objects must be determined according to the interaction between the situation and the region involved. Dynamic localization facts are translated into the static localization of the underlying path. This path is the trajectory of the motion described or the LE itself if the course of an elongated object was described. Parts of the path like beginning, end or pieces of the route are located according to the semantic facts. Often more than one phrase is used to describe the spatial features of a path as in the example (11). (11)

Die Frau geht aus dem Haus und steigt in ihr Auto. 'The woman went out of the house and got into her car.'

The result of the linguistic processing of (11) are two dynamic localization facts. The first one is a source-motion which starts inside the house and ends outside of it. The second is a goal-motion which begins somewhere outside the car and ends inside of it. The conceptual pre-processing creates in the first step two paths which are later combined into one single path corresponding to the whole motion of the woman. The

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beginning of the resulting path is located inside the house and its end inside the car. 11 The results of the pre-processing are one or more localization facts which describe the static localization of the object Ο or the part of a path Ρ inside a spatial region SR. Each of these facts is taken as input for an area constituting process which transforms the abstract region into a fully specified search domain. This is carried out by combining propositional and depictorial means for the first time. Thus the resulting localization area is a hybrid object with propositional and depictorial features. The result of the process of localization is a search domain G s for an object, or a part of a path together with the depiction of this area. The problem of partial localization of the LE that might lead to the conceptualization of relevant_parts(LE) is omitted in the implemented version of the process and in the remainder of this paper. In the following the LE is assumed to be conceptualized in a neutral way.

4. Conceptual processing This section examines in detail the specification of the abstract semantic representation to get a more detailed conceptual meaning representation. This is done by converting the spatial region SR used in the semantic fact into a maximally specified localization area, the search domain G s . While the region is only determined by the reference object RO and the spatial relation REL, the search domain takes other parameters into account, e. g., the entity to be located LE. In the first part of this section I will explain the computation of a search domain in general, while the second part focuses on those steps in the computation where distinctions emerging from contextual influences take place.

4.1. Computation of a search domain According to the characterization of localization in Section 3.1., the process of area construction involves the segmentation of the space under consideration in order to establish a primary area and the priorization of the primarily separated area. The result is a search domain G s which is composed of the primary area G and the priorization areas Gpj corresponding to the priorization Pi as described by definition (12).

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Gs = G ° Gpi ο Gp2 ° ... ° Gpn

The way in which the operation ° is interpreted depends on the kind of priorization considered (see 4.2.). The computation of the search domain uses in addition to RO and REL given by the spatial region other parameters like the LE, the textual context, e. g., the verb used, or the spatial context, e. g., other objects in the direct surroundings of the RO. A complete list of the parameters is presented in Habel — Pribbenow (1988). As expected, the construction of a search domain consists of two steps: A. the computation of the primary area G and B. the specification of G using priorizations. Step A starts with the definition of the primary localization area which is computed by propositional means, in our case by using rules. According to Section 2.2., each localization can be characterized by an LE- and a RO-conceptualization combined with a distance concept applied to these conceptualizations. As stated in 3.2., the LE is always conceptualized in a neutral way. So the rules compute an area definition which consists of a conceptualization of the RO and a distance concept. If not a neutral one is used the RO-conceptualization refers to the object concepts of relevant parts or orientation via reference systems. 12 But this definition provides only a characterization of an area and not a concrete part of space corresponding to this area. The concrete area must be built up by a depictorial process which evaluates the spatial concepts of the area definition. First, the conceptualization of the RO is evaluated by marking the appropriate part of the object. 13 The subsequent process interprets the distance concept with respect to the part marked in the first step. Although the propositional definition does not carry enough information to select a concrete primary area, it is a necessary step in the computation process because the definition provides the connection to the conceptual basis. Thus the regularities between spatial concepts can be used for the processing of areas. For example, the dichotomy of such concepts as proximity/distality, inclusion/nearness or opposite orientations like front/back can be inherited to pairs of areas defined by those concepts. For problem solving tasks like the answering of questions, the valid regularities can be used in an explicit manner, while on the depictorial level they remain implicit. The primary area is used as the basis for the second step B, the construction of the search domain. The processing of the priorizations is the best example of the interaction between the propositional and the

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depictorial module. What can serve as a priorization in principle is stated by propositional means. But only the depictorial module can decide what is applicable in a concrete case and evaluate the priorization (see the example of negative priorization in 4.2.). As stated in Section 3.1., the results of the priorization step are only of default status. So it must be assured that the results can be withdrawn on both the propositional and the depictorial level. But despite the uncertain status, the priorizations are important because they correspond to expectations about the location of the LE and therefore contain the information which makes a search effective. Before I examine the individual steps of the processing in more detail, I will give a small and rather simple example to illustrate the constitution of a search domain. (13)

Mein Auto parkte in der Bismarckstraße. 'My car was parked in the Bismarckstraße.'

The semantic analysis of sentence (13) computes a static localization fact locating an object, here the car, in a spatial region SR described by the RO Bismarckstraße and the spatial relation in. Additional pre-processing is not necessary because the semantic fact has the canonical form required (see 3.2.). The first step of the conceptual interpretation is the propositional definition of the primary area. As the distance concept, inclusion is chosen according to the spatial relation given by the region SR. The object concept of relevant parts is used to determine a RO-conceptualization which allows the containment of a car. Such a conceptualization is provided by the silhouette, which is a conceptualization of the street as a whole including the buildings on the side of the street and the hollow space between them. This definition of the primary area is interpreted by the depictorial system by evaluating the RO-conceptualization and the distance concept. The result is an area which corresponds to the space occupied by the whole street (see Figure 6). Each depiction of a localization is based on the picture of the RO, which is the basic depiction of the relevant category of objects modified according to individual features if necessary. For the depiction in Figure 6 the RO is given by a detail of a street in a 2-D projection, the bird's eye view. The street consists of the lane in the middle and the two sides including sidewalks, houses, and so on. The depiction of the primary area is the striped object overlying the picture of the street.

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street (detail) Figure 6. Depiction for example (13)

The second step of the area constituting process is the computation of the priorizations. Propositional world knowledge contains the information that — moving or parking — cars are normally located in lanes or in parking spaces (and not on sidewalks or inside houses). For example (13), the positive priorization given by the typical location of cars is assumed to be the only available priorization information. This fact is passed to the depictorial subsystem, which creates the dotted priorization area. Now the two localization areas can be combined — that means the operator ° of definition (12) is interpreted — by computing their intersection. 14 The intersection marked by the striped-dotted part of Figure 6 forms the final search domain. 4.2. Influence of contextual information In the following, I want to discuss the steps of the computation where meaning representations that are identical up to now can be distinguished according to different contextual influences. The distinction can take place at three different steps in the area constituting process: A. the propositional definition of an area which can evaluate the same spatial region by different combinations of RO-conceptualization and distance concept, B. the depictorial evaluation of the definition which can lead to different areas, and C. the computation of priorizations where different spatial contexts can lead to varying priorization areas and search domains.

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A. Prepositional definition For some localization expressions, the definition of the primary area by a combination of concepts only depends on the information given by the spatial region of the semantic fact, the reference object RO and the spatial relation REL. One example are localizations involving the preposition bei 'near', which are always mapped to the combination of the distance concept nearness and the neutral conceptualization of the RO. A non-trivial selection of concepts is necessary for two kinds of localizations: — localization with underlying functional aspects and — localization involving relations of the secondary deixis like vor 'in front' or links 'left'. The following expressions (14) show an example of the influence of functional concepts. (14)

a. das Kleid im Schrank 'the dress in the wardrobe' b. die Kleiderstange im Schrank 'the coat rail in the wardrobe'

In both localizations the distance concept of inclusion is selected, but the conceptualization of the wardrobe varies. In example (14 a) the wardrobe must function as a container for the LE, the dress. This functionality can only be supplied by the wardrobe if the dress is included in the space between the six sides of the RO. Therefore the conceptualization of hollow spaces is used to refer to the space associated with the wardrobe which is delimited by its sides. The coat rail as LE of (14 b) is assumed to be a part of the wardrobe itself. A part-whole relation between RO and LE is provided where the RO — excluding the LE — serves as a container for the LE. So the silhouette as the conceptualization pertaining to an object as a whole (see example (13)) must be used. There are also situations where more than one combination of concepts is adequate (see 14 c). (14)

c. der Nagel im Schrank 'the nail in the wardrobe'

The nail could be lying inside the wardrobe, e. g., having been left there by the people who built it, or it could be a part of it, e. g., holding a door of the wardrobe in its position. The first alternative corresponds to the situation in (14 a) and leads to the same conceptualization of the

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wardrobe; the second alternative to situation (14 b) and the concepts selected there. Sometimes the verb involved can be used to solve the problem: If the nail is lying in the wardrobe than the first alternative is accepted; if it is driven in the second one is chosen. The second alternative of a non-trivial selection of concepts are localization expressions involving prepositions like vor 'in front' or links 'left', which are called prepositions of secondary deixis. These prepositions invoke the distance concept of nearness and the orientation of the RO via reference systems corresponding to the specific spatial relation. The problem to be solved is whether the orientation of the RO must be computed with respect to the intrinsic or the deictic reference system. If the RO does not provide an intrinsic reference system then the deictic system is chosen. In all other cases the problem is not easy to solve as the different, sometimes inconsistent theories about this selection illustrate. 15 B. Depictorial evaluation of concepts The second step in making distinctions is the depictorial evaluation of the concept combination defining the primary area. The interpretation of conceptualizations based on an extrinsic reference systems and of most of the distance concepts are influenced by the objects involved in the situational context. (15)

a. der Tisch beim Schrank 'the table near the wardrobe' b. der Papierkorb beim Schrank 'the waste basket near the wardrobe'

For the two expressions in (15), the same propositional definition is computed: the combination of nearness and neutral conceptualization of the RO. This definition is passed to the depictorial subsystem to evaluate the definition. Because of the neutral conceptualization of the RO the distance concept of nearness is applied to the wardrobe as a whole. According to the meaning of nearness, the evaluation process has to select that part of the surroundings where the RO can serve as landmark for the LE as primary area. As Figure 7 shows, the adequate part of the surroundings is substantially bigger for the table (Figure 7 a) than for the much smaller waste basket (Figure 7 b). On the propositional level, such regularities can only be expressed by a rule of thumb like "the bigger the object the bigger the area". This rule

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b: waste basket near the wardrobe

Figure 7. The primary areas created for example (15)

applies to reference objects as well as to objects to be located, because the greater the size of an object, the better it can serve as a landmark or the easier it can be found. Similar rules are evaluated for the relevance or the visual salience of the RO. But, as discussed in section 4.1. for proportional definitions, these rules of thumb are not precise enough to determine the concrete extent of an area. This can only be done by depictorial means. An analogous argument applies to the influence of the spatial context that also determines the delimitation of areas. Normally, a wardrobe stands with its back to one wall of the room. This wall functions as a barrier for the process creating the area. As the two depictions in Figure 7 illustrate for the situation described in example (15), the wall restricts the area to that part of the surroundings that is inside the room in which the wardrobe stands. It would not be useful to take the whole surroundings because if the LE is in another room, it cannot be located with respect to the wardrobe any longer.

C. Priorizations Propositional means are used to describe the priorizations that are possible in a given situation and how they work. For example, typical localizations of the LE and typical relations between RO and LE provide positive priorizations. The resulting search domain is the intersection of the priorization area and the present localization area, intially the primary area. Objects competing with the reference object cause negative priorizations that restrict the present localization area (see the example above). But whether a priorization is applicable for a concrete localization and

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what the resulting search domain exactly looks like depend on the spatial context of the localization. As an illustration I will discuss example (16) of a negative priorization. (16)

Mein Auto parkte beim Denkmal. 'My car was parked at the statue.'

Figure 8 a shows the depiction of the primary area around the statue serving as RO. The priorization to be considered is the negative priorization provided by competing objects. A competing object CO is an object that can be compared to the R O with respect to size and relevance and therefore could serve as reference object itself. An LE which is nearer to the CO than to the original RO normally would be located with respect to the competing object. So the nearness-area of the C O forms a priorization area restricting the present localization area. In example (16), the passage whose location is known by the individual world knowledge of the system is a good candidate for a competing object. The Figures 8 a - 8 c depict the process of computing the resulting search domain based on the primary area as present localization area and the priorization area provided by the nearness-area of the passage serving as C O shown in Figure 8 b.

a: primary area

b: competing area

c: search domain

Figure 8. The construction of a search domain considering competing objects

In general, which part of the primary area gains a negative priority, that means loses priority, depends on the competing objects available and their location. For example, if a C O is too far away from the RO, so that its priorization area does not overlap with the present localization area, it will have no influence and will not lead to a specification of this area. So a concrete priorization with respect to competing objects varies with the spatial relation between CO and RO; in other words, with the

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spatial context of the considered localization. It should be noted that in the system presented, this influence of the spatial context can only be computed by the depictorial module.

5. Concluding remarks Most parts of the process explained in the Sections 3.2. and 4. were implemented by the LILOG-space project at the university of Hamburg. As stated in 2.1., the processing of localization expressions is embedded in the LEU/2 system, which is a prototype of a text understanding system developed by IBM Germany in co-operation with five universities. The propositional part of conceptual processing is represented in the form of rules using a kind of order-sorted predicate logic language developed in the LILOG project (see Pribbenow to appear or 1991 for an overview of the rule-based processing). The depictorial processing is based on cell matrices as a realization of depictions (see Khenkhar 1991). In the future, it will be interesting to investigate the extent to which the conceptual basis for localization and its processing can be used for other tasks besides the analysis of localization expressions in a text understanding system. Candidates for other domains are geographical information systems, e.g., natural language interfaces to such systems, or — in the more distinct future — computer vision or naive kinematics, the spatial aspects of physical commonsense reasoning.

Notes 1. The first object is called "entity to be located" and not "object to be located" because there is also the possibility to locate situations and motions as the examples (3) and (4) will show. 2. The third section will show why it is necessary to assume the localization of situations on the semantic level and how the localization of situations can be reduced to that of certain objects involved in the situation under consideration. 3. Another approach is given by Talmy (1983). Often his conceptual basis overlaps with the one presented in this paper, but some aspects such as the distance concepts are missing in Talmy's approach. 4. Talmy and Herskovits assume that the RO and the LE interact with each other according to the figure-ground principle of gestalt theory. The LE which they call figure is seen as isolated from the ground provided by the RO. But the experiments of Dittrich — Herrmann (1990) suggest that the figure-ground principle is too restricted to explain

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9.

10. 11.

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Simone Pribbenow the roles of RO and LE in all their aspects. So my general localization principle does not restrict the LE and the RO to pure figure/ground entities. According to Lynch (1960), a landmark can be provided by any object that is used for orientation tasks, for example a building or a crossing. Slightly different classifications of reference systems given by other authors can be found in Retz-Schmidt (1988). The term "distance" may be not the best choice because two of the distance concepts (inclusion and contact/direct nearness) describe the lack of distance. The term "search domain" is taken from Miller — Johnson-Laird (1976) who use the term in an abstract way, not only in spatial contexts but for all — concrete or conceptual — spaces that are searched for a special object. The linguistic and the conceptual level of the process in this figure correspond to the processing modules of the same name in Figure 1. The two transformation steps in Figure 5 are carried out by the propositional subsystem of the conceptual processing, the area constituting process by both the propositional and the depictorial subsystem of the system in Figure 1. For a complete description of the linguistic analysis see Maienborn (1990) or Pribbenow (to appear: 2.3). Unfortunately, the process of transforming dynamic localization facts is more complicated than it seems according to the brief description given above. The process is explained in detail in Pribbenow (to appear: 2.4). Remember that all other object concepts (form, dimensionality and plurality) are used for requirements to LE and RO. These requirements are used to reject given localization expressions and restrict the generation of new ones. The evaluation of a RO-conceptualization focuses only on parts of the object without forgetting the rest of it. This process is not a selection of pieces. The intersection of areas is one possible interpretation of the operator As example (16) will show, a different evaluation is needed for negative priorizations evocated by competing objects. Compare Retz-Schmidt (1988) for a collection of some of these theories.

References Andre, Elisabeth — Gerd Herzog — Thomas Rist 1988 "On the simultaneous interpretation of real world image sequences and their natural language description: The system SOCCER", in Proceedings of the ECA1-88, 449-454. Bierwisch, Manfred 1983 "Semantische und konzeptuelle Repräsentation lexikalischer Einheiten", in: Rudolph Ruzicka — Wolfgang Mötsch (eds.), 61-99. 1988 "On the grammar of local prepositions", in: Manfred Bierwisch — Wolfgang Mötsch — Ilse Zimmermann (eds.), 1-65. Bierwisch, Manfred — Ewald Lang (eds.) 1987 Grammatische und konzeptuelle Aspekte von Dimensionsadjektiven. Berlin: Akademie-Verlag.

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Bierwisch, Manfred — Wolfgang Mötsch — Ilse Zimmermann (eds.) 1988 Syntax, Semantik und Lexikon. (Studia grammatica 29.) Berlin: AkademieVerlag. Brachman, Ronald J. — Victoria Gilbert — Hector J. Levesque 1985 "An essential hybrid reasoning system", in: Proceedings of the 9th IJCAI, 532-539. Davis, Ernest 1990 Representations of commonsense knowledge. San Mateo, Cal.: Morgan Kaufmann. Dittrich, Sabine — Hermann, Theo 1990 "Der Dom steht hinter dem Fahrrad." — Intendiertes Objekt oder Relatum?. (Bericht Nr. 16.) Heidelberg/Mannheim: Arbeiten aus dem SFB 245 "Sprechen und Sprachverstehen im sozialen Kontext". Freksa, Christian — Christopher Habel (eds.) 1990 Repräsentation und Verarbeitung räumlichen Wissens. Berlin: Springer. Garrod, Simon C. — Anthony J. Sanford 1988 "Discourse models as interfaces between language and the spatial world", Journal of Semantics 6: 147-160. Habel, Christopher 1987 "Cognitive linguistics: The processing of spatial concepts", in: T.A. Informations — ATA LA (Association pur le Traitement Automatique des Langues) 28: 21-56. Habel, Christopher — Pribbenow, Simone 1988 Gebietskonstituierende Prozesse. (LILOG-Report 18.) Stuttgart: IBM. Herskovits, Annette 1986 Language and spatial cognition. An interdisciplinary study of the prepositions in English. Cambridge: Cambridge UR Herweg, Michael 1990 Zeitaspekte. Die Bedeutung von Tempus, Aspekt und temporalen Konjunktionen. Wiesbaden: Deutscher Universitäts-Verlag. Herzog, Otthein — Claus-Rainer Rollinger (eds.) 1991 Text understanding in LI LOG: Integrating computational linguistics and artificial intelligence. Berlin: Springer. Hobbs, Jerry R. — Moore, Robert C. (eds.) 1985 Formal theories of the commonsense world. Norwood, N. J.: Ablex Publishing Corporation. Johnson-Laird, Philip N. 1983 Mental models. Cambridge: Cambridge UP. Khenkhar, Mohammed 1991 "Object-oriented representation of depictions on the basis of cell matrices", in: Otthein Herzog — Claus-Rainer Rollinger (eds.), 645-658. Klein, Wolfgang 1990 Raumausdrücke. [Unpublished MS, Nijmegen.] Kosslyn, Stephen M. 1980 Image and mind. Cambridge, Mass.: Harvard UP. Lindsay, Robert K. 1988 "Images and inference", Cognition 29: 229-250.

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Lynch, Kevin 1960 The images of the city. Cambridge, Mass.: MIT-Press. Maienborn, Claudia 1990 Lokale Verben und Präpositionen: Semantische und konzeptuelle Verarbeitung in LEU 12. (IWBS-Report 119.) Stuttgart: IBM. Miller, George A. — Philip N. Johnson-Laird 1976 Language and perception. Cambridge: Cambridge University Press. Paivio, Allen 1983 "The empirical case for dual coding", in: Yuille, J. (ed.), 307-332. Pick, Herbert — Linda Acredolo (eds.) 1983 Spatial orientation: Theory, research, and application. New York: Plenum Press. Pribbenow, Simone 1990 "Interaktion von propositionalen und bildhaften Repräsentationen", in: Christian Freksa — Christopher Habel (eds.), 156-174. 1991a "Phenomena of localization", in: Otthein Herzog — Claus-Rainer Rollinger (eds.), 609-620. to appear Räumliche Konzepte in Wissens- und Sprachverarbeitung. Hybride Verarbeitung von Lokalisierung. Deutscher Universitäts Verlag. Retz-Schmidt, Gudula 1988 "Various views on spatial prepositions", AI Magazine 9/2: 95-105. Ruzicka, Rudolph — Wolfgang Mötsch (eds.) 1983 Untersuchungen zur Semantik. (Studia grammatica 22.) Berlin: AkademieVerlag. Schirra, Jörg 1990 "A contribution to reference semantics of spatial prepositions: The visualization problem and its solution in VITRA", in this volume. Stechow von, Arnim — Dieter Wunderlich (eds.) 1991 Handbuch der Semantik. Berlin: de Gruyter. Talmy, Leonard 1983 "How language structures space", in: Herbert Pick — Linda Acredolo (eds.), 225-282. Vandeloise, Claude 1985 Descriptions of space in French. (Paper A 150.) University of Duisburg: Linguistic Agency. Vieu, Laure 1991 Semantique des relations spatiales et inferences spatio-temporelles: Une contribution ä l'etude des structures formelles de l'espace en Langage Naturel. [Docteur these, L'Universite Paul Sabatier de Toulouse.] Wunderlich, Dieter — Herweg, Michael 1991 "Lokale und Direktionale", in: Arnim von Stechow — Dieter Wunderlich (eds.) Yuille, J. (ed.) 1983 Imagery, memory and cognition. Hillsdale, N.J.: Erlbaum.

A contribution to reference semantics of spatial prepositions: The visualization problem and its solution in VITRA Jörg R. J. Schirr a

1. On reference semantics in AI In AI research concerning natural language systems, the reference aspect of verbal expressions very often plays only a minor role. Nevertheless one has to consider that every verbal expression refers to something, and that the structure of this something has an influence on the use of that verbal expression, i. e., on its meaning. In other words: the meaning of any verbal expression is somehow anchored in the corresponding referents. This extra-linguistic influence is especially recognizable if we study the interactions of a natural language system with the world by means of sensor and motor systems, e. g., a vision system. But also in machine translation, considering the referents will help to overcome the gap between the conceptual systems of two languages which has so often trapped even approaches with a relatively deep semantic analysis of the source texts (cf. Zelinsky-Wibbelt 1990 a, 1990 b; Bateman 1990, and Grabski 1990). The (more or less) unique referent might serve as a fixed point during the transformation to the goal language: changes in the meaning structure necessary due to the different conceptual systems underlying the two languages are restricted to valid interpretations of that referent. The major question arising in this context is: What is the nature of the reference relationship? which can be split into (a): What are the referents? and (b): How does their influence on verbal behavior work? I will concentrate herein on a primitive form of spatial prepositions and their referents — essentially geometric relations — although some of these considerations are more general (cf. Schirra 1990 b). Analyses of spatial prepositions in the framework of reference semantics usually view geometric relations as in some sense objectively given, i. e., existing independently in the so-called "real world", external to any

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mind (e.g., cf. Dowty et al. 1981). However, a more careful examination leads to the conclusion that the needed referents cannot be provided by the world per se. Expressions of fictitious things show us one argument against this objectivist view of the reference relationship: there are no unicorns in the real world, hence no objectively given referents for the expression "The last unicorn went back into the silent forest". Is it possible that we can understand this expression even without referents? There are other simpler disadvantages of the objectivist view. Imagine that we speak about a journey around the world we want to take in the future. While standing in the middle of Europe, we might use a sentence like: "Afterwards, we will fly to New Zealand which is to the east of Australia." Here, we do not have the problem of nonexistent referents: "to the east" clearly refers to that de facto spatial relation we could perceive if only we would look for example from a spaceship at that part of the earth. But how can this referent have any influence on the dialog, i. e., on the use or meaning of verbal expressions, miles away on the other side of the earth? Thus, not only is the nature of the referents in some cases unclear — to say the least (cf. Figure 1). Also our second question

Figure I. How can the reference relationship overcome the distance?

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about the kind of influence referents have on verbal behavior remains essentially unanswered (cf. note 1). The alternative experiential view of the reference relationship assumes that referents are essentially percepts and therefore always mental constructs (cf. Lakoff 1987 and Johnson 1987). Thus, spatial prepositions refer mainly to visually perceptible relations between objects. Now, there are no obvious problems concerning the mechanisms of influence, as long as we only speak about perceived things. But the examples above still remain problematic. How can the spatial relation between Australia and New Zealand influence a dialog without being perceived? We seemingly need some kind of pseudo-percepts, if we speak about something not present or fictitious. It is this very nature of percepts as being mentally constructed which allows for constructing other mental entities and using them as substitutes for percepts. Obviously, we have to speak about these hypothetical mental entities in just the same manner as about percepts — which is exactly the way we speak about mental images (cf. note 2). Thus, if we consider the reference relationship experientially rather than from an objectivist point of view, it is possible to better understand visual mental images and their cognitive function: mental images have the cognitive function of making available visual referents in the case where, as for radio reporting of a sports event, they are not directly perceptible (cf. Figure 2).

Figure 2. Mental images as substitutes for percepts

Dealing with reference semantics in AI, one has to comprehend that the reference relationship consists of three parts: (a) the referents; (b) the

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propositions, which are the mental representatives of the meaning of verbal expressions; and (c) the connection between the two, the reference relation proper, so to speak (cf. note 3). These three entities all have to be modeled in an AI system in the framework of reference semantics (cf. Figure 3). referential level

the reference relation proper

propositional level Figure 3. The reference relationship — a first view

The propositional level is already well examined in AI: most formalisms of Knowledge Representation can be used for this purpose. On the other hand, the referent level — because of its connection to perception — has to be based on data structures used in corresponding perceptual systems, e.g., vision systems (e.g., cf. Marr 1982; Sung 1988; Herzog et al. 1989, and Mohnhaupt and Fleet 1988). At this point, one confusion of notions very often appears, blurring further discussions: since the results of perceptual systems in AI even on a very low level of processing are usually represented in a form similar to the above-mentioned formalisms used for the propositional level — sometimes even the very same knowledge representation languages are used — they are called propositional, as well. This use of the word "propositional" is different from the one introduced above. In this very broad sense, everything expressed in the knowledge representation formalism is called a proposition (cf. Pylyshyn 1981; note 4). In my terminology, only those expressions which are connected to referents by a reference relation are propositions. The difference between referents and propositions is not a question of form but of use. Referents have meaning, namely the propositions associated with them, but they do not refer to something else, e. g., an extra-mental set-theoretical model named "the world". Similarly, propositions do not have meaning; they only refer to something. There is neither a meta-level above the propositions which might include the meanings of propositions, nor is there a sub-level which could keep ready those objects the referents refer to (cf. note 5).

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The third and most important entity of the trinity of reference, the connection between referents and propositions, quite obviously has a very different character. In order to avoid an infinite regress, the realization of the reference relation proper cannot use propositions or referents (percepts) again. Actually, the system does not necessarily know anything about the structure of the reference relation, e. g., for a spatial proposition. It can only use its realization of the reference relation in order to establish the connection between referent and proposition, i. e., recognize spatial relations in a given percept or visualize spatial relations (construct the referent). Therefore, a procedural realization of the reference relation proper seems adequate. In the following sections, I will present an overview of the system SOCCER with special emphasis on how language can be grounded in visual perception using a simple kind of artificial percepts, and how mental images of the same simple kind can be reconstructed in a model of anticipated understanding. The reference relation is used for, and its realization restricted by, both purposes. Section 6, finally, presents the realization of the reference relation we have chosen in VITRA.

2. The project VITRA and the system SOCCER The project VITRA (Visual TRAnslator) which started in 1985 as part of the German special collaboration programme SFB 314, AI & Knowledge-Based Systems, examines the relations between speaking and seeing: a completely operational form of reference semantics for the visually perceived is to be developed. CITYTOUR and SOCCER are two systems constructed in VITRA which — broadly speaking — transform visual perceptions into language. Here, we will concentrate on SOCCER (for CITYTOUR cf. Andre et al. 1985, 1986 a, 1986 b; Schirra et al. 1987, and Retz-Schmidt 1988). SOCCER simultaneously analyses and describes in German short scenes from soccer games similar to a live radio report, i. e., simultaneously and in an objective manner to an audience which is not able to see the game themselves. For this purpose, a large number of quite complicated 'cognitive' activities has to be performed: e. g., perceiving the locations and movements of ball and players in the scenery, interpreting these movements with respect to the conventions of soccer games, especially assuming the intentions and plans of the agents in the field, and

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— last but not least — selecting which events to utter in which sequence and with which words. The input data of SOCCER, which in a way are its percepts, are called mobile object data — MOD — and generated by the motion analysis system ACTIONS (cf. Nagel 1988; Sung 1988; and Herzog et al. 1989). These percepts consist of the set of the two-dimensional spatial locations and the velocity vectors of every mobile object perceived in the soccer field from a bird's eve view. At every time quantum, ACTIONS delivers the corresponding data which, then, is entered successively into SOCCER. At present, all mobile objects are perceived as ideal points (zero-dimensional). The Mobile Object Data is analysed successively as soon as it is entered. It implicitly refers to the geometry of the soccer field which is known by the system as StaB — static background (cf. Figure 4). MIN

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SOCCER does not know the whole scene at once. Like a radio reporter, it has to analyse the scene during its occurrence. Therefore, all processing steps have to be done incrementally, i. e., a selection of already recognized events is verbalized simultaneously with further event recognition. Indeed, SOCCER already recognizes events before they have occurred completely.

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Scene

Figure 5. SOCCER: The core system

The power, but also the limitation of a rigorous grounding of language in perception is already demonstrated by the core system (cf. Figure 5): in a kind of pipelining, three components transform the perceptual data into a text similar to the protocol sentences (as they are called) of Vienna Circle philosophy (cf. Carnap 1933 and Neurath 1933): only directly sensed impressions are reported — indeed still too primitive a type of sports report. For example, compare text (a) with (b), both of which describe the same referent. a. Schmidt, the goal keeper of the Blacks, is standing in the left penalty area. Meier, the captain of the Reds, is running along the middle line. The ball is close to him. Now, the distance between the ball and Meier increases. The ball crosses the left half of field and comes near to Schmidt. Schmidt starts moving towards the ball. Now, the ball stops moving when it reaches Schmidt.

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b. Meier, the captain of the Reds, has the ball and is running along the middle line. Now, he tries to score with a long shoot, but Schmidt, the goal keeper of the Blacks, catches the ball in his penalty area. The first component of the core system, S O C C E R ' s Event Recognition, has two parts: first, elementary spatio-temporal relations are recognized in the current percept: propositions like (left player-5 player-7) or (greatervelocity ball 45) are constructed by algorithms which are procedural to S O C C E R . The core of these algorithms is always a graded classification function that associates visual percepts used as input to S O C C E R with abstract spatial relations by so-called applicability degrees (cf. Section 4). As a second step, these elementary relations are chunked into propositions describing more abstract relations: (running-with-the-ball agent: player-5 place: (in-front-of RightGoal)) or (running-parallel agent: player7 co-agent: player-2 direction: (along MiddleLine)). In contrast to the elementary relations, S O C C E R here uses knowledge in a declarative form: for each composed event, a so-called event model defines how elementary relations have to be combined to yield events of that type. The event recognition component works in a quasi-parallel way, thus recognizing simultaneously all spatio-temporal relations or events similar to a h u m a n observer ( S O C C E R event recognition: cf. Herzog and Rist 1988). While the event recognition is working, the Selection component already chooses subsets of the recognized propositions to be uttered and orders them into a queue. The head of this queue is passed to the Generation component as soon as it is idle. The time of generating the sentences is important since the order in the queue might be changed if new events which seem to be more relevant have been recognized in the meantime. Previously selected items might even be removed from the queue. The generation component transforms the event proposition chosen by the selection component into a continuation of the report. Here, the applicability degrees of elementary spatio-temporal relations are verbalized, using linguistic hedges (cf. Figure 6 and Lakoff 1972). Localizing phrases and even previously mentioned events can be used to disambiguate objects. Furthermore, anaphora are used to increase the coherence of the text (a detailed description of both selection and generation components is to be found in Andre 1988). Obviously, the S O C C E R core system is rather primitive compared to h u m a n perception and cognition: it "sees" only two spatial dimensions, namely soccer fields from a bird's eye view, and "perceives" players as

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appr behi

more or behind directly behind

Figure 6. Applicability degrees and linguistic hedges

zero-dimensional without inherent orientations. Correspondingly, its language use is restricted: spatial prepositions for example cannot be used in the differentiated way we use them. Especially, there are no metaphoric extensions of spatial prepositions. On the other hand, these limitations simplify the problems of realizing the reference relationship of spatial prepositions to a treatable complexity, and thus, even may serve as a base for further studying spatial metaphors. To overcome the handicaps of pure protocol sentences, the intention and plan recognition component REPLAI-II (cf. Retz-Schmidt 1991b) is added to the SOCCER core system (cf. Figure 7): we can actually speak about soccer games only if we assume that the players behave according to internal and not directly observable mental states like intentions and plans. If the ball moves into the goal after changing its direction while being very close to a player, SOCCER can only describe this event as "That player scored" if it presumes and tries to verify in its percepts that this player has certain soccer-specific intentions and plans. Although intentions are based in the perceived, as well, they are not totally grounded in percepts and require additional knowledge to be (hypothetically) recognized. Thus, REPLAI-II extends the strict reference semantics of the SOCCER core system (cf. note 6). Another extension of SOCCER is provided by its listener model.

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Figure 7. Extended architecture of SOCCER

3. The listener model ANTLIMA In order to follow Grice's Cooperative Principle ("Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged." Grice 1974) a speaker has to know how his utterance is understood by the listeners in the present context. He needs a model of the listener, e. g., to make sure that despite the maxim of economy ("Make your contribution as informative as is required [for the current purposes of the exchange]." Grice 1974) the listeners are still able to recognize all the relevant structures even from elliptic descriptions. Thus, a listener model serves as a device which balances between the divergent demands of economy and completeness ("Do not make your contribution more informative than is required" Grice, 1974). With this knowledge about the listeners, the speaker can rate how much information actually is required in the given case.

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Correspondingly, SOCCER also needs a component that can construct a model of the listeners' knowledge of the events that have already been described. This listener model enables the system to continue its description in a cooperative way by anticipating the listeners' understanding of the utterance just planned. With these anticipations, the plausibility of that utterance in the context already known can be rated and used in an anticipation feedback loop to improve the coherence (cf. Figure 7). Therefore, the main task is to find out whether and to what degree the listeners might be able to understand the planned utterance at all, and, as a second step, whether they understand it as intended (cf. note 7). There is little evidence that the listeners and the speaker use different kinds of semantics. Thus, we assume that the listeners understand the soccer report by reference semantics, as well. What does that mean? As a German linguist wrote in 1969, "The radio reporter has solved his task only if he describes the reality of a sports event so vividly and obviously to the listener that the listener believes he sees that reality." (Dankert 1969: 94 [transl. J. S.]) The reporter shall induce — so to speak — a cinema in the heads of his audience. This clearly refers to mental images just in the way we mentioned them in Section 1: if the listeners want to have a "deep" understanding of the report, they need access to the referents and should be able to reconstruct them, i. e., to construct (visual) mental images corresponding to the speaker's percepts (cf. note 8). Since the listener model of SOCCER anticipates how the listeners understand the planned continuation of the report, it also has to ground the meaning of these utterances and especially of spatial prepositions referentially: ANTLIMA — ANTicipation of the Listeners' IMAgery — must be able to reconstruct corresponding visual percepts — albeit in the limited sense of SOCCER as Mobile Object Data and Static Background (cf. Figure 8). In other words, it must visualize the abstractly described situation. It is our thesis that those pseudo-percepts reconstructed by SOCCER's listener model correspond to the listeners' visual mental images (cf. note 9). As the backbone of ANTLIMA, the event proposition chosen by the selection component of SOCCER has to be analysed conceptually, i.e., dealing only with propositions. The conceptual analysis provides the basis for the visualization and for the feedback to SOCCER: the definition of the considered event, i. e., its subevents and the spatio-temporal relations between them, must be expanded and adapted to the situational constraints in order to achieve spatio-temporal coherence with the context (cf. Schirra 1990 b). Additionally, it might be necessary to integrate

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Figure 8. Architecture of A N T L I M A

modifications given by optional deep case fillers (cf. Sondheimer 1978 and Marburger and Wahlster 1983). The construction of a corresponding mental image serves as a kind of focusing device for this reasoning (cf. Pribbenow 1988 and Schirra 1991, but also Schirra 1992 b). The intermediate result of the conceptual analysis, which is the basis for the visualization, is called the propositional elementary structure, the temporally ordered sequence of sets of elementary spatio-temporal relations. Visualization transforms this data to a sequence of Mobile Object Data in the Static Background, thus fixing particular locations and velocities for all considered objects at each time point. The generated mental image should not be compared directly with the original percept of SOCCER — coordinate by coordinate, so to speak. Although such a comparison seems to be necessary if we want to know whether the listeners will have got the correct referent, the system only compares propositions, not images. Why? In general, we lose information transforming an image to propositions. Therefore, we cannot expect that the listeners will reconstruct the very same picture from that selected set of propositions actually communicated. Their images — and equally the one generated by ANTLIMA — will usually be only more or less similar to the original percept. The question now is: which deviations are essential and which are not? If a player is standing in the middle of the right field — nobody near him — 50 pixels' difference normally will not matter. But if he stands at the edge of the field, or near some other player, or very close to the ball, even 10 pixels' deviation of his location might change the whole interpretation of the scene. Since the propositions just

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ignore irrelevant details by definition (cf. Section 4), A N T L I M A has to re-analyse its mental images first, i. e., describe them propositionally again (cf. Figure 8, component Re-analysis). Then, it can compare this new set of propositions with the set SOCCER "found" in the original percept or the set which was actually communicated. Now, substantial deviations result in a different set of propositions, e. g., an additional (outside player5 SoccerField) or a missing (at player-7 ball). Since these differences might have several causes, among them: (a) error of A N T L I M A during conceptual analysis or visualization; (b) error of SOCCER during selection; (c) expectation of an event which will be communicated next, and (d) implicit event which SOCCER expects A N T L I M A to know about without communicating it, the further processing is quite complicated. As it does not effect the discussion in this report, we do not deal with it herein (cf. Schirra 1991). Finally, plausibility ratings, correctly expected continuations of the report, and — if necessary — errors are given back to SOCCER's selection component, thus closing the anticipation feedback loop. Before the elementary visualization is described in greater detail in Section 5, we devote our attention to its counterpart, the recognition of elementary spatio-temporal relations, since this first use of the reference relation gives us a clue for the solution of the visualization problem.

4. Recognition of static spatial relations Dealing with the connection between seeing and speaking, the first of the problems we have to consider is establishing the reference relation at all: we have the task of finding a connection between perceptual and propositional level. In general, the transformation to the propositional level has the function of reducing the amount of information included in the percepts to those features important for further acting — reporting in our case. Therefore, the spatial relations we consider correspond closely to (German) prepositions. The location of an object is relevant only relative to other objects' positions. The first object is usually called LO — located object — the others ROs — reference objects (cf. note 10). Other information in the percepts, e. g., the precise coordinates of objects, is regarded as irrelevant, and ignored. The elementary level of recognition in SOCCER is formed by static spatial relations verbally described by prepositions such as "being left

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o f ' , "— at", and "— between" (actually, of course, in German) and represented by means of what I call "Spatial Concepts". Individual occurrences of a relation are represented by instances of the Spatial Concept and called "(spatial) propositions". More precisely, spatial propositions are combinations of one spatial relation — the type of the proposition — and a set of objects forming the arguments of the relation. Figure 9 shows a typical (static) percept for SOCCER. Corresponding to

Figure 9. SOCCER Percept with near and left of occurrences

the human uses of spatial prepositions, SOCCER should be able to interpret this percept as a "near" situation, i.e., by creating a proposition (near player-5 player-7). But it can instantiate the Spatial Concept "lefto f ' — with respect to the direction of movement, as well. Obviously, recognition is not a one-to-one association, i. e., simply combining one percept with one proposition (cf. Figure 3). Different propositions can stand for the same geometric configuration. The reference relationship in VITRA associates every percept with a set of propositions, all describing that percept (cf. Figure 10). But which of them should be used to describe the percept verbally? This decision is supported by the radial structure of spatial concepts: we have to consider that some referents are good, others bad examples of a proposition. In most cases, we can move the LO a little bit without changing the propositional description. But the referents gradually become poorer examples of that proposition. For most spatial relations, we

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Figure 10. The reference relationship (Part 2: Recognition)

find that the probability of their being used to describe a situation changes gradually as the LO shifts. Figures 11, 12, and 13 illustrate this phenomenon for "being in"; " — near"; and " — in front o f ' by means of a kind of probability clouds, each drawn for two different types of ROs. The

Figure 11. Probability cloud representation of "in" for two different kinds of objects

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Figure 12. Probability cloud representation of "near" for two different kinds of objects

dense centers of these clouds mark those positions rated as good examples for the relations. In VITRA, the probability of use of a spatial proposition which is associated with every possible position of the LO with respect to some given ROs is interpreted as a measure of applicability for the proposition. In Figure 10, the degree of applicability is indicated by the thickness of the connection. The higher the applicability degree of a proposition is for a given percept, the better this proposition can be used to describe the percept. Therefore, an essential part of the reference relation is encoded by a graded classification function associated with every proposition. Given a percept, these functions yield the applicability degree (in [0.0 ... 1.0]) of the corresponding proposition. For example, the applicability degree of "being at" is calculated by means of Formula 1 only depending on one parameter: "dist", the distance between the LO and the RO; "d" is a scaling factor. dist

1·

Aar (dist) =

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Figure 13. Probability cloud representation of "in front o f ' (extrinsic use) for two different kinds of objects

The connections between spatial concepts, propositions, percepts, and applicability degrees are shown in Figure 14 as signatures of abstract data types (ADT). Note that the reference relation and the abovementioned classification functions are hidden in the operation recognize. For reasons described in the next section, the applicability degrees are called "T-values". Ambiguity and gradation are both well described in linguistic literature: many investigations about the connection between object locations and applicable spatial relations have been carried out and can be used for our purpose (e. g., cf. Saf 1966; Fillmore 1971; Miller and Johnson-Laird 1976; Moilanen 1979; Talmy 1983; Herskovits 1985; Vandeloise 1986; Lakoff 1987; Bierwisch 1987; and Habel et al. 1989). But, to be sure, the simplicity of SOCCER's percepts does not allow for the full range of use German prepositions show: for example, metaphoric uses even in the spatial domain (cf. Schirra and Hays 1993) are totally excluded. Nevertheless, some of the features described by linguists can be and have been considered in SOCCER (cf. Sections 6 and 7, and note 11).

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Figure 14. Signature of the spatial concept system (I): Recognition

5. Visualization of static spatial relations Corresponding to the elementary recognition, the most elementary step of the visualization task is constructing the static image of a set of elementary static spatial propositions which should hold simultaneously (cf. Section 3 and note 12), e.g., (left player-5 RightPenaltyArea), (in-front player-5 player-7), (in player-3 RightHalfField), (near player-3 MiddleLine), (near player-7 OutfieldSidel), (at player-7 player-3), (near player-7 ball), (between player-7 player-3 player-5), or organized with respect to the LOs: player-5: [left RightPenaltyArea], [in-front player-7]; player-7: [between player-3 player-5], [at player-3], [near ball], [near OutfieldSidel]; player-3: [in RightHalfField], [near MiddleLine] This task, called the visualization problem in ANTLIMA, is just the reverse of the aforementioned classification task that is at the heart of perception: instead of abstracting away from a concrete situation, an abstract (propositional) description must be augmented, filled with life that is, and transformed into a plausible concrete form. Unfortunately, the advantage of classification, namely the possibility of ignoring irrele-

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vant details of the referent, produces for the visualization task a corresponding disadvantage: how, for example, can we fix a concrete (i.e., precise) position of a ball of which we only know that it is to the left of the penalty area? One way out of this problem is given by the already mentioned gradation of the Spatial Concepts: if we consider the reference relationship not from the viewpoint of a given percept with respect to which every spatial proposition is applicable to a certain degree, but conversely from the viewpoint of one such proposition, then several percepts are to varying degrees typical examples of that proposition. Whereas the problem of perceiving is essentially the question: Which (spatial) relation is most applicable to a (visually) given situation?, the visualization problem can be summarized as: Which situation (visual pseudo percept) is most typically intended by a given abstract description? (cf. Figure 15).

Therefore, I assume that listeners — and similarly A N T L I M A — always try to give an utterance its most typical interpretation. Furthermore, they expect that the speaker will explicitly mention any important deviation from the typical case. This again reflects the aforementioned criterion for deciding which of all applicable propositions should be used to describe the percept to the listeners: SOCCER chooses the propositions with the highest degrees of applicability for verbalization. Starting from a propositional description, that mental image must be constructed that realizes all of the given spatio-temporal relations with maximal typicality. For a given set of ROs, A N T L I M A has to locate the LO at a position where the classification functions, or typicality functions as they better might be called in this context, are maximal. The essential

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task then is finding the maxima of the typicality functions. This task is not too difficult for one proposition. However, we have to consider sets of propositions which should hold simultaneously. Some of the given relations may happen to conflict: they cannot be maximally typical for the same situation. Look, for example, at Figure 9: if the ball is to be located in the left goal and simultaneously near player-7, we are not able to find any location with maximal typicality for both restrictions. In those cases, compromises must be calculated: a renormalized addition of all the typicality functions (e.g., algebraic average) which are associated with each LO — meaning in this case: object to be located — describes the typicality distribution for the conjunction of the restrictions. We can illustrate these calculations as a combination of several probability clouds (cf. Figures 11 to 13): only where several dense centers overlap does the combined typicality reach really high values. Figure 16 shows the combination of three localizations: [near CenterCircle], [between player W3 RightGoal], and [at MiddleLine] (cf. note 13). With such combinations, compatible restrictions result in a combined typicality function with a quite high typicality maximum, as shown in

0:00.00 mm sec UfOO ,11 Propositions

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Figure 16. Combination of three applicability clouds with sectional view on the right side

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Graphic Pang

Figure 17. Combination of applicability clouds of compatible spatial propositions

Figure 17 for the combination of [in front of LeftGoal] and [near player7], whereas incompatible propositions, e. g., [in front of RightGoal] combined with [in front of LeftGoal], yield maxima of typicality with an extremely low value, since the maxima of the components do not overlap (cf. Figure 18 with maxima at 0.5). Thus, the maximal degree of typicality — or T-value — reachable for the set of propositions can be used as a rating for the plausibility the considered utterance has for the listeners. If only a low T-value can be reached while generating the mental image, i.e., reconstructing the referent of that utterance, incompatibilities must have been included. If a high typicality value can be reached, all involved restrictions could be satisfied in the mental image, and the listeners found (one of) the typical referent(s) of the utterance. Using again the signatures of abstract data types, we can represent the visualization as an operation of the same set of ADTs already used in Section 4. Figure 19 shows that the operation visualize takes an initial image and a set of propositions and yields another image (cf. note 14). The initial image is generated by an operation init-image which takes the

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Figure 18. Combination of applicability clouds of incompatible spatial propositions

Figure 19. Signature of the spatial concept system (II) Visualization

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set of all considered objects and locates them at arbitrary positions (cf. note 15). The special attribute of the resulting image cannot be represented in the signature. Instead, I use the following logical formula (cf. Formula 2):

2.

V P e 2proposiüom, V/ e referent: X (recognize (visualize (init-image I U ρε P

(arguments? (/?'))

Ve/> Ρ),

> Σ peP

ρ)) (recognize (I, ρ))

Or less formally: if we sum up the T-values (typicality/applicability values) of all propositions ρ in the given set of propositions Ρ with respect to the result of the visualize operation on P, this sum has to be at least as great as the sum with respect to any other possible image. In other words: the result is the (or one of the) most typical image(s) for the set of propositions P.

6. The operational form of the reference relation in VITRA In the preceding two sections, the reference relation was used in two directions, for recognition and for visualization. To that purpose, we introduced graded classification functions which encode substantial parts of the reference relation for SOCCER on an abstract level of description, hidden in the operations visualize and recognize (Figures 14 and 19). Can we bring them to a more concrete level which also expresses the relationship between these two operations? To that purpose, a new data type is introduced which explicitly represents the graded classification functions. It is called TYPOF — Typicality Potential Field (cf. Figure 20). This data type stands for the third part of the reference relationship, the 'arch' between the two 'columns of the bridge', namely images and propositions. As mentioned in Section 1, for SOCCER, this part has to be essentially procedural; SOCCER does not know (in the strict sense) anything about this data type and only can apply the corresponding operations. But both the recognize and the visualize operations can now be expressed simply by using TyPoFs.

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Figure 20. Signature of the spatial concept system (III): TyPoFs

Each proposition is associated with exactly one TyPoF (cf. operations prop? and TyPoF? in Figure 20). The recognize operation simply can be expressed now by asking for the value of the classification function (Formula 3). 3.

recognize (proposition, referent)

Ξ

get-T-value (referent, TyPoF? (proposition))

As mentioned above, the visualize operation is to find the maxima of the classification function: therefore, an operation gradient is defined. It yields the component-wise differentiation of the classification function

for the position of the LO in the percept. This two-dimensional vector always points in the direction of the closest local maximum. Its length is proportional to the local slope of the classification function. At the maximum, we get the zero vector. If the initial position of the LO is favorable, we find the maximum of the classification function by moving the LO in the direction of the local gradient. One step of this hill climbing

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algorithm for one proposition is indicated in Figure 20 by the operation approx-1: the considered object is shifted in the referent a little bit in the direction of the given vector (cf. Yamada et al. 1988, and note 16). If we iterate the combination of these two operations as shown in Formulas 4 to 6 until the gradient is zero, we find the maximum, or at least a local maximum depending on the initial position of the LO. 4.

V, > 0: recognize (prop, image, + ,) > recognize (prop, image,)

5.

image 0 ξ init-image (arguments? (prop))

6.

image^ + υ (prop) ξ approx-1 (gradient (TyPoF? (prop), image, (prop)) image, (prop), LO? (prop))

To get faster and better results, we can use typical positions associated with the object type of LO. For example, the goal keeper typically will be located near or in the goal, which usually is already close to the most typical position in a particular case. Thus, the approximation of his position should start with a position in the goal. In A N T L I M A , we

of ApproK-Activ· O b j e c t s

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i n (SO ^ ' θ Μ ) »it f w U 6 iVMlii i n (3S 488453 4S 102077} a i t t - v a l u e 0 7784682S l-RIGtfT-DEFEHDER i n (40 438843 42 1S8833) » i t t - v a l u e 0 969099t b e e n d e t ·

Figure 21. Demonstration of the approximation for different starting points

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usually will use the positions of the objects at the time quantum before as the initial position. Then, velocity restrictions can give further hints as to where the objects will be (cf. note 17). Since the proposed algorithm reacts sensitively on the starting position, the influence of the context conditions on the localization is rather naturally included. Figure 21 demonstrates the approximation for [near CenterCircleLine] for several starting positions. Depending on the starting positions which play the role of conditions of context, different solutions of the visualization problem are constructed. Furthermore, an object to be located with respect to a second object to be located will follow that second LO until both have reached their optimal positions. Figure 22 shows the approximation paths for two players localized by (left of player5 player-8 (extrinsic from the lower left corner)) and (in front of player8 LeftGoal). After about 5 steps, player-5 already reached a position left to player-8, and has to follow him until he also has reached his final position. The operation TyPoF-Addition combines several TyPoFs for one LO by arithmetic average in order to simplify the approximation by reducing

Graphic Pana

Figure 22. Demonstration of the approximation for depending objects

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the number of TyPoFs to be considered simultaneously. The basis for this operation was described in Section 5. Remember that TyPoFs are associated with individual propositions, like (left player-3 player-5). Since there are quite a lot of these individual propositions even in such a simple system as SOCCER, the task of determining every single TyPoF would be too complicated. In fact, the reference relation depends on all parts of the proposition: that is, both the type of the relation, i.e., the Spatial Concept, and the arguments influence the shape of the typicality function. Can we extract from their instances unique descriptors of the influence of the Spatial Concepts, and thus, separate both kinds of influences in order to get a formalism which is easier to deal with? Although the typicality distribution for different propositions of one type are more or less similar, the kinds of objects and especially their dimensionality, size, and shape modify the typicality distribution of a single proposition, stretching it, adapting it to the shape of the RO (cf. Figures 11 to 13). Therefore, the assumed influence of the

Figure 23. Signature of the spatial concept system (IV): Typicality schemata

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arguments, i.e., the objects involved, has to transform the proposed influence of the Spatial Concept underlying all of its instances. To cover the similarity between all instances of a Spatial Concept, we assume one function for each Spatial Concept which describes the typicality distribution not with respect to the coordinates of the objects, but with respect to what I call "essential parameters". The typicality distribution of every instance of a spatial relation is derived from this function. It differs from the distributions of other instances only with respect to how the essential parameters are calculated from the objects' coordinates. The ADT for these functions is called Typicality Schema (cf. Figure 23). The essential parameters, e. g., distance, angles, and scaling factors, are abstractions from the concrete coordinates. Figure 24 visualizes three Typicality Schemata — i.e., functions from essential parameters to Tvalues. For example, the Typicality Schemata for proximity and contiguity (or the near and at concepts) both depend on two essential parameters: the distance between LO and RO and a scaling factor (cf. note 18). How both parameters are connected to the actual coordinates of LO and RO depends on the dimensionality and size of the objects.

Figure 24. Three examples for typicality schemata

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Typicality schemata can be combined by multiplication. In ANTLIMA, the Typicality Schemata of the projective relations "being left o f ' , " — right o f ' , " — behind", and " — in front o f ' are defined as combinations of the Direction and the Proximity Schemata, and thus, have five essential parameters: distance r, distance scaling G, the reference system δ, the angle 0 with respect to δ, and the scaling of the angle G'. In summary, VITRAs Spatial Concepts are essentially defined as combinations of simple graded functions (multiplication of basic Typicality schemata) of essential parameters (cf. note 19). The influence of the objects is encoded by TyPoF Instantiation Rules (for short: I-rules). In addition to its Typicality Schema, each spatial concept is associated with a set of I-rules. We can say that, in a way, Irules spread the typicality distributions encoded in the Typicality Schema around the ROs in the percept, thus developing the appropriate Typicality Potential Field, which, then, directs the LO towards its optimal position. Each I-rule specifies, according to the object attributes, a set of functions for calculating the essential parameters. These "parameter functions" as I call them, transform the coordinates of the objects, i. e., the information in the percept, to the essential parameters needed by the Typicality Schemata. Since, for example, Distance, the essential parameter of the Proximity Schema, is defined only between zero-dimensional objects, we have to reduce — or idealize — higher-dimensional objects to points in order to apply the Proximity Schema. In other words, to find the distance between two two-dimensional objects, we first have to look for those two points of the borders of both objects which are closest to each other (cf. Figure 25, and also Figures 11 to 13). These points are viewed as those objects, their distance is the distance between the objects. Actually, this object coercion is the important part of the parameter function, since the calculation of distance per se remains unchanged in every I-rule: the Euclidean distance between two points. Similarly, Angle in the Direction Schema is only defined for two lines — the zero line of the reference system and the line between RO and LO. The geometric situations in the percept have to be adapted to this restriction: e. g., the zero direction of the reference system can be derived either from inherent object properties of the RO (intrinsic use) or from another object in the context (extrinsic use) which defines exactly one line to the RO (cf. note 20). Again, the coercion of the original percept to an idealization plays the major part of the parameter functions used for the Direction Schema. In every particular case, the angle is calculated in the same way from the idealization.

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rtiffemnl

ideal caüfi

Scaling Factors

points dualizing the general caw;

object«

Figure 25. Illustration for distance f u n c t i o n s and scaling f a c t o r s

For both cases, I-rules have to be defined. The size of the objects, which was ignored by the essential parameters Distance and Angle, has an influence by means of the scaling factors. For [near player-5] and [near PenaltyArea], the Typicality Schema of Proximity not only has been spread differently around the ROs with respect to their shape, but also 'stretched' to different diameters corresponding to the size of the ROs (cf. Figure 25, and also Figures 11 to 13). In summary, hidden in the I-rules of a spatial concept in VITRA are functions which coerce parts of the percept to a more abstract, sketchlike form which is the basis for calculating the essential parameters for the Typicality Schemata. This sketch is not explicitly modeled in VITRA yet, though, and further studies have to be carried out about their relation to reference semantics of spatial concepts (cf. Section 1). The whole algorithm for visualizing elementary static spatial relations can be sketched as in Figure 26. Originally starting from the temporally ordered sets of elementary spatio-temporal propositions (the Propositional Elementary Structure), we consider here only one time quantum and the corresponding set of static spatial propositions. For each proposition in this set, we find the type and the associated Typicality Schema (operation: TySc? (type? (p))); additionally, we get the set of I-rules of the Spatial Concept (operation: I-rules (type? (p))). The aruments of the proposition choose one of the I-rules, which, then, transforms the Typi-

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Propositions Elementary Structure

propos-

propos-2 TyPoF-

Spatial Concept

Typicality Schema

Initial Mental Image

transforms

chooses

TyPof-2

Final Mental Image Referent for t-6

Figure 26. Algorithm of A N T L I M A ' s visualization of static spatial propositions

cality Schema to the appropriate TyPoF by specifying the appropriate parameter functions: 7.

TyPoF? (ρ) ξ apply-I-rule (choose (I-rules? (type? (p)), Arguments? (p)), TySc? (type? (p)))

By TyPoF-addition, all TyPoFs belonging to one LO in the set are combined. Thus, we finally consider a set of LOs, each associated with one TyPoF. With the init-image operation, we then construct a first mental image with all the objects used as arguments in the original set of propositions (cf. note 21). The aforementioned hill climbing approximation (cf. Formula 6) transforms this initial image to the most typical

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image, the referent we looked for. T h e n , the sum of all T-values finally reached is used as a first a p p r o x i m a t i o n of the plausibility of the description f o r the listeners.

7. A comparison with Herskovits' analysis of the semantics of spatial prepositions O n first view, the separation of the influences on the typicality distributions described in the previous section seems to reflect the distinction between several aspects A. Herskovits introduced in her analysis of the semantics of spatial prepositions in English. Is this similarity only superficial, or can we also interpret the operational f o r m of the reference relationship in S O C C E R as a simplified realization of Herskovits' analysis? T h e following c o m p a r i s o n is still on a very coarse level a n d will be elaborated f u r t h e r in the future. In order to avoid polysemy f o r spatial prepositions, Herskovits (1986: 39) suggests an ideal meaning of a spatial preposition underlying all uses of t h a t preposition. In her own words: The ideal meaning of a preposition is a geometrical idea, from which all uses of that preposition derive by means of various adaptations and shifts. An ideal meaning is generally a relation between two or three ideal geometric objects (e.g., points, lines, surfaces, volumes, vectors) — in fact, ideal meanings are usually those simple relations that most linguists and workers in artificial intelligence have proposed as meanings of the prepositions. These relations play indeed an important role, but as something akin to prototypes, not as truth-conditional meanings. Coincidence of points, inclusion of a point in a line or in an area, contiguity of two surfaces — these are some examples of relations used as ideal meanings. A substantial p o i n t is m a d e in the last sentence of the quote: a l t h o u g h the ideal m e a n i n g underlies every occurrence of a spatial preposition, it m a y be " d e f o r m e d " , " w e a k e n e d " , partially "overwritten" or " e x t e n d e d " a n d serves merely as a "gravitational center" f o r the meanings of different occurrences, n o t as an accurate and complete description. Actually, for Herskovits, the meaning of single occurrences of a spatial preposition is derived f r o m the ideal m e a n i n g by three steps (cf. F o r m u l a 8):

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In a particular use of a preposition, the ideal meaning may have been transferred to another relation, one that is in some way closely related; [step 1] this new relation may in turn be only approximately true. [step 2] Moreover, the objects related are mapped onto geometric objects (matching the categories specified for the arguments of the ideal meanings) by processes of geometric imagination, idealization and selection. [step 3] These mappings onto geometric descriptions, corresponding to various geometric conceptualizations and metonymies, are accomplished by a variety of functions. [Herskovits 1986: 40, with comments by JS] A n d later, defining technical terms f o r the t r a n s f o r m a t i o n s : The geometric meaning of a locative expression is thus a proposition involving a relation applying to geometric descriptions [3] of the objects, and that relation may be the result of two transformations applying in succession to the ideal meaning, which I call sense shifts [1] and tolerance shifts [2], (Herskovits 1986: 40, numbers added by JS) 8.

[T [S [IM]]] (G, (Of), G 2 (02))

with: Τ S G, IM

— — —

Tolerance Shift — (step 2) Sense Shift - (step 1) G e o m e t r i c Idealization of Object O, — (step 3) Ideal M e a n i n g

Although the spatial prepositions in S O C C E R ' s language are quite restricted c o m p a r e d to o u r everyday language use, the reference-semantical mechanism controlling this reduced language is already r a t h e r c o m plicated, as we saw. It is m y thesis that this m e c h a n i s m can be m a t c h e d with parts of Herskovits' analysis. Already on first view, o n e notices a relationship between Spatial C o n cepts in S O C C E R a n d ideal meanings. Spatial concepts represent the meaning of spatial prepositions per se, so to speak; they f u n c t i o n as reference points with respect to which p r o p o s i t i o n s a b o u t the perceived spatial e n v i r o n m e n t are f o r m u l a t e d . In general, they are defined by c o m b i n a t i o n s of Typicality Schemata. Similarly, an ideal m e a n i n g stands f o r the m e a n i n g of a spatial preposition itself, a n d is defined as a conjunction of elementary spatial relations which are "perceptually salient relations", i. e., "easily, quickly a n d accurately perceivable" (Herskovits 1986: 54, a n d n o t e 22). O f course, it is n o t just by chance t h a t m y examples f o r Typicality S c h e m a t a — Proximity, Contiguity — all can be f o u n d in the list of examples f o r elementary relations used as ideal

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meanings. Indeed, also the procedural aspect of ideal meanings is stressed: "We can conceive of this core schema [i. e., the ideal meaning of 'in' (JS)] as a logical predicate, but its psychological realization is most certainly a routine [Ullman 1985], a procedure which checks whether spatial inclusion holds" (Herskovits 1989: 13). Though I could not find an explicit record, it seems probable to me that Herskovits' elementary relations correspond to mathematical concepts which encode clear, binary classifications: a set of arguments either stands in a given relation, or it does not (cf. note 23). The second step of adaptation mentioned above, the tolerance shift, supports this assumption. We have already considered the fuzziness of the applicability of spatial prepositions in Section 4. To cover this phenomenon of ordinary language with the mathematically accurate definitions of ideal meanings, the sharp borders of applicability of the mathematical relations have to be softened. Then, coincidence of points can be true in a weaker sense — or in other words: the relation is less applicable — for two points which do not actually coincide but only are close together. In contrast to that, SOCCER already considers the fuzziness on the level of Spatial Concepts: Typicality Schemata describe/define weak, fuzzy forms of some of the mathematical relations mentioned above. This may reflect a more empiricist view, assuming that the spatial concepts somehow evolve from perception, which is assumed to be always vague or fuzzy. There is no obvious reason why spatial concepts should lose this quality. Herskovits, on the other hand, seems to adopt a more rationalist point of view, starting by a clear, simple, and especially binary classification which is somehow innate, and which afterwards has to be blurred in order to fit the phenomena (cf. note 24). As a consequence, there is no need for a distinction of the second type of transformation Herskovits mentioned, the tolerance shifts, from other kinds of transformations in SOCCER. Every transformation of Typicality Schemata necessarily changes the "tolerance" for the applicability of that preposition in a particular manner, e. g., spreading and stretching the Typicality Schema around the RO. In principle, something equivalent to sense shifts, the first step in adapting ideal meanings to a particular instance, can occur on combinations of Typicality Schemata, as well. Skipping one of the conjuncts or adding one more are the most prominent examples for sense shifts (cf. Herskovits 1986: 94), and both can be performed similarly on Typicality Schemata. Although, the domain of SOCCER is still too simple (or

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better: SOCCER perceives it in a too improverished manner) for an example of such a shift to be found yet. Most interesting for this comparison is the remaining step in Herskovits' derivation scheme (no. 3), called geometric description. As mentioned above, the objects used as arguments of the prepositions have to be transformed to the simple geometric objects used as arguments of ideal meanings. Since the relations defining the ideal meanings or their derivates by sense and tolerance shifts only apply to simple geometric objects, coercions have to be found which also can be viewed as different conceptualizations of the objects: when an object is described as 'being at' some RO, both objects are conceptualized as points. To this purpose, a broad set of geometric description functions was collected by Herskovits (cf. Herskovits 1986, Chapter 5). Usually, several coercions apply in sequence until the appropriate conceptualization is found. Pragmatic factors like salience, relevance, and tolerance influence the decision as to which sequence of coercions is applied (cf. also Hays 1987). Obviously, something similar is hidden in the I-rules in VITRA; as discussed in the previous section, I-rules specify parameter functions which calculate the essential parameters from the percept — the coordinates of the objects. To that purpose, the objects first have to be transformed to idealized forms appropriate to calculate the essential parameters — points, lines etc.: a sketch-like representation of parts of the referent is generated implicitly, so to speak. However, there is one main difference between Herskovits and VITRA: the coercion in VITRA always depends on all objects simultaneously, whereas in Herskovits' scheme the geometric description functions apply to each object separately. I assume that this difference is a consequence of the selection principles. Whereas Herskovits considers in her much broader framework pragmatic principles which coordinate the idealizations of all involved objects, in VITRA until now only idiosyncratic rules are defined: the condition part of Irules refers to attributes of the involved objects like dimensionality, size, type, etc., and specifies explicitly for each relevant class of combinations one set of parameter functions with the corresponding coercions. General rules have not been considered yet (cf. Formulas 9 and 10). 9.

TS [PF, (LO, RO), PF 2 (LO, RO), ... PF„ (LO, RO)]

10.

PF, (LO, RO) = F (Idealize,, (LO), Idealize, 2 (RO))

with: TS — Typicality Schema

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PF, — Parameter Function of the i'h Essential Parameter F — the pure parameter function (e.g., distance of points) To conclude, the solution of the visualization problem in VITRA has led us to a conception of the reference semantics of spatial prepositions which is comparable to a simplified form of A. Herskovits' theoretical framework (cf. Formulas 8, 9 and 10). As in her approach, we assume a core meaning of each spatial preposition — the Spatial Concept with its defining Typicality Schema. Individual occurrences are derived by spreading the schema appropriately over the mental image by means of I-rules. This spreading can also be viewed as idealizing the objects in the mental image to simple geometric objects — which corresponds closely to Herskovits' derivation step 3. Because VITRA alludes to a totally operational form of reference semantics for spatial prepositions, the comparison offers a computational realization of a substantial part of Herskovits' analysis. Furthermore, using this realization to derive additional hints for future elaborations of the framework seems a plausible path to follow.

8. Summary The problem of integrating vision and natural language systems has led us in the project VITRA to investigate the nature of the reference relationship (cf. Figure 27). This resulted in a rejection of the objectivist view due to its rather obvious weak points: essentially, objectivist reference theories cannot explain adequately how the objects in the world,

Figure 27. The reference relationship — final view

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which are viewed as the referents, conduct their influence on verbal behavior. Instead, we view mental entities like percepts and mental images as referents, thus adopting in VITRA an experientialist theory of the reference relationship (cf. note 25). In the system SOCCER, this decision resulted in an operational realization of the reference relation proper: algorithms are being developed that bind exactly in the spirit of experiential reference semantics the usages of spatial prepositions to SOCCER's percepts, the results of an image understanding system. The core of these algorithms is always a classification function which associates the percepts to a graded Spatial Concept. A degree of applicability allows us to distinguish between good and less good occurrences of such a graded concept and is reflected on the verbal surface by linguistic hedges. Combining the demands of experiential reference semantics with the Gricean Cooperative Principle furthermore compelled us to reconstruct in the form of mental images the referents of the text SOCCER plans to generate in order to anticipate the understanding of the listeners. SOCCER, thus, is able to improve its texts. This leads directly to the visualization problem: since we usually lose information when we transform percepts to propositions, the inverse transformation from propositions to mental images has to produce additional information somehow. In fact, both transformations have to use the reference relation: reinterpreting it, i. e., the classification functions, as typicality functions and correspondingly the degrees of applicability as degrees of typicality allows us to solve this task by generating the most typical mental images as reconstructed referents. The operational realization of the reference relation in VITRA rests on the classification/typicality functions: Typicality Potential Fields encode these functions, and are used both for recognizing spatial relations from percepts and for reconstructing mental images from propositional descriptions. Furthermore, we distinguish between two components which define the TyPoF for a particular case: Typicality Schemata bring in the general influence of the spatial concept and are transformed by I-Rules that depend on the objects involved. Although technical reasons originally forced this distinction, the separation of the two components seems to reflect a deeper, cognitively important structure of the reference relation; a comparison with the analysis of A. Herskovits revealed a significant degree of similarity between ideal meanings and Typicality Schemata on the one hand, and geometric descriptions of objects and parts of the transformations in the I-rules on the other. Sketchlike idealizations which

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are hidden in the I-rules in VITRA and rather overtly included in Herskovits' framework point to structures integral to the reference relationship which are connected to visual abstraction and metaphoric extension; these will have to be examined further. In summary, with its system SOCCER, VITRA demonstrates — albeit still on a very coarse and primitive level — the benefits of investigating reference phenomena in an operational form.

Acknowledgements I would like to thank heartily Ellen Hays who not only had a critical look at my English but "obstetrically" helped me to clarify my ideas during hours of discussion. Also my colleagues in Saarbrücken are to be thanked for comments and critiques on earlier versions. Furthermore, all participants of the workshop on the Semantics of Prepositions in Saarbrücken 1990 contributed with their discussion to the present form of the paper.

Notes 1. General arguments against every realistic approach of reference can be found in Empiricus (1985) and Wittgenstein (1963); both authors base their arguments on a reflexive turn: asking how we could refer to the reference relationship itself they are led to sceptical consequences which "destroy" the presuppositions of objectivist reference theories, namely the possibility of access to an independently given world. 2. I use the expression "mental image" not only to refer to visual images although only those are considered in this paper; since they are connected so closely to perception, mental images seemingly can arise in all modalities of perception; cf. Lakoff (1987: 444): "The term 'image' is not intended here to be limited to visual images. We also have auditory images, olfactory images, and images of how forces act upon us." 3. By the way: "propositions" in this context might best be related to "symbolic cognitions" in the sense of Leibniz (cf. Leibniz 1937, §24); in connection with corresponding referents, they become "adequate cognitions"; the expression "reference relation proper" corresponds closely to the term "concept" in the traditional terminology; cf. Schirra (1993, Sect. 1.4). 4. This usage is closely connected to the procedural/declarative distinction; cf. Winograd (1975); cf. also the distinction of different uses of the expression "proposition" in Johnson (1987: 3). 5. This does not exclude (mental) entities to be used at one time as referents and at another time as propositions. This is typically demonstrated by (percepts of) sketches, e. g., of the sun: the sketch itself is a concrete thing which can be perceived and used as referent — as for example in this sentence. But normally, we do not look at the sketch itself, but at what it represents. We use the sketch as a set of propositions about something else — the referent of the sketch which is the sun in our example (cf. Eco 1973: 208). Similarly, when speaking about percepts the corresponding mental entities

Spatial prepositions: The visualization problem

6. 7.

8.

9.

10.

11.

12.

13.

14. 15.

509

are used as propositions: the percepts of something. In this article, no such metamorphosis is considered. More details of the system REPLAI-II which also includes strategies to recognize plan interaction and failure are to be found in Retz-Schmidt (1991 a). Additionally, but not described in this report, the listener model is used to control the generation of noun phrases, anaphora, and ellipses; cf. Jameson and Wahlster (1982); Andre (1988); and Schirra (1991). This does not mean that listeners of broadcasted sports reports always generate visual mental images. The reconstruction of the referents constitutes an already very high level of understanding; cf. Craik and Lockheart (1972); and also Leibniz (1937 §24). Though, these listeners are assumed to function mentally in a way corresponding to the simplicity of SOCCER; i. e., they perceive similarly to S O C C E R and know more or less the same about spatio-temporal relations and composed events. If radio reporters could not rely on such an assumption of cognitive equivalence with their listeners, sports reports would have to be of a very different form than they actually are. "LO" and " R O " are the most common abbreviations used, e.g., in Habel and Pribbenow (1988) and Herskovits (1986); alternative terms used in linguistics are listed in Retz-Schmidt (1988). This influence is documented for example in: Andre et al. (1985, 1986 a, 1986 b, 1987, 1989); Wahlster 1988; Schirra et al. 1987; Retz-Schmidt 1988; Schirra 1990 a, 1989; Hays 1990, 1989; and Herzog et al. 1990. The input for the complete visualization task is the temporally ordered sequence of those sets (plus elementary velocity restrictions), called the propositional elementary structure; the complete referent of a composed event proposition is constructed by chunking static images appropriately together to form an image sequence. In the right window, a sectional view cutting through the typicality cloud at its maximum is shown, called "Traverse" and following the arrow in the graphic pane from the right to the left; the maximum for this localizing combination is reached at a T-value of approximately 0.9. Dotted arrows mark those operations described earlier. This is not completely true, but it will suffice here; cf. Section 7; In S O C C E R , all mobile objects are zero-dimensional. Thus, it is easy to define the position of such an object. An object of higher dimensionality could be idealized to its "center of gravity" or a particular point of its border (e.g., the one closest to the RO) which represents the object's location. The extension of such objects is considered by different mechanisms (cf. I-rules in Section 6).

16. The term typicality potential field is motivated by interpreting the classification function physically as a potential field whose associated force field (the vector field resulting the gradient operation) pulls the LO into its optimal position (with maximal potential energy); similar to a negative field of gravity, the TyPoFs pull the LOs always "uphill to the summit of the typicality mountains". Note that the moving of the imaginative LO during approximation also can be used to direct (visually) searching for the perceived LO: if we want to find an object which position is described verbally, our visual focus of attention moves — as if controlled by the typicality distribution — toward the most typical positions associated with the verbal description. 17. These hints for finding good starting positions have to be used in the aforementioned init-image operation; cf. Schirra (1993).

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18. Thus, the Typicality Schemata are actually two-dimensional; the scaling dimension was skipped in the sketch as an autonomous axis for the sake of simplicity. 19. Obviously, the combination of TyPoFs (which is actually a renormalized addition of functions) and the combination of Typicality Schemata (which is a plain multiplication of functions) serve different purposes: the first combination integrates the simultaneous influences of several restrictions for one LO, whereas the second combination allows for defining compound Spatial Concepts. 20. A special case of extrinsic use is the deictic use: the object that determines the orientation is the speaker/listener and is normally not explicitly mentioned; cf. Retz-Schmidt (1988). 21. If a whole image sequence is to be constructed, this step is only needed at the beginning or when a new object enters the scene; otherwise, the image for one time quantum is used as the initial image for the approximation of the next time quantum; with this, the algorithm always automatically consideres the context. 22. In Herskovits (1986: 55), one finds a list of relations Herskovits takes into consideration: "enclosure, contiguity with line or surface, order of three points on a line, order of two points on an oriented line, coincidence of two points, line in/on a plane, alignment of points, parallelism of lines, alignment with direction, orthogonality of lines, support, on line of sight, on orthogonal to line of sight". 23. Remember that these relations apply to geometric concepts derived from the argument objects; Herskovits' discussion of "at" (Herskovits 1986: 51) and "to the right" (p. 184) as "graded concepts" points toward an understanding similar to VITRA's; although it remains unclear whether the gradation is part of the ideal meaning or not. At least, the ideal meaning of "at" (p. 128) is simply defined as: "for a point to coincide with another". Similarly, the ideal meanings finally proposed for the projective prepositions (p. 190) do not include gradation: the LO has to be located (exactly) on the corresponding axis of the reference system. 24. This presentation of Herskovits' handling of tolerance phenomena is rather simplified; cf. especially Herskovits (1986, Chapter 6.3, 'Tolerance and Idealization'); the "blurring" is assumed to be either idiosyncratic or controlled by pragmatic factors. 25. Further investigations considering some problems inherent to the mentalist point of view of the reference relation are to be found in Schirra (1992 a); cf. also Tugendhat (1982, Section 20) and Schirra (1992 b). (Figures 1 and 2 are produced on the base of two drawings of Charles M. Schultz and a picture of the earth taken from LIFE and Banett)

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Habel, Christopher — Michael Herweg — Klaus Rehkämper 1989 Raumkonzepte in Verstehensprozessen — Interdisziplinäre Beiträge zu Sprache und Raum. Tübingen: Niemeyer. Hays, Ellen M. 1987 A computational treatment of locative relations in natural language. [Technical Report MS-CIS-87-31, Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA.] 1989 "Two views of motion: On representing move events in a language-vision system", in: D. Metzing (ed.), GWAI-89, 312-317. Berlin: Springer. 1990 "On defining motion verbs and spatial prepositions", in: C. Freksa — C. Habel (eds.), Repräsentation und Verarbeitung räumlichen Wissens, 192-206. Berlin: Springer. Herskovits, Annette 1985 "Semantics and pragmatics of locative expressions", Cognitive Science 9: 341— 378. 1986 Language and cognition — an interdisciplinary study of the prepositions in English. Cambridge: Cambridge University. 1989 The linguistic expression of spatial knowledge. L. A. U. D. Report A 248, Linguistic Agency University of Duisburg, Duisburg. Herzog, Gerd — Thomas Rist 1988 Simultane Interpretation und natürlichsprachliche Beschreibung zeitveränderlicher Szenen: Das System SOCCER. [Memo 25, Fachbereich Informatik, Universität des Saarlandes, Saarbrücken. Diplomarbeit.] Herzog, Gerd — C.-K. Sung — Elisabeth Andre — W. Enkelmann — H.-H. Nagel — Thomas Rist — Wolfgang Wahlster — G. Zimmermann 1989 "Incremental natural language description of dynamic imagery", in: W. Brauer — C. Freksa (eds.), Wissensbasierte Systeme, 153-162. Berlin: Springer. Herzog, Gerd — Thomas Rist — Elisabeth Andre 1990 "Sprache und Raum: natürlichsprachlicher Zugang zu visuellen Daten", in: C. Freksa — C. Habel (eds.), Repräsentation und Verarbeitung räumlichen Wissens, 207-220. Berlin: Springer. Jameson, Anthony — Wolfgang Wahlster 1982 "User modeling in anaphora generation: Ellipses and definite descriptions", in. Proceedings of the 5 th European Conference on Artificial Intelligence, Orsay, France, 222-227. Johnson, Mark 1987 The body in the mind — The bodily basis of meaning, imagination, and reason. Chicago: Chicago University Press. Lakoff, George 1972 "Hedges: A Study in meaning criteria and the logic of fuzzy concepts", in: P. M. Perantean — J. N. Levi — G. C. Phares (eds.), Papers from the 8th Regional Meeting, 183-228. Chicago: Chicago Linguistics Society. 1987 Women, fire, and dangerous things — What categories reveal about the mind. Chicago: Chicago University Press. Leibnitz, Gottfried L. 1937 "Discourse on metaphysics", in: Discourse on metaphysics, correspondence with Arnauld, and monadology. Lasalle, 111.: Open Court Publishing Company. [Transl.: George R. Montgomery.]

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Connecting visual and verbal space — Concerning mental images in a listener Model. Bericht, SFB 314, VITRA, Universität des Saarlandes, Saarbrücken. [Forthcoming 1993.) 1992 b Connecting visual and verbal space — Preliminary considerations concerning the concept "mental image". Bericht 90, SFB 314, VITRA, Universität des Saarlandes, Saarbrücken. [To appear also in: Proceedings of the 4th European Workshop on Space, Time, Movement and Spatio-Temporal Reasoning, Universite Paul Sabatier, Toulouse, 1993.] forthcoming Zur Verbindung von visuellem und sprachlichem Raum — Eine interdisziplinär orientierte Untersuchung im Rahmen der KI am Beispiel von Bildvorstellungen in einem Hörermodell zur Bildbeschreibung. [Doctoral thesis, Fachbereich Informatik, Universität des Saarlandes, Saarbrücken.] Schirra, Jörg R. J. — Guido Bosch — C. K. Sung — G. Zimmermann 1987 "From image sequences to natural language: A first step towards automatic perception and description of motions", Applied AI 1: 287-305. Schirra, Jörg R. J. — Ellen M. Hays forthcoming Solvitur ambulando — An imaginative walk toward an understanding of spatial metaphor. Bericht, SFB 314, VITRA, Universität des Saarlandes, Saarbrücken. Sondheimer, Norm K. 1978 "A semantic analysis of reference to spatial entities", Linguistics and Philosophy 2: 235-280. Sung, C.-K. 1988 "Extraktion von typischen und komplexen Vorgängen aus einer langen Bildfolge einer Verkehrsszene", in: H. Bunke — O. Kübler — P. Stucki (eds.), Mustererkennung 88. Berlin: Springer. Talmy, Leonard 1983 "How language structures space", in: Η. Pick — L. Acredolo (eds.), Spatial orientation: Theory, research, and application, 225-282. New York: Plenum. Tugendhat, Ernst 1982 Traditional and analytic philosophy: Lectures on the philosophy of language. Cambridge: Cambridge University Press. Ullman, Shimon 1985 "Visual routines", in: S. Pinker (ed.), Visual cognition, 97-159. Cambridge, MA: MIT Press. Vandeloise, Claude 1986 L'espace en franfais. Paris: Editions du Seuil. Wahlster, Wolfgang 1988 "One word says more than a thousand pictures — on the automatic verbalization of the results of image sequence analysis systems", T.A. Informations, Special Issue: Linguistique et Informatique en Republique Federale Allemande. Winograd, Terry 1975 "Frame representations and the declarative-procedural controversy", in: D. G. Bobrow — A. Collins (eds.), Representation and understanding, 3582. New York: Academic Press. Wittgenstein, Ludwig 1963 Tractatus logico-philosophicus. Frankfurt/M.: Suhrkamp.

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Index

Prepositions are printed in italics: D = Dutch, Ε = English, F = French, G = German aan (D) 37 about (E) 75, 82, 95, 124, 306 above (E) 31, 106 ff„ 110, 125, 330 abstraction 2 in the mental lexicon 363 of essential properties 369 across (E) 31, 106, 119, 122, 332 active zone 39 adposition spatial 20 after (E) 121, 315 f. ago( E) 314 all across (E) 331, 334 f. all along (E) 336 all around (E) 334 all over (E) 331, 334 all through (E) 334 f. along (E) 19, 30, 119, 155 f., 336, 360, 368 f. als(G) 301 ambiguity 161 lexical 11, 355, 385 an( G) 307,452 analysis in natural language processing 1, 353 of source language 375 ANTLIMA 480 applicability degree 478, 486, 504 argument external 223, 225 f., 229, 245 internal 238 f., 245 argument structure 101, 113 f., 118, 129, 139, 141 around (Ε) 1 9 , 3 0 , 1 5 5 , 3 3 4 artificial intelligence 357, 436, 441, 446 a s ( E ) 301 as soon as (E) 301 aspect 19, 168 at (E) 7, 19, 74, 76, 93, 108, 111, 127, 133, 305 f., 310, 329, 336, 371

attention distribution of 373, 376 focus of 366 auf (G) 452 autonomy 30 away from (E) 329,336 axis horizontal 15, 254, 288 identification of 407, 420 maximal 234 observer 1 5 , 2 2 6 , 2 5 4 , 2 6 0 , 2 6 5 , 2 7 2 , 288 vertical 6, 15, 254, 371 axis-based sides 254 background 3, 9 base 8, 31 basic cognitive domains 357 because (E) 112 before (E) 102 ff., 106, 314, 316 behind (E) 31, 3 3 , 1 0 3 , 1 1 0 , 3 3 0 bei (G) 306, 448, 452, 463 below (E) 125,330 beneath (E) 330 beside (E) 122 between (E) 155,333,360 between ... and (E) 315 bevor (G) 316 bis (G) 309, 316 f., 321 Boolean algebra 401,415 bottom of object 257 intrinsic 281 boundedness 338 of reference objects 198 f., 201, 209 f., 279 mental closure of, see Gestaltschließung bounding 5, 17, 190, 201, 368 by (E) 79, 119, 124, 128, 136, 140, 309, 317 by the time (E) 316

518

Index

C-selection 102, 126, 133 calculus of individuals 401 case accusative 312 genitive 308 inherent 107, 136, 141 structural 107 case property 106, 122, 129, 139, 141 Case Theory 107 categorization natural 205, 207 of perceptual data 339 semantic 4, 10, 13 category discrete 3 functional 105 lexical 100 f., 122, 139, 143 natural 205 prototypical 21 schematic 21 semantic 4 vague 3 chains of meaning 18,76 classification function and typicality 488, 491 binary 504 graded 478, 486, 493 close to (E) 125 coercion of spatial objects 499, 505 cognition adequate and symbolic 508 disposition 351 equivalence 509 Cognitive Grammar 3 f., 8, 12, 14, 18, 20, 363, 365 cognitive routine 3 structure 339 coincidence situation 263 f., 278 compositionality 357 computational linguistics 18, 362 concept abstract 5 autonomous lexical 29 geometrical 258, 435 spatial 5, 441, 484, 503 topological 258

conceptual information 221, 224 ff., 229 f., 236, 245 f. conceptual properties functional 15 gestalt 15 structural 15 conceptual representation 279 conceptual structure (CS) 221, 236, 269, 272 conceptual variants 124, 126, 130 conceptualization 3 f., 8, 21, 179 f., 354 and specificity 352 metonymic 360 of spatial objects, see idealization principles of object conceptualization 16, 180 f., 212, 214 condition communicative 11 contextual 14, 481, 496, 510 necessary and sufficient 4, 11, 32, 179, 188, 190, 203-206 pragmatic 4, 9, 353, 365 configuration of landmark 17,338 of trajector 338 spatial 16, 21, 39, 210, 367 f., 373 configurational information 344 conjunction, temporal 21 constraints contextual 4 constraints on linguistic expressions cognitive 352 f. context marked 431 non-verbal/extra-linguistic 270, 397 normal 432 context conditions see condition contextual context of discourse see discourse context conventionality 3 f., 10 cooccurrence restrictions 19, 88 f., 94, 107, 109 cross-linguistic relation 344, 352 dans (F) 16, 18, 41 f., 179, 183, 185, 187 f., 190, 192, 394, 401, 417, 422 ff., 429, 431 f., 434

Index deductions 394 default meaning 359 defaults of semantic relations 358 defeated, see knowledge, defeasible depictorial representation 16, 23, 446, 467 depth assignment 261 f., 265, 276 derriere (F) 183 devant( F) 183 dimension adjectives 256 Dimension Interpretation 256 f., 262, 264, 288 dimension projection mental process of 210 dimension reduction mental process of 196, 210 dimensional expressions 249 dimensionality 5, 37, 39, 45, 50, 59, 62 f., 159, 199, 213 and boundedness 50-53, 197, 199 designation of 250, 281 of objects 5 , 1 5 , 1 7 , 1 5 9 , 1 9 0 , 1 9 9 , 201 f., 209, 213, 279, 449, 450 of related entities 37, 39, 62, 364, 368, 372 of the landmark 156, 159, 341, 373, 376 disambiguation of word senses 96, 167, 353 discourse context 358, 360 discourse domain 21 discourse situation 8 f., 363, 370, 374 ff., 385 disposition spatial 374 distance adjective 256, 259 Distance Interpretation 256 ff., 262, 288 domain abstract 19, 76, 354 basic 13 mental 73 semantic 8, 120, 123 spatial 89, 446 specific 13, 21 temporal 20, 368

519

domain of discourse see discourse domain down (E) 106, 155, 330 durch (G) 15,221-246,449 during (E) 119, 306 f., 310 f. dynamism in the lexicon 357 economy in computational linguistics 362 in mental categorization 362 encounter situation 263, 277 encyclopedic see meaning, encyclopedic entlang (G) 449 environment 8 spatial 4 events simultaneous 300 temporal ordering of 315 experience physical 4 preconceptual 4 experiential approach 255 extension of predicates 3 metaphorical 3, 10, 18, 20, 85, 380 ff. metonymic 10, 18, 380 semantic, of prepositions 85 semantic 3, 13, 18, 19, 73, 362, 380, 382 spatial 5 temporal 5 family of concepts 13, 14 family resemblance relation see family resemblance structure family resemblance structure 10, 16 f., 29, 44, 56, 206, 362 feature necessary and sufficient 29 semantic 1 figure 9, 31 figure-ground reversal 370 flexibility in computational linguistics 362 f. in the use of prepositions 371 lexical 355

520

Index

for (Ε) 11, 119, 140, 169, 170f., 312ff„ 317, 322, 359 foreground 3, 9 formalism 385, 394 inferential properties of 394 propositional 16 from (E) 75 f., 84, 103, 134, 332 f., 336 from ... behind (E) 103 f. from ...on (E) 316 from ...to (E) 315,331,333 front of object intrinsic 281 front-based region 266 function 6, 18, 21 graded 17 typical 372, 374, 376 f., 432, 434 functional properties 234 ff., 238 f. für/auf {G) 313, 318, 322 fuzziness 16, 60 gegen (G) 306 generalization 203 schematic 358 generation in natural language processing 1,17, 21 of a semantic representation 358 genericity 10 geometric property 354, 367, 446 geometry projective 401 gestalt mental 4f., 225 f. gestalt properties 222, 225 f., 233-239, 241 Gestalt Psychology 4, 9, 365 Gestaltschließung cognitive principle of 209 f. process of 193, 197, 368 f. gradation see graded classification function 484, 489 grammaticalization 19 f., 100, 141 f. granularity of space in natural language 401 gravity 352, 366, 423 Grice's Cooperativity Principle 480

ground in Gestalt psychology 9, 31 in metaphorization 384 head lexical 101,107,111,113,118,121, 139 f. semantic 101, 107 syntactic 101, 107 high{E) 256 highlighting contextual constraints on 4, 360 f. hinter (G) 252, 264 hoch (G) 258 Horizontal 266 idealization of geometrical and topological properties 360, 368, 374, 376 of spatial objects 499, 503, 506 identification 285 image mental 17 image schema 4, 89, 153, 364 immobility 273 implicatures 372, 430 in (D) 16 f., 35, 43, 56, 60 in (E) 7, 28, 64, 74, 78, 102 f., 111, 126 ff., 131, 133 f., 137, 143, 155, 308, 310, 329, 335, 360, 364, 377, 384 in (G) 310, 322 in back o / ( E ) 330 in front o / ( E ) 7, 30, 122, 330 inference 381,427,434 information processing 1, 2 economical 356 flexible 356 distribution of 1 functional 233 f., 236, 238 f. prototypical 29 informativity 19, 169 inmitten (G) 450 innate structure 21 innerhalb (G) 311 interlingua 353 internal argument 443 Internal Localization Noun (ILN) 394

Index interpretation computational 15 linguistic 4 propositional 352 f. semantic 352, 355 into{E) 7, 102, 330 f., 335 jenseits (G)

453

knowledge about typical use 18 background 352, 359, 368 classificatory 363 conceptual 12, 362 contextual 12 defeasible 18 encyclopedic 13 flexible use of 357 indefeasible 18 lexical 12 pragmatic 18 semantic 12, 362 stereotypical 362 landmark (lm) 6, 9, 16, 19, 27, 153, 365 f., 369, 422 ff. language performance 351, 357 later {E) 315 lattice theoretical analysis 17, 413 level depictorial 461, 464 functional 17, 400, 410 geometrical 17, 397, 400 f. grammatical 443 linguistic 444 of conceptual representation 12, 14 f., 182, 265, 444 ff. pragmatic 400 propositional 460 f., 474, 508 semantic 14, 446 lexical acquisition 353 lexical change 354 lexical entry 258 lexical variant 108, 123 f., 142 lexicalization 19, 124, 133, 143, 357 language-specific 11 lexicalization patterns 355 lexicon semantic 13, 356 f.

521

LILOG 15,467 linguistic hedges 17 links (G) 252 listener model 480 localization 453 dynamic 15, 456 ff. static 15 typical 16 located entity (LE) see located object located object (LO) 9, 15, 442 f., 448 ff., 452 ff., 456, 459 f., 463 f., 466 location 15 random 160 vertical 86 logic 394 first-order predicate 18 non-monotonic 18, 363, 397, 432 order-sorted predicate 467 mass terms 414, 416 meaning extensions of prepositions see extension, semantic of prepositions meaning conventional 355 encyclopedic 16, 327, 362 functional 16, 396, 435 generic 355 ideal 363 f., 371, 376, 385, 502 indexical 360 intrinsic 10, 353, 374 lexical 28, 118 linguistic 3 f., 13 prototypical 2, 14, 17, 206 f. schematic 14 spatial 16, 384 mental closure of object boundaries see Gestaltschließung mental completion of material boundaries see Gestaltschließung mental image 4 7 3 , 4 8 1 , 4 8 9 , 4 9 3 , 5 0 1 , 506 mental manipulation of object conceptualization principles of 193, 196 f., 199, 202, 207215 mental model 444

522

Index

mereology 401, 415 meronomy 412, 416, 419, 421, 423 f., 426 f., 430 metaphor 362, 380 and abstract meaning 384 established 384 frozen or dead 384 in computational linguistics 380 spatial 377 metaphorization 5, 209, 214 f. metonymic 9 metonymy 5, 257, 362 f., 373, 380 logical 362 mind 1 , 2 mobility 5, 7 modularity 268, 435, 445 motion 7, 9, 82 nach (G) 315 nachdem (G) 316 naive physics 396, 401, 410, 436 natural language processing (NLP) 1 f., 21 f., 353, 441 near (Ε) 118,122,125,137,330 neighbourhood region 253, 258, 260 side-based 288 network model 152 next (E) 122 object catagorization processes of 6, 16, 181, 212, 214, 278 object category see object concepts object concepts 181,272,447 interaction with prepositions 177-217 spatial properties of 177-217, 188, 456 Object Schema (OS) 15, 234 f., 241, 254, 269, 278, 285 objects spatial 476, 483, 497, 499 observer 31 observer-related sides 263 f. of (E) 107, 109, 127, 129, 137, 140 off (E) 75, 119, 329, 332, 335 on (E) 7, 19, 28, 74, 77, 125, 128, 130 f., 133, 136, 306, 329, 335, 364 f., 373, 376, 378 f. on top ο / ( Ε ) 122, 330

onto (Ε) 332, 335 ο/? (D) 32,156 orientation 7 ff., 15, 18, 272, 396, 408 actual 6 f. canonical 6 f., 273, 281 contextually induced 6, 274 f. deictic 411 fixed 273, 281 inherent 6, 274, 281 intrinsic 6 , 2 8 1 , 3 7 0 , 3 7 4 , 4 1 0 spatial 5 f. orientation-point see point of orientation out o / ( E ) 75, 128 ff., 143, 155, 329, 330f., 335 over (E) 32, 83, 95, 107, 155, 330, 371 f. parameter 14, 21, 221, 224f„ 230 configurational 338 innate 338, 348 of structure 338 path 15, 229, 231, 233, 239, 246 relational 338 semantic 285, 459 f. past (E) 31 perception 17 perfectivity 158 period of time 79, 305,310 periods simultaneous 303 perspective 2, 8, 352 perspectivization 6 f., 261, 263, 265, 273, 275, 281 canonical 276 f. contextually induced 277 inherent 277 plasticity in categorization 356, 371 plurals 413,418 point in time 79, 305, 308 point of departure 84 point of orientation 74, 76 metaphorical 77 point of view observer's 6 speaker's 7, 9, 372 f. points simultaneous 303

Index polysemy 10, 12, 32, 151, 354, 362 f., 380 position 9, 15 positional variation 281 postposition Japanese 328 predicates prepositional state 86 predication function of 8 relational 8 scope of 8 preposition accompaniment 80 area 85 ff. case 20, 137 f., 140 f. cause 93 ff. circumstance 565 ff. connection 79 contact 77, 85 deictic use of 7, 31, 165, 452, 464 directional 330-334 dynamic 80 enclosure 78 formal definition of 394 German projective 249-288 instrument 90 intransitive 173 intrinsic use of 7, 31 lexical 19 locative 334 manner 90 means 85, 90 movement 82 multiplex 19, 155 non-lexical 19 path 64, 81, 221, 223 f., 236 projective 7, 14, 17, 256 projective, extrinsic use of 14 proximity 75 separation 75, 84 ff. simplex 19, 155 source 74, 84 spatial 27, 221 f., 471, 473, 479, 483, 502 static 35 f., 80, 85, 87 temporal 21, 295, 298 temporal ordering 315 vertical space 75

523

preposition stranding 138 prepositional variants 100 Primary Perceptual Space (PPS) 15, 261, 254 ff., 273 Principle Lincencing 116 principle of maximum trajector 432 of minimum landmark 433 relevance 8, 372 salience 8, 369 f. tolerance 371 typicality 8, 370 principles biological 8 cognitive 8, 16, 20, 182f., 208, 212, 214 f., 352, 367, 369, 385 see also mental manipulation of object conceptualization fixation 431 localization 448 of mentally creating boundary 211 of subsumption 209,212 pragmatic 8, 18, 21, 397, 430, 434 f. spatial 441 processing conceptual 459-467 of semantic representation 12,180, 182 ff., 187 f., 208, 211 profile 8, 31 projection geometrical 408, 420 projection properties 101, 106, 111, 139, 141 Prototype theory 12 prototypicality 13, 62, 362 psycholinguistics 435 purpose 8 quantifiers floated 136 quantity of objects 18 radial structure 96, 484 reanalysis 130, 143 rear of object intrinsic 281

524

Index

rear-based region 266 reasoning analogical 355, 384 human 17 spatial 441 rechts (G) 252 redundancy lexical 358, 363 reference object (RO) 9, 15 f., 252 f., 257, 260, 264 f., 285, 442 f., 448, 449-455, 459, 463 reference relation 471 experiential 473 objectivist 472, 508 realistic, see objectivist reference semantics in Artificial Intelligence 471 of spatial prepositions 471 operational 475, 493, 506 reference system extrinsic 451 intrinsic 451 referent 471 fictitious 472 perceived 473 spatial 471 relation antonymy 259, 260, 288 between trajector and landmark 374 common sense spatial 17 default 370 directional 7 dynamic 7 functional 17, 370 ordering 17 part-whole 17, 35 f., 55, 412, 416, 418, 421, 452, 463 positional 7 projective 7 spatial 8, 19, 21, 27, 456, 459 spatial universal 367 static 7, 80 temporal 409 topological 7 relational information 344 relevance communicative 372

of parts of objects or situations 2, 18, 21, 352, 367, 373, 375 ff., 385, 433 f., 450, 465 representation lexical 18 semantic 3 right of (E) 360 round (E) 122,306 rule lexical 20 S-selection 144 salience 8 of parts of objects or situations 2, 21, 352, 367, 375 f., 382, 385, 465 of shape 372 ff., 377 schema 13 f., 363 schema theory 362 schematic structure 5 schematization 21, 367, 370, 375 ff. and translation 374 principles of 375 schematization type 368, 371, 382, 384 transfer of 381 f., 384 f. search domain 16, 454 f., 459 f., 466 seit (G) 1 1 , 3 1 4 , 3 1 8 , 3 2 2 , 3 5 8 seit (dem) (G) 316 selection properties 108 f., 116, 123, 135 selection tree 22, 295, 319 selectional restrictions of preposition 358 semantic form 221 f., 224, 227, 237, 243, 265, 269 semantic representation 14 of spatial prepositions 14, 16, 181 ff., 188, 203 ff., 207 f., 211 f., 214 semantic structure 1, 229 f. semantics cognitive 27, 181, 206 common sense 362, 441 formal 3, 393 437 lexical 27 f., 206 modularized 17 naive 362, 396 procedural 400, 475, 478, 493, 503 prototype 205 f., 207, 358, 362 reference, see reference semantics

Index semantics and pragmatics 3, 357, 435 situation 363 sense abstract 19 durative 22 lexical default 362 f., 374 novel 18 polysemous 18 set-theory and basic spatial relations 366 shape 5, 15, 407 sidedness 15 similarity judgements 206 f., 209 since (E) 11, 108, 125, 314, 316, 359 situation of discourse see discourse situation sobald (G) 301 S O C C E R 17, 475, 483 sous (F) 183, 434 space absolute 401 Newtonian conception of 31 physical 31 relativistic 31 structure in natural language processing 401 specification 285 state 21 passive 86 stevent (state or event) 296 sur (F) 18, 183, 394, 401, 412, 4 1 9 ^ 2 2 , 428, 434 synthesis in machine translation 1, 353, 382 system conceptual 13 image understanding 1 , 1 7 machine translation 21 natural language processing 373 question answering 446 semantic 13 text understanding 15, 17, 446 tegen (D) 317 Thematic Dependency Requirement ( T D R ) 136 thematic roles see theta roles

525

therefore (E) 112 theta binding 1 1 7 , 1 3 2 theta grid 113,118,129,145 theta identification 116 theta marking 114, 117 theta roles 235 Theta Theory 113 three-level a p p r o a c h 393-437 through (E) 19, 75, 77, 108, 155, 159, 331, 335, 373 throughout (E) 331, 334f. time of discourse 21, 296 time of event 21 time of state 21 time-point see point in time time-span see period of time to (E) 1 2 7 , 1 3 4 , 1 3 7 , 1 4 0 to the left of {E) 31, 33, 330, 332, 336 to the right of (E) 3 1 , 3 3 , 3 3 0 tolerance 16 t o p of object 257 intrinsic 281 topic in metaphorization 384 topological property 17, 354, 367, 446 topology 369, 401 toward(s) (E) 119, 333 trajector (tr) 6, 9, 16, 19, 27, 153, 365 f., 369 f., 395, 422 f. transfer in machine translation 353, 377 metaphorical 384 transitivity of meronomies 427, 429, 431 f., 433 f. translation 352 f. h u m a n 351 machine ( M T ) 1 , 3 , 3 5 1 , 3 5 3 , 385 of prepositions 355 process of 375, 385 two-level a p p r o a c h to semantics 4, 8, 12, 14ff., 16, 181 f., 249, 254f., 267f., 272, 285, 444 f., 447 two-level model see two-level approach typicality 18, 21, 364, 367, 385, 431, 489

526

Index

Typicality Schema 498 and ideal meaning 503 TyPoF 493 Instantiation Rules 499, 505 über (G) 252, 258, 449 uit (D) 43 um (G) 305 f., 449 under (Ε) 19, 31, 75 f., 83, 95, 330 underneath (Ε) 330 universality in grammatical structure 337, 340 in semantic structure 20, 153 unter (G) 252 until/till (E) 103, 111, 121, 309, 316 up (E) 104, 155 usage patterns difference in 352 f. use-type 190, 192, 195, 197, 199, 200 f., 208 ff. utterance situation 21, 367, 372 vagueness 11, 17, 355, 362, 368, 373, 385 valency 19, 168 vehicle in metaphorization 384

verbalization of visual information 17 Vertical 254, 258, 261, 272, 287 f. via (E) 332, 336 viewpoint see point of view visualization 471, 488 VITRA 475 von ... (an)/ab(G) 316 von ... bis (G) 315 vor (G) 252, 264, 314, 452, 464 während (G) 301, 311, 317, 321 wenn (G) 301 when(E) 301 while (E) 301 wie (G) 301 with (E) 75, 80, 94, 127 within (E) 311 world-knowledge 19, 167, 397, 431, 462 X-bar theory

19, 100, 102, 130

zwischen (G) 450 zwischen ... und (G)

315