Questions in Discourse : Volume 2: Pragmatics [1 ed.] 9789004378322, 9789004378315

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Questions in Discourse Volume 2

Current Research in the Semantics/Pragmatics Interface Series Editors Klaus von Heusinger (University of Cologne) Ken Turner (University of Brighton)

Editorial Board Nicholas Asher (Université Paul Sabatier) Johan van der Auwera (University of Antwerp) Betty Birner (Northern Illinois University) Ariel Cohen (Ben Gurion University) Paul Dekker (University of Amsterdam) Regine Eckardt (University of Constance) Markus Egg (Humbolt University Berlin) Donka Farkas (University of California, Santa Cruz) Brendan Gillon (McGill University) Jeroen Groenendijk (University of Amsterdam) Yueguo Gu (Chinese Academy of Social Sciences) Larry Horn (Yale University) Yan Huang (University of Auckland) Manfred Krifka (Humboldt University Berlin)

Chungmin Lee (Seoul National University) Claudia Maienborn (University of Tübingen) Alice ter Meulen (University of Geneva) Jaroslav Peregrin (Czech Academy of Sciences and University of Hradec Králové) Allan Ramsay (University of Manchester) Rob van der Sandt (Radboud University Nijmegen) Kjell Johan Sæbø (University of Oslo) Robert Stalnaker (Massachusetts Institute of Technology) Martin Stokhof (University of Amsterdam) Henk Zeevat (University of Amsterdam) Thomas Ede Zimmermann (University of Frankfurt)

volume 36

The titles published in this series are listed at brill.com/crispi

Questions in Discourse Volume 2: Pragmatics

Edited by

Malte Zimmermann Klaus von Heusinger Edgar Onea

LEIDEN | BOSTON

The Library of Congress Cataloging-in-Publication Data is available online at http://catalog.loc.gov

Typeface for the Latin, Greek, and Cyrillic scripts: “Brill”. See and download: brill.com/brill‑typeface. ISSN 1472-7870 ISBN 978-90-04-37831-5 (hardback) ISBN 978-90-04-37832-2 (e-book) Copyright 2019 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill, Brill Hes & De Graaf, Brill Nijhoff, Brill Rodopi, Brill Sense, Hotei Publishing, mentis Verlag, Verlag Ferdinand Schöningh and Wilhelm Fink Verlag. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Authorization to photocopy items for internal or personal use is granted by Koninklijke Brill NV provided that the appropriate fees are paid directly to The Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, USA. Fees are subject to change. This book is printed on acid-free paper and produced in a sustainable manner.

Contents 1 Introduction 1 Malte Zimmermann, Klaus von Heusinger and Edgar Onea 2 Focus, Questions and Givenness Daniel Büring

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3 The Scalar Particle har’i in Ngamo (West Chadic) Mira Grubic

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4 Question-Answer Pairs in Sign Languages 96 Annika Herrmann, Sina Proske and Elisabeth Volk 5 Inferring Meaning from Indirect Answers to Polar Questions: the Contribution of the Rise-Fall-Rise Contour 132 Marie-Catherine de Marneffe and Judith Tonhauser 6 Constructing QUD Trees Arndt Riester

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7 Underneath Rhetorical Relations: the Case of Result 194 Edgar Onea 8 Two Alternatives for Disjunction: an Inquisitive Reconciliation Floris Roelofsen Index

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chapter 1

Introduction Malte Zimmermann, Klaus von Heusinger and Edgar Onea

Over the past two decades, questions have become a primary topic of linguistic research at the semantics-pragmatics interface. In response to this development, the research network Questions in Discourse was funded between 2011 and 2016 by the German Science Foundation (DFG). This research network was initiated by Edgar Onea and Malte Zimmermann, and it enabled a large group of scientists working on the semantics and pragmatics of questions to discuss their research at regular meetings. The network’s overall goal was to work towards a better understanding of the nature of questions as linguistic and semantic objects, on the one hand, and the role of questions in the interpretation of natural language discourse, on the other. The network focused on three distinct aspects of this complex interaction: Firstly, on the role of implicit and explicit questions in the realization and interpretation of information structure; secondly, on the role of implicit questions in discourse structuring, in interpreting discourse particles, in the projection properties of presuppositions, and related phenomena. Finally, the network addressed the more general questions of how to model questions and question-answer paradigms, and how to distinguish between different types of questions, including implicit, explicit, embedded, and concealed questions, among others. Following a series of inspiring and fruitful meetings in Frankfurt am Main, Paris, Stuttgart, Amsterdam, Berlin and Göttingen, this two volume publication summarizes a significant part of the research activity of the network: Whereas vol. 1 (see von Heusinger et al. 2019) concentrates on aspects of the semantics of questions, the present volume focuses more on pragmatic aspects of questions, even though the distinction is not always that clear-cut – with many of the individual contributions targeting issues at the semantics-pragmatics interface. Vol. 1 includes an overview paper by Onea & Zimmermann (2019), which contains a short introduction to the formal semantic analysis of questions in general. In addition, it gives a short overview and critical evaluation of the main topics of current research on questions at the semantics-pragmatics interface. The central purpose of this overview is to make it easier for readers to access the contents of the individual contributions in both volumes, and to situate these within the current state-of-the-art in question research. We expect this overview to be of particular use to scholars new to the field. However, because

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of its wide coverage of empirical phenomena and analytical tools, it will serve as a useful reference manual for experts as well. The role of questions in pragmatics and at the interface between discourse and grammar has been given considerable attention in recent years, and there are some important empirical areas for which this claim holds in particular. To begin with, it is a central task of formal linguistic theory to formulate an adequate theory of intonation and stress. Such a theory will have to incorporate the interlocutors’ communicative aims, such as, for instance, questions posed for answering at any given state of a discourse (Onea, 2016), or more general, extralinguistic discourse goals (Roberts, 2012). But it also has to make reference to structural features of the discourse context, such as the information status of the linguistic expressions used as given, new, contrastive etc. (Schwarzschild, 1999). Discourse goals and information-structural properties interact in complex and not alwas properly understood ways. At the same time, questions seem to play an important role in discourse structuring itself, as repeatedly argued in the literature following Klein & von Stutterheim (1987) and Roberts (1996). Finally, questions have been argued to play an important role in the interpretation of discourse particles (only, even) and other information-structural markers (but): Questions provide an anaphoric background against which to interpret such expressions. Various papers in this volume address these problems, while focusing on different empirical and theoretical aspects. The contribution by Daniel Büring Focus, Questions and Givenness proposes a formally explicit theory of intonation and stress in the framework of unalternative semantics. This novel approach significantly improves on previous accounts by distributing the explanative power between the question-answering nature of focus (contrast), on the one hand, and the information status of the relevant constituents (givennew), on the other. Crucially, the paper argues that givenness alone is only a necessary, but not a sufficient condition for deaccenting, in stark contrast to much recent literature, and that the possibility of deaccenting also depends on focus contrast. In addition, it is argued that the contextual question licensing such focusing need not be contextually salient, pace Rooth (1992), but merely identifiable and relevant. The contribution The scalar particle har’i in Ngamo (West Chadic) by Mira Grubic investigates the interaction between the context-structuring role of questions and the interpretation of focus particles in the under-studied Chadic language Ngamo, spoken in Northeastern Nigeria. The article focuses on the interpretation of the generalized scalar particle har(’i), which covers a range of meanings expressed by the English counterparts even, until, as far as, and already, respectively. Grubic proposes a unified analysis building on the as-

introduction

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sumption that har(’i) is (i.) scalar and (ii.) alternative-sensitive, for which reason it must be interpreted relative to the question under discussion. The paper includes a detailed comparison to English even, showing how different syntactic configurations lead to more complex scales for har(’i) to associate with, thereby giving it a wider range of scalar usages. Sign languages are also under-studied, especially when it comes to their (discourse) semantics. Sign languages are of particular interest for the study of information structure and intonation at the discourse-grammar interface because they differ significantly from spoken languages in how the different functional components are linguistically realized. Next to in situ and ex situ wh-questions, some sign languages also exhibit wh-doubling and so-called question-answer pairs as structural options for highlighting the questioned constituent. Question-answer pairs are particularly interesting, as they consist of a wh-expression and its corresponding answer within a single utterance: JOHN BUY WHAT BOOK. Drawing on recent discussions of the syntax of questionanswer pairs as sentential units in American Sign Language, the contribution Question-answer pairs in sign languages by Annika Herrmann, Sina Proske and Elisabeth Volk presents the findings of two empirical studies that compare the possible positions of wh-words in wh-questions and question-answer pairs in German Sign Language (DGS). Based on the empirical findings, the authors suggest that question-answer pairs in sign languages should not be analyzed as clefts. Rather, they are complex declarative clauses with specific pragmatic functions. Question-answer pairs (in spoken languages) often come in the direct answer paradigm. For example, polar questions are frequently answered directly with yes or no, modulo some complicating factors; cf. Roelofsen & Farkas (2015). The contribution Inferring meaning from indirect answers to polar questions: The contribution of the rise-fall-rise contour by Marie-Catherine de Marneffe and Judith Tonhauser zooms in on the interpretation of indirect answers to polar questions. The authors present the results of an experimental study on the role of intonation in the intepretation of indirect answers. It is shown that listeners tend to infer significantly more negative responses to polar questions when the indirect answer is realized with a marked rise-fall-rise contour as when compared to realizations with the neutral contour. These findings show that the prosodic realization of indirect answers is relevant for discourse semantics, as it provides important cues to speakers’ intended meanings. The two contributions Constructing QUD trees by Arndt Riester and Underneath rhetorical relations. The case of result by Edgar Onea adopt a more global perspective on the role of questions in structuring discourse, the structure of which can be modelled by means of so-called question trees, which

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sub-divide a discourse into sequences of questions and answers. Both authors assume that question trees are formal devices well-suited for complementing better established structural representations of discourse, such as Segmented Discourse Representation Theory (Asher & Lascarides, 2003). Riester suggests that Questions under Discussion trees can be derived from SDRT graphs in a systematic fashion. However, the original Questions under Discussion theory, as spelled out in Roberts (1996), requires significant revisions in order to yield an adequate formal account of naturalistic data. The article discusses whether Questions under Discussion can replace discourse relations, and it develops and illustrates a novel method for identifying implicit Questions under Discussion from naturally occuring corpus data. Onea pursues a similar goal, but instead of focusing on the modelling of naturalistic data, the central objective is the rigid formalization of Question under Discussion-trees as a formal tool for modelling discourse structure. A novel empirical contribution consists in showing that the question-tree representation allows for a more finegrained analysis of some discourse relations in SDRT, such as eg. result, which is somewhat problematic in allowing for two distinct construals in SDRT (subordinating vs coordinating). The question-based analysis unearthes the deeper underlying reasons for these two surface construals. This suggests that a question-based discourse representation may indeed be necessary for supplying information that is missing in traditional SDRT-analyses. In further support of this point, the paper concludes with a unified, question-based analysis of the German adverbial particle schließlich, which can associate with a heterogeneous range of discourse relations. The final contribution Two alternatives for disjunction: an inquisitive reconciliation by Floris Roelofsen returns to the fundamental question of how the two notions of disjunction and questionhood are related, a topic mainly addressed in vol. 1 of the present collection. The author compares the two ways in which disjunction has been analyzed in the formal semantic literature, and he argues for a synthesis of the two approaches within inquisitive semantics. Traditionally, disjunction was analyzed as expressing the algebraic operator join in a Boolean algebra. More recently, it was proposed that disjunction can apply to any two objects of the same semantic type, thereby yielding the set consisting of these two objects. Roelofsen shows that it is possible to unifiy these two perspectives by adopting a notion of meaning that does not only comprise truth-conditional informative content, but also inquisitive content. In closing this introduction, we would like to express our gratitude to all members of the Questions in Discourse Network for their presentations, their active participation, and for the lively and productive discussions in the meetings. In particular, we would like to thank David Beaver, Floris Roelofsen and

introduction

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Arndt Riester for their unwavering commitment, their valuable contributions, and their insightful comments, without which this network would not have been even half as succesful, and without which this volume would not have come about. Whereas all of the papers in the present two volume-collection have benefited in one way or other from discussions in the network meetings, this collection constitutes only a subpart of the network’s overall research output. Next to the present contributions, many more papers have been, or are in the process of being, published in other publication outlets. Most of the additional publications are referenced in the individual contributions of the present collection. Finally, we wish to acknowledge additional financial support by the German Research Foundation, which took the form of financial support for research project C04 Conceptual and referential activation in discourse, as part of the collaborative research centre SFB 1252 Prominence in Language at the University of Cologne.

Bibliography Asher, N., & Lascarides, A. (2003). Logics of Conversation. Cambridge University Press. von Heusinger, K., Zimmermann, M., & Onea, E. (Eds.) (2019). Questions in Discourse. Volume 1: Semantics. Leiden: Brill. Klein, W., & von Stutterheim, C. (1987). Quaestio und referentielle Bewegung in Erzählungen. Linguistische Berichte, 109, 163–183. Onea, E. (2016). Potential Questions at the Semantics-Pragmatics Interface. Leiden: Brill. Onea, E., & Zimmermann, M. (2019). Questions in discourse: An overview. In K. von Heusinger, M. Zimmermann, & E. Onea (Eds.), Questions in Discourse. Volume 1: Semantics (pp. 5–117). Leiden: Brill. Roberts, C. (1996). Information structure in discourse. In J. Yoon, & A. Kathol (Eds.), OSU Working Papers in Linguistics volume 49 (pp. 91–136). Ohio State University. Roberts, C. (2012). Information structure: Afterword. Semantics and Pragmatics, 5, 1–19. Roelofsen, F., & Farkas, D.F. (2015). Polarity particle responses as a window onto the interpretation of questions and assertions. Language, 91, 359–414. Rooth, M. (1992). A theory of focus interpretation. Natural Language Semantics, 1, 75– 116. Schwarzschild, R. (1999). Givenness, AvoidF and other constraints on the placement of accent. Natural Language Semantics, 7, 141–177.

chapter 2

Focus, Questions and Givenness Daniel Büring

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Claims and Proposals

1.1 Preview of the Main Claims This paper argues for a particular division of labor between givenness and contrast in accounting for stress and accent patterns in English and similar languages, sketched in figure 1. Figure 1 contains a number of new terms (printed in boldface), which will be explicated in what follows. To a first approximation, prosodically demoted corresponds to ‘deaccented’ in existing accounts, focal target to a Q(uestion) U(nder) D(iscussion), and ‘compatible with the focussing’ to ‘among the utterance’s F-alternatives’; contrast, relevant and identifiable more or less have their common sense meanings, which I will also elaborate on below. The main theses of the present papers are: – There is no such thing as givenness deaccenting; all manipulation of stress placement involves focusing, and all focusing is truly contrastive. – Targets for contrastive focussing need not be salient/given in the context, as long as they are, among other things, identifiable. – Givenness is a necessary (but not sufficient) condition for any departure from the default stress pattern, which can indirectly constrain the possibility of realizing a focus. Though based on (almost) familiar concepts, the picture advocated here is, I believe, novel. First, those previous approaches which utilize both givenness and contrast (also often simply called ‘focus’) have contrast/focus override givenness where in conflict, i.e. given elements are nevertheless accented if in narrow focus;1 on the present view, both are necessary conditions for marked prosody, so there is no such thing as ‘givenness deaccenting’ without concomitant contrastive focussing; no conflict between focussing and givenness can arise.

1 E.g. Féry & Samek-Lodovici (2006), but also, if not in these terms, Selkirk (1984, 1995).

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focus, questions and givenness

figure 1

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Proposal in a nutshell

Second, the target for focussing is usually taken to have to be contextually salient – like the antecedent for givenness deaccenting;2 on the present view, it is not, which opens up a wider range of focal targets. Third, there is no consensus in the literature regarding the question to what extent focussing is contrastive (and what exactly this means);3 on the present view, focussing is strictly contrastive. Though this paper is hardly the first place to opt for such a contrastive meaning for focussing, the consequences of such a move are rarely discussed explicitly; a precondition of the treatment advocated here is the insight that focus (and deaccenting) can be taken to invariably be contrastive precisely because we do not require that the contrasting alternative(s) under discussion be contextually salient; figure 2 attempts to schematize this network of ideas. 1.2 Preview of This Paper In order to make the empirical side of the proposal advocated here plausible, I will present a number of related but different arguments. First, that, by themselves, neither givenness of an element, nor the presence of a pragmatically plausible and identifiable contrast, are sufficient to allow for prosodic reversal (section 2). 2 This is most clearly the case in Schwarzschild (1999), but quite arguably also in Rooth (1992b,a), if we take serious the idea that the focus variable C is anaphoric; in many cases I found it surprisingly hard to decide whether a given paper takes, in particular, a Question under Discussion to have to be contextually salient or not, so I will not attempt to classify any more papers to belong to one camp or the other here, see the overview in Onea & Zimmermann (2019). 3 Again, Rooth (1992b,a) and Schwarzschild (1999) are the most explicit to state that focusing is not contrastive, whereas Wagner (2012) is perhaps the most explicit to argue for obligatory contrastiveness; given that contrast itself is rarely defined precisely (a notable exception being Katzir, 2013), the subsequent question of how to treat answer focus seems rarely discussed in sufficient detail.

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figure 2

büring

Core ideas (gray, top), their interdependencies, and consequences (white, bottom)

Second, that not all focal targets that are required for a working theory of contrastive focus are given; this argument has two parts, one regarding associated and other obviously contrasting foci, and one foci in narrative contexts and answers. This is the subject matter of section 4. Third an finally, I will offer, in section 5, some more speculative remarks about cases in which, I would argue, we have foci with non-given backgrounds, which, however, are not prosodically demoted, but promoted as foci of their own.

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Contrast and Givenness Are Necessary Conditions for Prosodic Reversal

2.1 Givenness Alone Does Not License Deaccenting Consider example (1), a case of focussing which is neither an answer focus, nor obviously contrastive to a contextual target. (1) [one thief to another] I’m afraid I’m developing a moral conscience lately. Last week, I went to a book store and BOUGHT a book.

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There are, in principle, two ways of analyzing an example of this kind: One could postulate a broad, e.g. VP, focus (or no focus at all), and analyze the accent shift from book to bought as a function of givenness/anaphoric deaccenting: the mentioning of bookstore makes books contextually salient, and hence book given. Or one could claim that I BOUGHT a book contrasts with ‘I stole a book’, i.e. has only V interpreted as focus. Only the latter view, however, successfully captures the difference between (1) and (2), in which deaccenting seems considerably less natural, if possible at all. (2) [regular person] I’m bored. I’ll go to the book store and … a. … buy a BOOK. b. # BUY a book. If the stress pattern in (1)/(2b) inevitably involves focussing bought, a straightforward story emerges: there has to be a focal target of the form ‘I R a book’; in (1) this is ‘I stole a book’. The contrast between stealing a book and buying a book is relevant here, because the latter, but not the former, offers motivation for the earlier claim a about a growing moral conscience. In (2), on the other hand, no similarly obvious focal target exists. For one thing, it is not clear that doing something else with a book at a bookstore would contrast in a relevant way as not relieving boredom. For another, even if we think of things that might in fact provide a relevant contrast, say, looking at a book, or taking a picture of a book (or perhaps not buying it), we get no contextual or encyclopedic cue as to which of these is intended here; the focal target is not identifiable; I will return to the details of this story in section 3.4 below. I would like to emphasize that the main argument here – that givenness of a word or phrase alone is not sufficient to license its prosodic demotion – is made by the contrast between (1) and (2), regardless of the question of what exactly is required for prosodic demotion in addition. I hypothesized that what is required is that the demoted (and given) element can be interpreted as the background of a focus, and the the larger constituent containing that focus and its background can be contrasted with a focal target. And more specificially yet, that a focal target must be identifiable and relevant vis-à-vis the literal meaning of the focused sentence. The gist of the argument, however, should remain valid even if the latter two points turn out to be in need of refining. Equally notably, the claim that givenness alone does not license prosodic demotion is closely related to the claim, also pursued here, that focusing is truly contrastive. To illustrate, where a concept like ‘book’ is contextually salient, as in (2), it is usually not too hard to come up with some proposition that is

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technically a focus alternative of the required sort. For example both ‘go to a store that sells’ and ‘see’ as alternatives to BUY in (2b) would lead to sentential focus alternatives – ‘I go to a store that sells books’ and ‘I see books’ – that are contextually salient after uttering I’ll go to a bookstore,4 wrongly predicting the accent pattern in (2b) to be acceptable, even as a result of focusing.5 In other words, excluding (2b) requires both ruling out prosodic demotion as a reflex of privative givenness of book, and using ‘I see/go to a store that sells books’ as a focal target for (I) BUY a book. The latter should arguably be achieved by requiring focal targets to be truly contrastive, an issue more thoroughly discussed in section 4.2 below. Yet inversely, it is important to keep in mind that our account must prohibit prosodic demotion due to privative givenness in its own right, because otherwise a ban on non-contrastive focusing would not show any effect. 2.2 Contrast Alone Does Not License Deaccenting The mirror image argument to that presented in section 2.1 is based on examples like (3). (3) a. (The store across the street sells refurbished computers, but) # we sell NEW printers. b. (This store sells new and refurbished computers, but) # it only sells NEW printers. These, specifically the deaccenting of printers, sound odd. But it is perfectly easy to identify a matching focal target here, namely ‘sell used printers’. Not only is ‘used’ salient after the mentioning of refurbished, it is arguably the obvious alternative to ‘new’ in this context on purely encyclopedic grounds. And equally certainly, the choice between selling new or used printers is relevant here, because only the former justifies the use of but, and the juxtaposition of the two clauses. The diagnosis here seems rather straightforward: the problem with the sentences in (3) is that printers has been prosodically demoted, despite the fact that it is not given. So justifying the accent pattern indicated in (3) by an identifiable and relevant focal target is simply not sufficient. 4 By encyclopedic bridging in the latter case: She who goes to a book store will see books. 5 This property is elegantly exploited in Schwarzschild’s (1999) notion of GIVENness, which, however, if the line of argument initiated in Wagner (2006, 2012) and pursued by Katzir (2013), Stevens (2013), Büring (2012), as well as in the present paper is valid, also suffers from exactly that feature.

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The same argument carries over to Questions Under Discussions: If one thinks that focusing new in (3) targets the question ‘what kind of printers does the store sell’ (rather than the proposition that it sells used printers), then what these examples show is that a QUD alone is not sufficient to license prosodic demotion in an answer. Note that in the buy/steal a book examples in section 2.1 above, the demoted constituent a book was indeed given (due to the previous mentioning of bookstore). Those examples, combined with the ones presented in this section, then, argue that neither givenness nor focusing alone are sufficient for prosodic demotion, but both a are necessary, which is the main empirical claim of the present paper. The acceptable book-example (1) also illustrate that it is not the actual focal target that needs to be given (which is what the theories in Schwarzschild, 1999, and, arguably, Rooth, 1992b entail), but merely those constituents that need to be prosodically demoted in order to realize the focusing: ‘steal a book’ is not contextually salient, only ‘a book’ is.6 This is the next central empirical claim of this paper: the background of a contrastive focusing need not be given. Section 4 argues this claim in more detail.

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Implementation in Unalternative Semantics

Before going on, I will present a more formal implementation of the concepts crucial to our arguments, first and foremost, the distinction between focus– background and prosodically demoted–non-demoted (as well as strong– weak). It is crucial for the analysis given here that there is no one-to-one correspondence between these distinctions and that, in fact, no grammatical properties – other than interpretive ones – correspond, even loosely, to the notions ‘focus’ and ‘background’. This implementation is couched in the formalism of unalternative semantics (Büring, 2015, Forthcoming), which expresses the independence of the above notions in a particular clear way. The main claims, however, could presumably be implemented in more ‘standard’ varieties of alternative semantics as well.

6 It is irrelevant that ‘steal’ is arguably contextually salient in the context of (1), too. For one thing, this would not explain why just a book, rather than steal a book is prosodically demoted. For another, as shown convincingly e.g. in Williams (1997:pp. 598 f.), two givens do not add up to a given; that is to say, ‘steal a book’ is not automatically contextually salient, just because ‘steal’ and ‘book’ separately are.

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3.1 Prosody Prosody is represented in the form of metrical s(trong)–w(eak) annotations, as in (4a) and (4b), which translate into stress and accent patterns.7 (4) a.

b.

The tree in (4a) shows what I take to be default prosody; the tree in figure (4b), accordingly, has non-default prosody. Specifically, Miller in (4b) is said to have been prosodically demoted; the VP node has undergone prosodic reversal (which ultimately translates into kissed bearing the final pitch accent in the sentence, as indicated by capitalization). The terms prosodic reversal and prosodic demotion cover any case in which the metrical weights of two sisters are the opposite of what the default says. ‘Deaccenting’, as the term is usually used in the literature – shift of the nuclear stress/accent to the left of its default location – is one instance of prosodic reversal: the default strong node is to the right of the weak node(s), so that after reversal the default strong node is post-nuclear (after the strongest stress), and hence remains accentless (see clause (iib) in note 7). Other cases of prosodic reversal involve the opposite: the main stress shifts to the right, e.g. in cases where the right element is a pronoun (or other functional ele7 … by the following rather standard conditions: (i) Metrical Tree to Stress Grid: An assignment of degrees of stress to the terminals of a metrically annotated phrase marker T is legitimate iff for any branching node N in T, N’s s(trong) daughter dominates a terminal with a higher degree of stress than that of any terminal dominated by a w(eak) daughter of N. (ii) Stress–Accent Association: An association of pitch accents (PA s) to a metrical grid G is legitimate only if a. no PA is associated with a column to the right of the highest column of G, and, as far as compatible with that b. if a column of hight n is associated with a PA, every column of hight n or higher is associated with a PA.

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ment) – default KISSED them vs. reversed kissed THEM – or a predicate to the left element – default have your SHOES polished vs. reversed have your shoes POLISHED. In this sense, prosodic reversal is the broader of the two notions; the conditions on any of its instances are, I argue, the same: givenness of the demoted element, focusability of the promoted one. For the bulk of this paper, the difference between ‘prosodically demoted’ and ‘deaccented’ is immaterial, but for compatibility with papers such as Büring (2015, Forthcoming) I will stick to the former term. The distinction between default and non-default prosody is the only information unalternative semantics requires to calculate focus alternatives. In a nutshell, this is done by two simple rules: Weak Restriction, which applies to all nodes whose daughter nodes have default metrical weights (such as VP in (4a), and S in (4a) and (4b)) and says ‘if weak daughter is focal, strong daughter is, too’. And Strong Restriction, which applies to all nodes which have undergone prosodic reversal (such as VP in (4b)) and says ‘strong daughter is focal, weak daughter is not’.8 Combined, these yield the characterizations in (5); as indicated in the bottom lines, the resulting possible focusings are exactly the expected ones (parenthesized are discontinuous foci, which are of no concern in the present paper, see Büring, Forthcoming, for discussion). (5) a.

if kissed is focal, Miller is focal if Smith is focal, kissed Miller is focal possible foci: Obj, VP, S (Sbj +Obj) b.

8 ‘Is focal’ here abbreviates ‘is, contains, or is part of a focus’; it roughly corresponds to ‘is F-marked’ or ‘gets to introduce (non-trivial) alternatives’ in standard systems. I will also sometimes say that these nodes can be interpreted as focused.

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kissed is focal, Miller is not if Smith is focal, kissed Miller is focal possible foci: V (Sbj+V) 3.2 Semantics In their official form, Weak and Strong Restriction are semantic rules. They characterize what are usually called focus alternatives. A basic idea of unalternative semantics is that focus alternatives are restricted as we go towards the root of the tree, rather than introduced or propagated (as is the case in standard Roothian alternative semantics). Weak Restriction – defined in (6) – applied to e.g. [VPsaw JOHN] excludes all VP-alternatives of the form ‘R\saw John’, where R\saw ranges over transitive verb meanings/relations other than ‘saw’.9 All other VP meanings are permitted alternatives. This amounts to saying that [VPsaw JOHN] could express VP focus, or just object DP focus, but not narrow V focus. A handy way to notate this is R\saw john, to be read as: no alternatives of the form ‘R John’, except ‘saw John’. Accordingly, ‘called John’, ‘kissed John’, ‘likes John’ etc. are the unalternatives after which the idea is named. (6) Weak Restriction If the relative stress among sisters Sstrong and Sweak accords to the default, exclude all alternatives that differ in the weak sister, but not the strong one, for short x\S Sstrong weak

Figure 3 illustrates how Weak Restriction derives unalternatives step by step. Note that there are two restrictions at the S level, one from applying Weak Restriction to the meanings of the subject and the VP, one from propagating the restrictions introduced (by Weak Restriction) at the VP level (for a formal version of Propagation, see section 7 below). These two characterize one set of

9 For ease of exposition, I will feel free to characterize meanings as ‘of the form …’, where ‘…’ is a formula or similar expression, rather than the more accurate but more convoluted ‘meanings expressible by formulae of the form …’. I also, throughout this paper, mean to be agnostic about the question whether focus alternatives are restricted by semantic type alone (e.g. ‘all relations in De,et ’), or additionally by ‘natural expressibility’ (e.g. ‘all transitive verb meanings’), or some other criterion, though I may use either way of characterizing alternatives, depending on which seems more transparent. The unalternative semantics system should be compatible with either view, given that it propagates restrictions, rather than the sets of alternatives allowed by these restrictions.

focus, questions and givenness

figure 3

15

Unalternatives calculated at the VP, (i), and S level, (ii); (iii) shows how the (weak) restriction introduced at the S level, and the weak restriction propagated from the VP level can be combined into a single restriction.

allowed alternatives however, and can be subsumed by the single restriction in figure 3(iii). Since terminals do not introduce any restrictions, propagation has no consequences at the first branching level, VP in figure 3. The third and final mode besides Weak Restriction and Propagation, Strong Restriction, introduces a restriction saying of one daughter that it has to be interpreted as focussed. (7) Strong Restriction If the relative stress among sisters Sstrong and Sweak does not accord to the default, allow only alternatives that differ in the strong sister, but not in the weak one, for short x Sweak \Sstrong

As said above, Strong Restriction is triggered in English in cases of Prosodic Reversal, as illustrated in figure 4(i), where the left daughter of VP is prosodically stronger than the right, contrary to the default. Since prosodic relations at the S level are normal again (VP stronger than the subject), Propagation and Weak Restriction apply here as usual, see the tree in figure 4(ii), where in this case the former properly subsumes the latter, 2.4(iii). The restrictions introduced by Strong Restriction are characterized positively in (7) and figure 4 – ‘only alternatives of the form R\saw John’; formally Strong Restriction, too, describes unalternatives, excluding all VP-meanings

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figure 4

Strong Restriction. Note that the propagation of the strong restriction from VP to S results in a restriction that properly subsumes the weak restriction introduced at the S level.

other than ‘R\saw John’ (this could be written as (Det ∖ R john) ∪ {saw John} or P\R John but I will stick to the more transparent positive characterization notation R John). \saw

\saw

3.3 Pragmatics In choosing one of the metrical patterns discussed, a speaker relates her utterance to what I call a focal target – a question, or perhaps a previous assertion. In this paper I uniformly model focal targets as questions – sets of propositions. The nature of the rules that relate metrical patterns to possible focal targets is the subject matter of focus pragmatics. The rules of focus pragmatics make reference to the (un)alternatives derived by focus semantics. Like virtually all proposals for focus pragmatics, unalternative semantics assumes that the focal target must be made up of focus alternatives of the utterance; focus alternatives thus delimit the class of focal targets of an utterance (for this reason I also call focus alternatives potential focal targets). In the case of unalternative semantics this means that the focal target must not be made up of unalternatives. (8) gives a definition in the form of a variation on Rooth’s (1992b) squiggle operator, where clause (8a) corresponds directly to Rooth’s condition that the value of C be a subset of S’s focus alternatives.

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(8)

is well-formed only if there is a value α, the focal target, for C s.t. a. α contains at least one element that is neither an unalternative, nor the literal meaning, of S. b. α is a proper question, c. α is relevant to the participants at the time of the utterance of S d. the participants can unambiguously identify α given the utterance of S Clauses (8b), (8c) and (8d) impose additional restrictions on α (the denotation of C), which I will discuss in the remainder of this paper. Crucially for now, nothing in (8) requires that the focal target must be previously mentioned, nor even contextually salient; all that it requires is that that it be made up of focus alternatives/potential focal targets (and that it be a proper, identifiable and relevant question). A stricter requirement is imposed on elements that are prosodically demoted, such as Miller in (4b)/(5b).10 These need to be coreferent, synonymous or hypernymous to a previously mentioned word or phrase. Following the common use in the literature I call such elements given and their meanings contextually salient. So while words and phrases in the background of a focus do not, according to (8), need to be given, prosodically demoted elements must be: (9) Condition on Prosodic Reversal A prosodically demoted node must be given (i.e. it is coreferent, synonymous or hypernymous to something that was contextually salient before the utterance).

10

Where branching nodes have a strong left daughter by default, prosodic reversal will actually result in a ‘rightward shift’ of the main PA, often in the form of accent addition. Thus the prosodic defaults in (ia/b) have the left daughter strong and the right daughter weak and unaccented. (i) a. a TRAIN arrived b. SAW her Prosodic reversal here results in nuclear pitch accents on arrived and HER, with the possibility of prenuclear pitch accents on train and saw, i.e. no obligatory deaccenting. This is also the situation characteristic of the VP in Germanic OV languages like Dutch and German.

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In effect, then, prosodic reversal is subject to two necessary conditions: givenness of the demoted daughter, and focusability of the promoted daughter. Unalternative semantics naturally allows to link these two, since focus alternatives, too, are calculated depending on the question ‘prosodic reversal or default?’ That is, the difference between default prosody and prosodic demotion is already an integral part of the algorithm to calculate focus alternatives (and it is, hence, particularly easy to add a givenness condition like (9) to it). Finally, turning to the technical terms used in (8), I will only offer informal characterizations of relevance and identifiability in this paper, and point out what role they should eventually take in explaining the data patterns. As to ‘relevant’, the idea is that it must matter to participants which answer to the question is true. As a stand-in I will say for now that participants must entertain the various propositions in the question as real possibilities, and that their behavioral dispositions vary depending on which of them is true. Clause (8d) replaces the (ostensible) requirement that C needs to be anaphoric by the weaker notion of identifiability – ‘after the fact’, as it were. I will say a little more about this below, but generally the same pragmatic conditions that govern and restrict the interpretation of a non-anaphoric pronoun should be expected to apply here. The notion of proper question will be formalized in section 4.2 below. Intuitively, a proper question is one whose answers contrast with one another. Did you use a hammer, or a screw driver? and Is this car expensive, or cheap? express proper question, Did you use a hammer, or a tool? and Is this car expensive, or red? do not. Note at this point that the answers to a proper questions need not strictly be exclusive: one may well use a hammer and a screw driver. But intuitvely it sounds coherent to say a hammer, not a screw driver, but incoherent to say a hammer, not a tool. In section 4.2 this intuition will be cashed in formally, building on Katzir’s (2013) use of innocent exclusion. When it comes to predicting which focusings are possible and which are not, there is noticeable overlap between relevance, identifiability and proper question-hood (clauses (8b), (8c) and (8d)), as the reader will see in the remainder of this paper. I suspect that definition (8) can ultimately be simplified by unifying some of its sub-clauses. On the other hand, I submit that (8b) and (8c) express very general conditions on Questions under Discussion (and that (8d) applies to non-anaphoric pronouns in general); none of these is specific to focusing.

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3.4 Illustration Jointly, conditions (8b)–(8d) are meant to make sure that even though we allow for focal targets to be concocted on the fly, not everything goes. Take the case of (10), repeated from section 2.1 above. (10) Last week, I went to a book store and BOUGHT a book. In the case of the thief complaining about their newfound conscience, C is identified as {speaker bought a book (and did not steal any), speaker stole a book (and did not buy any)}, plausibly because buying is made salient by the utterance itself, and stealing is what thieves do. Certainly, an addressee who knows they are talking to a thief will also entertain both of these possibilities, and the choice between them is relevant: stealing a book would fail to substantiate the claim that our thief is in fact becoming honest. All of this is different if (10) is uttered by a law-abiding citizen. First and foremost, no particular alternative to buying immediately jumps to mind, i.e. is identifiable: what else would we expect a bored (but honest) person to do with a book in a book store? Yet, suppose, for the sake of argument, that addressees could still identify some very general question like speaker R\bought a book (‘what non-buying relation obtains between the speaker and a book?’), essentially the set of potential focal targets. Wouldn’t this suffice, given that C needs to be identifiable only after the utterance of (10)? No, since this question is not a proper question: it includes answers like ‘bought a book’, ‘saw a book’, ‘skimmed a book’ etc. which are ‘orthogonal’ to one another. Furthermore, the addressee has no clue how to identify which of these should be used to form a proper question, and hence a fortiori cannot identify the question C – the focal target the speaker had in mind – in the sense of clause (8d). Finally, again for the sake of argument, what if the addressee took the question to be something along the lines of {speaker bought a book and did nothing else with it, speaker did something other than buying with a book}, i.e. the most general proper question to be baked from the potential focal targets? Such a question, I would like to argue, fails to be relevant. Given the overarching issue of how the speaker escapes boredom, non-buying a book subsumes things that could serve that purpose (reading it in the store, stealing it) and things that could not (ignoring it, looking at its title, misplacing it in the store). Knowing, in particular, that the speaker non-bought a book is of no use to the addressee in this context and hence makes the question non-relevant. As said before, there are probably ways to achieve the desired effect of excluding (10) in the law-abiding context (and similar cases to be discussed) in fewer steps, with fewer conditions. I leave this for future research. In the

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meantime, proper-question-hood, relevance and identifiability between seem to sufficiently cover what may and what must not be used as a focal target. In the case of contrastive focus, α is simply the alternative question formed from the literal meanings of the correction and the ‘correctee’. This is illustrated in (11) (here and henceforth I annotate the focal target on the variable C for perspicuity). (11) (Kim hates chocolate –) No,

The question alluded to in (8) above then would be {Kim loves chocolate, Kim hates chocolate} – or informally: ‘does Kim love or hate chocolate?’ In the case of focus in an answer to an overt constituent question Q, Q itself can serve as the focal target, as illustrated in (12). (12) (Who closed the door? –)

QUD: Did Kim open the door, or did someone else? Note that the literal meaning of the sentence is an unalternative in both (11) and (12). This is irrelevant though, as long as the focal target contains at least one other element that is not an unalternative, which is the case here.

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4

21

Non-given Focal Targets

In this section I aim to substantiate the claim that ‘being in the background of a focus’ is indeed independent of being given, or put differently, that focal targets need not be contextually salient. Obviously, to show this we have to have a way of establishing a focus–background partition, or its focal target, without using an overt question or target of correction/contrast (which would automatically make the focal target and hence everything in the background of the focus contextually salient). I can see two ways of doing so. The first was already touched upon in the discussion of the buy/steal a book examples in section 2.1 above: show that the target of contrast must be something different than what is contextually salient; this method will be picked up again in 4.2–4.4. The second way is to use the interpretation of focus sensitive elements like only to determine a focus and its focal target; this is pursued in section 4.1section. 4.1 Non-given Alternatives for Only The argument in the subsection hinges on elements that are in the background of a focus, but not prosodically demoted. This is typically the case if they linearly precede the focus and hence the main stress of the focus domain. The verb likes in Kadmon & Sevi’s (2011) (13) is an example of this. (13) (What’s peculiar about Granny’s dog?) She only likes JOHN. As Kadmon & Sevi note, (13) is curious in that, as an answer focus, the sentence’s focus alternatives (or potential focal targets as I call them here) must be ‘granny’s dog Q’ (VP-focus), whereas the domain of only consists of properties ‘like x’, i.e. object focus (as witnessed by the interpretation: (13) say that the dog does not like anyone else, not that it does not have any other properties). This suggests, on the one hand, that one stress pattern can simultaneously realize two different focus–background structures (the F-less system of course ‘natively’ has this feature). More importantly in the context of the argument pursued here, the focal target restricting only is not contextually salient: whom the dog (or anyone for that matter) likes has not been under discussion or otherwise salient. (14) Claim: The background of a focus associated with only need not be given (if it is not prosodically demoted). (14) presupposes, of course, that only associates with a focus in the first place (see Beaver & Clark, 2008, for a battery of arguments in favor of that view), or,

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put in present terms, that the quantificational domain of only is grammatically restricted to consist of focal targets compatible with the focusing in only’s syntactic sister.11 This is inherent to the type of argument made here: only is used to detect a focus, independent of a contextual focal target (without only there would be no reason to suspect that there is a narrow focus on John in (13)). Again, let me conclude this section by dissecting the argument further: Kadmon & Sevi’s (2011) (13) alone illustrates the validity of Claim (14), without the parentheses, which lends support to the more general claim made here that focal targets need not be contextually salient. The generalization about when this is possible is specified in the parentheses in (14). Note that it could not be stated without differentiating between the pragmatic concepts of ‘being in the background’ and ‘being given’ on the one hand, and the prosodic concept ‘being prosodically demoted’ on the other – thereby providing motivation for the introduction of the latter. Standard systems of focus interpretation interpret patterns of F- and/or G-markers. The prosodic realization of these markers (in terms of prosodic reversal, or deaccenting, for that matter) is governed by independent realization principles such as ‘stress F’, ‘don’t stress G’, or focus projection rules relating F-markings to accents. Rules of focus interpretation do not make reference to either stress nor accents directly. But, as just pointed out, neither ‘being G-marked’ nor ‘being in the background of a focus’ correspond to ‘being prosodically demoted’ one-to-one. Being prosodically demoted entails both being given and being in the background, but asymmetrically so, which is why (14) – or any theory that derives it – cannot be stated in terms of G- or Fmarking. While one could presumably add the notion of ‘prosodically demoted’ to a theory of interpreting F/G-markers (with or without a marker of its own), the system of unalternative semantics achieves the same results in an arguably more parsimoneous way: focal targets, too, are calculated directly off the metrical tree.

11

The argument as presented also presupposes that the focusing associated with only remains ‘active’ as a contrastive focus outside of the c-command domain of only, pace Rooth (1992b); while I take this to be hardly controversial (see in particular Schwarzschild, 1993, for arguments), the argument does not hinge on this at all: what is relevant is the focus associated with only, the background of which is not given. Whether there is a free, answer focus in (13) is not relevant.

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4.2 Non-given Targets for Contrastive Focus: Convertibles Wagner (2006, 2012) points out the surprising contrast in (15). (15) (Mary’s uncle, who produceshigh-end convertibles, is coming to her wedding. I wonder what hebrought as a present.)

a. He brought a [CHEAP convertible]. b. # He brought a [RED convertible] c. He brought a red CONVERTIBLE. Wagner argues, correctly I think, that (15b) is odd because ‘he brought a red convertible’ cannot contrast with ‘he brought an expensive convertible’. Two of the core claims of the present paper directly reflect that insight: that givenness of convertibles alone is not sufficient to license prosodic demotion, and that focusing involves true contrast. In the present context I want to show that, in addition, examples like these also require the third of our assumptions: that focal targets need not be contextually salient (pace Wagner, 2006, 2012). Before doing so, in section 4.2.2 above, though, it is time to clarify the notion proper question, which, in the present paper, implements the intuition that some alternatives truly contrast and others do not. 4.2.1 Proper Question As said in 3.3, the proper question clause (8b) in the definition of the squiggle above is meant to restrict focal targets to questions whose answers, intuitively, contrast; for any two propositions p, p′ in it, it should sound felicitous to say ‘p, not p′ ’. This should, among others, exclude questions like those in (16). (16) a. # Did you use a hammer, or a tool? b. # Did you bring an expensive car, or a red one? To approximate this, I will start with the following, preliminary definition:12 (17) (to be revised:) a set of propositions Q is a proper question iff for any p ∈ Q, p ∖ ⋃(Q ∖ {p}) ≠ ∅ (‘p and none of the others in Q’ is coherent)

12

The following section is my attempt at adapting the use of Innocent Exclusion in Katzir (2013) to apply to question meanings, rather than – necessarily complete – sets of focus alternatives.

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(17) excludes any two p, p′ of which one entails the other (such as (16a)), but also any p, p′ , …px whose negations jointly (‘neither p nor p′ nor … px ’) exclude another p∗ ∈ Q. To understand the latter, take the question ‘what kind of wine did Kim bring?’, assuming for simplicity that ‘what kind’ ranges only over the colors or countries of origin, and that all wines are either red or white, and either French or Italian. This question is not a Proper Question in the sense of clause (17), since if Kim brought neither red nor white wine, she brought no wine at all, and that excludes bringing French wine (as well as bringing Italian wine). The more specific questions ‘did Kim bring white or red wine?’ and ‘did Kim bring French or Italian wine?’, on the other hand, are both proper, since non-red wine allows for bringing white, and non-French for Italian wine (and nothing changes if more colors, or countries, respectively, are added). So intuitively, clause (17) excludes answer alternatives along ‘different dimensions’. Alas, (17) does not yet rule out alternative questions like (16b), which are, in a manner of speaking, random subsets of the kind of question just excluded; ‘expensive, but not red’, as well as ‘red but not expensive’ are both coherent. What we need to do here is to first transform this question to its Minimal Completed version, with the TAMs {you brought an expensive car, you brought an inexpensive car, you brought a red car, you brought a non-red car}; that question is ruled out by (17) for the reasons just discussed: ‘you brought an expensive (and not inexpensive) and not red and not non-red car’ is incoherent, as would be any other version of asserting one answer and negating all others. Unfortunately, the only way to do this that I could think of requires a fair bit of machinery, which I will introduce in the remainder of this section. Readers that are satisfied with the gist of the procedure as outlined so far are invited to skip the rest of this section. First, we have to think of questions as an Abstract plus a set of Term Answer Meanings (TAM s) (rather than just sets of propositions). Thus (16a) will be represented along the lines of ⟨λx.you used x,{a hammer, a tool}⟩, (16b) as ⟨λP.you brought a P car, {expensive, red}⟩ etc. If 𝒬 = ⟨A, tas⟩ is such a pair, the corresponding set of propositions is then straightforwardly defined as propset(𝒬) = propset(⟨A, tas⟩) = {A(ta) | ta ∈ tas} or {ta(A) | ta ∈ tas}, whichever is defined. The next, intermediary step is to define the Complement Answer of a TAM:13 13

Clause (18a) is only defined for simple functions, not for functions ‘ending in t’ in general, for example functions in D⟨e, ⟨e,t⟩⟩. The generalization is straightforward, as any more complex function is equivalent to a function from tuples of meanings to {0,1}. The two clauses of this definition are more similar than they may look, since (18a) is equivalent to (⋃{0, 1}Domτ ) ∖ ta.

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(18) For any Term Answer Meaning ta, the complement answer of ta, ta is a. λψτ .ta(ψ) = 0 if ta is a function from Domτ to {0,1}, b. λP ∈ D⟨e,t⟩ .∃x ∈ De [P(x) = 1 ∧ x ≠ ta] if ta is an individual

The crucial clause for the red or expensive case is (18a), which gives us ‘be nonred’ as red and ‘be non-expensive/inexpensive’ as expensive. We want to add these complement answers to the set of TAMs in red or expensive-type cases, i.e. cases where these are intuitively lacking. For that I define … (19) given a question 𝒬 = ⟨A, {q1, …qn }⟩, the minimal completed question MC(𝒬) is the pair consisting of A plus the smallest set tas s.t. a. (i) {q1, …qn } ⊆ tas if q1, …qn are functions in some domain Dτ,t , and (ii) {λP.P(x) = 1 | P ∈ De,t ∧ x ∈ {q1, …qn }} ⊆ tas if q1, …qn are individuals b. for any term answer ta ∈ {q1, …qn }, if propset(⟨A, ({q1, …qn } ∖ {ta}) ∪ {ta}⟩) is a proper question, ta ∈ tas

Since the TAMs of concern are all functions in Det , we apply (19a-i). Take 𝒬=⟨λP.you brought a P car, {expensive, red}⟩. According to (19b) we take each ta ∈ {expensive, red} and check whether {non-expensive, red} and {expensive, non-red}, respectively, make for proper questions in the sense of (17). This comes down to the questions whether i) ‘you brought an expensive car, and you didn’t bring a non-red car’ and ‘you brought a red car, and you didn’t bring a non-expensive car’ are coherent. Since they are, both non-redand nonexpensive must, by (19b) be in tas, giving us (20) as the Minimally Completed Question corresponding to 𝒬. (20) MC(⟨λP.you brought a P car, {expensive, red}⟩)= ⟨λP.you brought a P car, {expensive, red, non-expensive, non-red}⟩

Crucially the Minimal Completed Question in (20) itself is not a Proper Question; for example ‘you brought an expensive, red and non-red car’ (≡ ‘expensive, non-red, non-inexpensive, non-non-red’) is incoherent, as is ‘you brought a red, non-expensive, non-non-expensive car’ etc. Now take ⟨λP.you brought a P car, {red, blue}⟩, which corresponds to the intuitively acceptable question Did you bring a red car, or a blue car?. What will be the corresponding Minimal Completed Question? Again we apply (19b), asking whether i) ⟨λP.you brought a P car, {red, blue}⟩ and ii) ⟨λP.you brought a P car, {red, blue}⟩ are Proper Questions. It turns out they are not: ‘you brought a red car, but not a non-blue car’ as well as ‘you brought a blue car, but not a

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non-red car’ are incoherent. Therefore, the Minimal Completed version of this question is simply the question itself, no additional answers are added, and the result is itself a Proper Question. We thus replace (17) with (21):

(21) A question denotation 𝒬, where 𝒬 = ⟨A, {q1, …qn }⟩ is proper iff the set of propositional answers to its Minimal Completed version can each be coherently coordinated with the negation of all others, formally: for each p ∈ (propans(MC(𝒬))), p ∖ ⋃(propans(MC(𝒬)) ∖ {p}) ≠ ∅

Finally, for the sake of completeness, consider a run-of-the-mill constituent questions like Who was there?, formally ⟨λx.xwas there, {y ∈ De | y is a person}⟩, assuming for the purpose of discussion that the only persons are Kim, Sam and Jo. By (18b), the complement answers to these are, respectively: ‘someone other than {Kim, Sam, Jo} was there’. Since ‘someone other than Kim, and not Sam and not Jo, was there’ is incoherent, as are ‘someone other than Sam, and not Kim and not Bo’ and ‘someone other than Jo, and not Kim, and not Sam’, the question is Complete as it is, and Proper to boot. In fact, the only questions of this type that would be non-vacuously completed by (19a-ii) are those of the form ⟨λx ∈ Dτ .Φ, {y}}⟩, for any y ∈ Dτ ; for example, ⟨λx.x was there, {Kim}⟩ would be completed to ⟨λx.x was there, {Kim, someone-other-thanKim}⟩. With this much in our tool box we now turn to the question what the focal target in the convertible examples really is. 4.2.2 The Domain of Convertible Foci Wagner (2006, 2012) suggests that the contrast between (15a) and (15c) can be dealt with at the level of the nominal: ‘cheap convertible’ contrasts with ‘highend convertible’, but ‘red convertible’ does not. Since ‘high-end convertible’ is made salient by the previous utterance, this analysis only requires contextually salient focal targets. However, Katzir (2013) shows that the domain of contrast, and hence the focal target, needs to be bigger than assumed by Wagner. Katzir notes that ‘red convertible’ and ‘high-end convertible’ may very well be intuitively contrastive – as witnessed by the deaccenting of convertible after red in example (22b).14

14

His (20), with high-end where Katzir has expensive, to guarantee minimal contrast with Wagner’s example.

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(22) (The people in this club are very particular about the cars they collect. Mary, for example, collects high-end convertibles.)

a. And John collects CHEAP convertibles. b. And John collects RED convertibles. Evidently, the larger domain of the focus makes the difference here: {John collects red convertibles, John collects high-end convertibles} is a proper question as defined in section 4.2.1. By analogy, the domain of the focus in example (15) above should then be brought a cheap convertible; that, however, does not have a salient target (we have ‘high-end convertible’ and ‘bring something for the wedding’, but not ‘bring a high-end convertible’). So … (23) Claim: focal targets for a free focus domain need not be contextually salient. One might still argue with (23): in Katzir’s example (22), the focal target ‘collect high-end convertibles’ actually is given. And we still haven’t established that the focus domain in Wagner’s (15a) must be bigger than red/cheap convertible (which has a salient focal target). Perhaps the NP is sufficiently large a domain in (15a) to establish a contrast between high-end and cheap convertibles; perhaps only the ‘red’–‘high-end’ contrast in (22b) requires the larger domain (which, again, does have a salient focal target). Examples like (24) are needed to complete the argument. Here, deaccenting convertible is odd, even though cheap convertible does have a contextually salient focal target in ‘expensive convertible’. (24) (Yesterday, I left my expensive convertible at home and took the bus. As luck would have it, …)

a. # the bus was hit by a CHEAP convertible b. the bus was hit by a cheap CONVERTIBLE (… and never got me where I needed to go). Intuitions are again quite clear in this case: It is irrelevant whether the bus was hit by a cheap or by an expensive convertible; that question is not a relevant focal target. This jibes with the general spirit of the Wagner/Katzir position that focussing is contrastive, but it also shows that contrastiveness cannot be established at the level of the NP. If the contrast ‘high-end convertible’ v. ‘cheap convertible’ (without regard to any larger constituent) were sufficient to license deaccenting in Wagner’s (15a), there is no reason it shouldn’t be in (24). If, on

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the other hand, one always needs to consider a larger, perhaps propositional,15 domain to establish contrast and relevance, we can correctly rule out (24) and (15b), and rule in (15a) and (22b); provided we allow, at least for the case in (15a), a focal target that is not contextually salient – Claim (23). Before leaving the world of convertibles we need to revisit one potential loophole in ruling out (15b): why can we not simply take the focal target to be, for example, ‘he brought a blue/non-red convertible’, which would truly contrast with (15b)? The fact that ‘he brought a blue/non-red convertible’ is not contextually salient cannot be the problem, given present assumptions. Arguably, the focal target ‘he brought a blue convertible’ can be ruled out by reason of identifiability. Unlike in the case of ‘used’–‘new’ in section 2.2 above, there are many different, equally plausible alternatives to red – blue, green, white etc. –, so the hearer cannot know which of these the speaker would have in mind. The case of ‘he brought a non-blue convertible’, on the other hand, is different. I assume that in general, the negation of the focused sentence (or more technically: the exhaustified disjunction of all possible focal targets) is an identifiable focal target. This is what is arguably going on in example (25). (25) (Like most girls, Mary went through an ‘all pink’ phase, followed by an ‘I hate pink’ phase. Unfortunately, her godfather, who has a teddy bear factory, wasn’t aware of the change and) brought her a PINK teddy bear.

Note that in (25), there is no specific contextually salient alternative – ‘white teddy’, ‘brown teddy’ …; rather, we understand the focusing to contrast with ‘rather than a teddy of any other color than pink’. Since the context does not mention ‘non-pink’, I conclude that this potential focal target is identifiable as a kind of default. Moreover, the context in (25) makes the contrast between pink and non-pink teddies relevant, which is, I submit, where (25) differs from (15b): even if ‘non-red convertible’ is identifiable as the intended focal target in (15b), the question whether the convertible Mary’s uncle brought was red or some other color does simply not seem relevant in the context – unlike whether the teddy Mary got was pink or not. It is important to stress that relevance is a stronger condition than informativity. Given that (15c) is an acceptable answer, we must conclude that the color of the convertible is interesting enough to merit mentioning in general, as it is informative to the hearer(s). The point is that it is not crucial. Nothing 15

Which is arguably a consequence of Katzir’s approach. A crucial case to investigate this further are farmer examples as discussed in Rooth (1992b); I have to leave this for future research.

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else of interest would follow if the convertible had been non-red. The focus in (15c), on the other hand, is presumably on red convertible. This means that the focal target would be ‘he brought something other than a red convertible’; this is already more promising, since evidently, the question what he brought is relevant in (15), so it will make a difference whether he brought a red convertible or, say, a cake cutter. 4.3 Non-given Targets for ‘Anaphoric Deaccenting’ Wagner’s (2006, 2012) convertible argument does not just argue that there is such a thing as truly contrastive focus, it argues that all focusing is contrastive (how else to rule out a case?). This presents a conundrum, since the original impact of examples like (26) was precisely to argue that, since there was no narrow contrast target for make (‘eat French toast’?; ‘buy French toast’?), this could not be (contrastive) focussing but had to be (anaphoric, non-contrastive) givenness deaccenting (Ladd, 1980). (26) (Let’s have some French toast! –) I’ve forgotten how to MAKE French toast. Wagner (2012), discussing parallel examples like (27), suggests that, pace Ladd, the focus here is not narrow, but broad, on a police officer arrested (after movement of Smith to a position external to it). (27) (Smith walked in. A minute later,) a police officer arRESted Smith. Wagner argues that a police officer arrested (or: the property of being arrested by a police officer) contrasts with ‘walk in’ in (27). Intuitively, however, these two feel hardly more contrastive than ‘red’ and ‘high-end’. And in fact, neither by Wagner’s (2012) own condition on the red convertible-type deaccenting, nor by Katzir’s (2013) more elaborate condition, does ‘being arrested by a police officer’ qualify as a contrasting with ‘walking into the store’.16 Wagner (2012) has to assume two distinct focus conditions – a truly contrastive one along the lines spelled out by Katzir – and a barely (if at all) contrastive one to capture cases like (27), each with a different syntactic domain of application, stipulated so as to fit the observations. In fact, no existing theory has, to my knowledge, succeeded in formulating a single focus condition that is at the same time contrastive enough to rule out ‘red convertible’–‘high-end convertible’ type juxta16

Conversely, the True Contrast condition Wagner does apply to cases like (27) would, if extrapolated to the A+N cases, equally permit {he brought a red convertible, he brought a high-end convertible} as a proper question.

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positions, and non-contrastive enough to allow juxtaposing ‘walk into the story’ and ‘get arrested by a police officer’. The missing piece, I want to suggest, is to permit that the focal target in examples (26) and (27) need not be contextually salient. The focussing on the police arrested does not relate to a contextually salient property like ‘walk in’ as its focal target; rather, its focal target is ‘Smith wasn’t arrested’ or ‘Smith’s store visit commenced without unexpected interruptions’.17 These do form proper questions in the sense of 4.2.1, and they are relevant; they are just not contextually salient. An entirely parallel story suggests itself for the French toast type of example. Again, focus here is wide, on forgotten how to make. But the contrastive target for ‘forgotten how to make French toast’ is not ‘have French toast’, but ‘know how to make French toast’. That in turn is not contextually salient, but that does not matter. Deaccenting of toast on the other hand, is only possible because it is – also – given. Like these narrative sequences, the usual cases of anaphoric deaccenting in question–answer focus do not easily fit the mold of the ‘contextually salient target’ view either. Take example (28).18 (28) (What did KIM’s mother do when you complained about Kim’s behavior? –) She deFENded Kim. Neither defended nor she defended find an obvious contrastive target in this mini-context;19 this is why deaccenting Kim is usually seen here, too, as a reflex of (privative) givenness of Kim alone. On the other hand, privative givenness, recall, would wrongly allow deaccenting of a given element in the red convertible example (15b) above – Wagner’s original argument for contrastiveness. Under the present proposal, we get the best of both worlds. A fitting focal target for (28) is ‘Kim’s mother shared your criticism of Kim’s behavior’ (which again seems to jibe with intuitions). That takes care of the focussing. That Kim is given merely is a precondition for expressing that focussing by post-focal deaccenting (rather than, say, two intermediate phrases). 17

18 19

I thus concur with Wagner that a police officer arrested is interpreted as the focus in example (27), with Smith as its background. Unlike Wagner (2012) I am not committed to analyzing a police officer arrested as a syntactic constituent. The official implementation using unalternative semantics allows for discontinuous foci (as well as discontinuous backgrounds). Slightly modified from Schwarzschild’s (1999) example (9). ‘she is-the-mother-of’ may qualify in a very technical sense such as Schwarzschildian GIVENness, but it certainly should not count as Truly Contrastive in Wagner’s.

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4.4 Non-given Targets in Contrastive and Answer Focus In the discussion of the contrastive focus example (11) in section 3.4 above, repeated here, I already indicated how these should be analyzed within the present proposal: the focal target is the alternative question formed from the meanings of the utterance to be corrected and of the correction itself. (29) (Kim likes chocolate. – No,) Kim HATES chocolate ~ C{Kim likes chocolate, Kim hates chocolate}

On this analysis the focal target (the value of C) is not itself contextually salient, providing another instance of the pattern being documented in this section; this will generally be the case for contrastively used foci. This case is less pressing empirically, though. If, as in Rooth (1992b) we had given a disjunctive definition of the ∼operator – with one clause for questions focal targets (Rooth’s ‘Set Case’) and another for declarative focal target (the ‘Individual Case’) – we could analyze (29) by making ‘Kim likes chocolate’ itself the focal target, so no ‘derived’ focal target question would be required. The present proposal, on the other hand, cashes out the intuition that the relation between contrasting utterances like those in (29) is essentially the same as that between an answer to a constituent question and the other potential answers to that question: proper contrast. This is possible because the meaning of the targeted utterance may be ‘transformed’ into a question, used as the focal target. Some proposals have attempted to go the same route, but in the opposite direction. Discussing The POLICE arrested Smith as an answer to Who arrested Smith?, Wagner (2012:sec.1.2.6) argues that … ‘[t]he context makes available a set of propositions of the form x arrested Smith […] [T]he stress shift an be explained in the same way as we would explain it if the context included the statement Sally arrested Smith.’ In other words, the answer focus/set case is assimilated to the contrastive focus/individual case, not the other way around, by picking one individual answer as the contrasting element. Empirically, these two strategies probably converge on the same predictions. I would argue that it is conceptually more plausible to think that a focal target can be identified by all participants, as is implied by the present proposal; note that, on Wagner’s proposal, the addressee will not actually know which other potential answer the speaker of the answer is intending to contrast with – if indeed they are (and not just relating to the question as a whole).

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What is more crucial to note in the present context, though, is that on Wagner’s proposal, too, examples like (29) require focal targets that are not contextually salient. Note that the above quote contains the phrase ‘make available’ to characterize the relation between the question Who arrested Smith? and any one of its potential answers, e.g. ‘that Sally arrested Smith’. But note that that particular answer is not contextually salient in the sense the term is usually used. For example, it is not possible to deaccent the corresponding clause in an answer to the constituent question, as (30) shows. (30) (Who arrested Smith. –) a. # I really DOUBT that Sally arrested Smith. b. I really doubt that SALLy arrested Smith. On the other hand, if the context includes the actual statement, thereby making it given, as in (31), such deaccenting is flawless. (31) (Sally arrested Smith. –) I really DOUBT that Sally arrested Smith. This shows that the equivocation in the above quote from Wagner (2012) is not correct. Nor is, accordingly, the underlying premise of the argument in that paper that an answer focus can, in the general case, be analyzed as directly contrasting with a single contextually given proposition. The bottom line is: Answer focus and contrastive focus can only be unified at the price of admitting non-salient focal targets; whose existence, of course, is the very point argued here. 4.5 Why Contrastive Focal Targets Are Not Accommodated How different is the position taken in the present paper – that the focal target of contrastive focusing may be discourse new, as long as it is relevant and the addressees are able to identify it – from one that invokes accommodation to maintains that all focusing is anaphoric (and, hence, that all focal targets must be contextually salient)? Cases of (apparently) non-salient focal targets then would really just be cases of ‘accommodating saliency’: the focal target is treated as though it had been contextually salient. Wagner (2012:119) contemplates (and arguably adopts) this latter position, saying e.g. in the context of example (32) that ‘maybe the question “what kind of wine shall we get?”, clearly relevant …, is accommodated here – it’s as if someone had asked it, but it was not necessary to say it out aloud because it’s quite an expected next step’.

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(32) A: Shall we bring some wine to the party? B: Yes, let’s bring some FRENCH wine. Of course, (32B) is also compatible with the present analysis, in particular since wine is evidently given, regardless of whether the question ‘what kind of wine shall we bring?’ is. To tease the two positions apart, we need to look at examples in which the putatively accommodated question contains concepts that are not contextually salient, for example (33). (33) (Let’s go to Kim’s party! –) Yes, # let’s bring some FRENCH wine. Surely the content of the question that would need to be accommodated – ‘wine from which country should we bring?’ – is as clear in (33) as it was in (32); the same, I would argue, is true for the relevance of the question. So why, then, should that question – once accommodated – not license the deaccenting? On the present perspective, the problem is simply that wine is given in (32), but not in (33) (this same point was already illustrated by the printer examples in section 2.2 above). On the ‘accommodated question’ perspective an explanation for the contrast seems to be missing. Strictly speaking, I did not demonstrate that e.g. the question ‘what kind of wine should we bring?’ has not been accommodated in (32) or (33);20 I have merely shown that, even if accommodated questions exist, they do not have the same effect on prosody ‘as if someone had asked’ them: they do not license deaccenting (of a focal background) – otherwise the hallmark of things that were actually said. Once we agree on that, I do not see much use for a concept like ‘treated as though it had been uttered, except it does not license additional deaccenting’, though strictly speaking I would not know how to show that it does not exist.

5

Double Focus without Double Givenness

I want to close the empirical part of this paper with a look at another phenomenon that I believe to illustrate the dissociation of ‘background’ and ‘given’, and offer a novel perspective on ways to analyze it.

20

Given the general lack of consensus about what accommodation is and how to detect it, I wouldn’t know how.

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5.1 Double Focus Kehler (2005) and Büring (2012) discuss the contrast between (34) (from Schwarzschild, 1999) and (35). (34) John cited Mary, but … a. … he DISSED SUE. b. ? … he dissed SUE. (35) Fred read the menu and then … a. … he ordered a HAMburger. b. # … he ORdered a HAMburger. Starting from intuitions again, (34a) seems to be a case of double contrast: dissed is contrasted with ‘cited’, and Sue with ‘Mary’. No comparable contrast between ordering and reading, or the menu and a hamburger exists in (35a). If the prosodic pattern indicated by double capitalization – by assumption an intermediate phrase accent on V, followed by an intermediate phrase break between V and object – indicates double contrast, the infelicity of (35b) is explained. In this section I want to pursue an analysis that cashes in on this intuition. A crucial ingredient to this will be – again – that focal targets need not be contextually salient; therefore, the focal targets in (34a) can be ‘did he diss Sue, or Mary?’ and ‘did he quote, or diss Sue?’ A second ingredient is that Sue, not being given, cannot be prosodically demoted, so other means are required to realize narrow focus on dissed, namely the pattern with two intermediate phrases, each with its own nuclear pitch accent. This aspect of the analysis is novel and requires some additional machinery, to be introduced in section 5.2. In a nutshell, a sentence with two intermediate phrases will be allowed to have two sets of potential focal targets (≈ two sets of focus alternatives). Corresponding to these, there are two squiggle operators, each retrieving one of those, and each accompanied by a different focal target, call them Cdissed/quoted and CMary/Sue , the two questions mentioned above. Before going into the technical details, however, let me motivate a little more the assumption that there may be two sets of potential focal targets in a sentence like this. To do so, I will again use sentences with focus-sensitive particles. (36) shows that the narrow focus on V can serve as the associate to such a particle. (36) (John quoted Mary at great length but) he only MENtioned SUE.

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35

In the context given in (36) we understand only to exclude John discussing Sue to any greater extent than mere mention, i.e. the alternatives here are ‘R\mention Sue’. (37) demonstrates the parallel fact for interpreting the object as focused: John did not quote anyone but Sue. (37) (John used insights from various scholars, but) he only QUOTed SUE. Finally, (38) – though somewhat contrived – completes the demonstration; here we see that both foci may be used by two different particles within the same structure. (38) John’s discussion of other peoples’ work was sketchy, as usual. But at least their work was discussed a little bit. He only only CITED SUE. ‘the only person he merely cited (not discussed even a little bit) is Sue’ The crucial point about all these cases is that the alternatives only quantifies over – ‘John R-ed Sue’ in (36) (and (38)), ‘John quoted x’ in (37), and ‘John only cited x’ in (38) – are not contextually salient. That is, any analysis on which the restriction on only needs to be anaphoric runs into problems with cases like these. An analysis on which the restriction on only is merely constraint by focus does not, provided we allow for non-anaphoric focal targets – the line of analysis pursued in the present paper. 5.2 Prosodic Domain Splitting How to derive two sets of potential focal targets of these structure? Prosodic configurations like that in (34a) are beyond the reach of the purely relational metrical representation assumed so far: what is special about it is not that relative metrical weights between sisters are reversed, but rather that the absolute metrical weight of one element is greater than expected. Concretely: The stress/accent on dissed is stronger than a regular pre-nuclear accent, perhaps even equally strong to that on Sue (again, something not expressible in standard relational metrical trees), but the stress/accent on Sue is what is expected, i.e. Chris is not prosodically demoted. As said earlier, I will assume that there is an intermediate phrase boundary between dissed and Sue, so that each of the two pitch accents is nuclear (regardless of the question whether one of them is eventually stronger, being the head of a higher prosodic category such as the intonational phrase). For all intents and purposes we may see example (34a) above as the realization of a mother node with two strong daughters. The anticipated result is shown in structure (39).

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(39)

The two restrictions are clearly incompatible; trying to unify them would exclude any alternative whatsoever. The structure thus genuinely has two separate sets of unalternatives, i.e. two different focussings, that need to be related to two separate focal targets (whence the comma between the two restrictions, see below for an implementation).21 How do these come about? The weak restriction R\dissed sue is what is expected since the default strong daughter Sue is not prosodically demoted. The strong restriction R sue is what we would get if prosodic reversal had taken place and dissed were the (non-default) strong daughter. So far I have not been precise about whether Strong Restriction is invoked by prosodic promotion or by prosodic reversal, since both always went hand in hand. Taking into consideration the case of ‘equalization’ in (34a)/(39) we can now see what the correct choice is: Strong Restriction happens whenever a node is stronger than predicted by default; this is the case in prosodic reversal, but also in prosodic promotion without concomitant demotion, i.e. equalization. The overall picture then can be summarized as follows: \dissed

(40) a. if the structurally designated strong daughter is in fact strong, apply Weak Restriction (in addition to Propagation) b. if the structurally designated weak daughter is not in fact weak, apply Strong Restriction (in addition to Propagation) c. if the structurally designated strong daughter is not in fact strong, it must be given Clause (40c), the givenness condition, does not apply in example (34a) above, since nothing has been prosodically demoted. Unlike in previous cases, clauses (40a) and (40b) both apply in (34a)/(39): dissed, being stronger than by default, triggers a set of strongly restricted focus alternatives: ‘R sue’. Sue, being strong by default and in reality, triggers a set of weakly restricted focus alternatives ‘R\dissed sue’. \dissed

21

In Büring (2015) I argue that nodes for which the result of Weak/Strong Restriction is incompatible with those of Propagation are ill-formed. I have to assume that only a conflict between the two types of Restriction can be resolved by having two disjoint sets of unalternatives.

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figure 5

37

Full derivation for a double-focus example; for perspicuity, restrictions are removed where they are matched by a squiggle/focal target. The question {he dissed Mary, he dissed Sue} here corresponds to the contrast ‘he dissed Sue, not/unlike Mary’.

A full derivation for example (34a) is given in figure 5, where the two ‘foci’ are retrieved by two separate squiggles, each relating them to a different focal target. Summing up, the double focus configuration is one where two metrically equally strong sister constituents introduce incompatible restrictions on their focal targets. To get the analysis of these off the ground it is crucial that the individual focal targets need not be contextually salient (this is the part where the analysis in Büring, 2012, actually failed). A side-effect of this configuration is that the backgrounds of the two foci are not subject to the givenness condition. Put differently, the double focus configuration may generally come to the rescue where an intended focus cannot be realized by prosodic demotion. For example, the contrast intended in the earlier inacceptable examples (3), repeated in (41) below, can be felicitously rendered with a double-peak pattern instead, as in (42). (41) a. (The store across the street sells refurbished computers, but) # we sell NEW printers.

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b. (This store sells new and refurbished computers, but) # it only sells NEW printers. (42) a. (The store across the street sells refurbished computers, but) we sell NEW PRINTERS. b. (This store sells new and refurbished computers, but) it only sells NEW PRINTERS. Once the possibility of this kind of configuration is realized, one actually finds them not infrequently. As Max Prüller (p.c.) pointed out to me, example (43), from Büring (2013/15), presupposes that the quantificational domain of only can be ‘where should one wear sweat pants?’, which does not seem to have to be contextually salient for the entire sentence to be felicitous. (43) (One should only wear hats outside, just like) one should only wear SWEAT pants at HOME. I (conveniently) overlooked this riddle in Büring (2013/15), which shared the assumption that all quantificational domains for focus-sensitive elements must be anaphoric. Given what is proposed in the present paper, example (43) no longer constitutes a conundrum: there is no deaccenting of sweat pants, hence no givenness requirement. The focus on at home, on the other hand, relates to the QUD ‘where should one wear sweat pants?’, which is identifiable, relevant and proper in this context.

6

Summary

This paper argued for a number of distinct, yet interconnected claims: that prosodic demotion, but not backgrounding in general, is subject to an anaphoric givenness condition. That focusing is generally contrastive, but that its focal target need not be contextually salient. And that prosodic demotion always requires focusing in a larger domain (in addition to givenness of the demoted constituent). A particularly noteworthy consequence of this is that there cannot be such a thing as ‘pure givenness deaccenting’ or ‘anaphoric deaccenting’, a position empirically forced upon us anyway by the convertible-type examples. The present paper is, I believe, the first to propose a complete and reasonably formalized analysis of this empirical domain. The main obstacle to this in the past was, I would argue, the incompatibility of a strongly contrastive view of focussing (as necessitated by the convertible-examples) with an anaphoric

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view of focal targets: overt focal targets are in many instances – like focus in answers or apparent anaphoric deaccenting – not properly contrastive, necessitating a weak and, in some cases overly permissive, condition on focusing, like those in Rooth (1992b) and Schwarzschild (1999). On the other hand, any alternative approach that completely jettisons the anaphoricity of focal targets and instead freely allows focal targets (then usually called QUD s) to be accommodated or simply introduced implicitly is in need of a supplementary theory of what I here called prosodic demotion, so as to rule out prosodic demotion of non-given elements, as discussed in section 2.2 above. In the present paper this is accomplished by making privative givenness a necessary and inviolable, but not sufficient, condition for prosodic demotion – again a position I believe to be unique to the present proposal. Formally, the proposal was couched in terms of unalternative semantics, rather than the more traditional alternative semantics of the kind introduced in Rooth (1985, 1992b). As mentioned in several places, the central positions mentioned just above could presumably be implemented in other frameworks as well. This is certainly true for the assumptions that focusing need not be anaphoric, but is always contrastive, which could directly be superimposed onto a Rooth-style system. Things are a little trickier when it comes to the generalizations about non-default prosody argued for here, since the notion of prosodic demotion has no counter-part in terms of F-marking, or accenting, or absolute stress, relying, as it does, purely on the metrical, relational default/non-default distinction. It is a hallmark of unalternative semantics that exactly the same distinction, and only it, is referred to in the calculation of focus alternatives. As such, it sits particularly well with the overall picture advocated in the present paper which can be somewhat provocatively, but I believe accurately, described as claiming that the notions ‘focus/background of a domain’ have no role to play in the grammatical analysis of the phenomena at hand.

7

Appendix: Definitions

The basic rules of unalternative semantics are summarized in more formal form in definitions (44)–(48) below. A restriction in the sense used above is, technically speaking, a set of unalternatives, i.e. the same type of semantic object as Rooth’s focus semantic values (namely sets of ordinary meanings). Since a single node can be associated with more than one restriction, I introduce the function ⟦ ⟧𝒰 which maps a syntactic (sub)tree onto a set of restrictions (i.e. a set of sets of unalternatives).

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As in standard Roothian alternative semantics, restrictions/unalternative sets, once introduced, are propagated to a mother node κ by point-wise combination of the unalternatives of the daughters. This combination may be by means of function application, or whatever other rule the ordinary compositional semantics use for a node like κ. I agnostically write ⊕κ for the ordinary composition rule, and ⊗κ for the same rule applying to sets of meanings (for example, if ⊕κ is rightward function application, ⟦[κ α β]⟧𝒪 = ⟦α⟧𝒪 ⊕κ ⟦β⟧𝒪 = ⟦α⟧𝒪 (⟦β⟧𝒪 ), and ⟦[κ α β]⟧ℱ = ⟦α⟧ℱ ⊗κ ⟦β⟧ℱ = {a(b) | a ∈ ⟦α⟧ℱ &b ∈ ⟦β⟧ℱ ). I first define semantic operations that calculate Propagation, Weak Restriction and Strong Restriction based on single meanings and single restrictions. (44) Let τw , τs be semantic types, and 𝒲, 𝒮 be sets of meanings in POW(Dτw ) and POW(Dτs ) respectively, and κ be a syntactic configuration s.t. the standard composition operation ⊕κ for κ can compose a member of 𝒲 with a member of 𝒮 (i.e. the domain of ⊕κ is Dτw × Dτs ), then the Propagation of 𝒲 and 𝒮 by κ, Prop(𝒲, 𝒮, κ) is (Dτw ⊗κ 𝒮) ⋃(𝒲 ⊗κ Dτs )22 (45) Let τw , τs be semantic types, ω, σ be meanings in Dτw and Dτs respectively, 𝒲 be a set of meanings in POW(Dτw ), and κ be a syntactic configuration s.t. the standard composition operation ⊕κ for κ can compose ω and σ (i.e. the domain of ⊕κ is Dτw × Dτs ), then the Weak Restriction of ω, σ and 𝒲 by κ, weakRes(ω, σ, 𝒲, κ), is (𝒲 ∖ ω) ⊗κ {σ}

(46) Let τw , τs be semantic types, ω, σ be meanings in Dτw and Dτs respectively, 𝒮 be a set of meanings in POW(Dτs ), and κ be a syntactic configuration s.t. the standard composition operation ⊕κ for κ can compose ω and σ to D ×D yield a meaning in Dτκ (i.e. ⊕κ ∈ Dτκτw τs ), then the Strong Restriction of ω, σ and 𝒮 by κ, strongRes(ω, σ, 𝒮, κ), is Dτκ ∖ ((𝒮 ∖ σ) ⊗κ {ω}) Based on these definitions I now define the rules for ⟦ ⟧𝒰 , i.e. the rules associating syntactic structures with sets of restrictions. 22

κ here stands for whatever influence syntax has on semantic composition. Suppose all composition were function application, or at any rate purely type-driven, then κ must give us the semantic types of the daughters as well as their linear order, e.g.

. On

the other hand, κ could also include information about the syntactic categories of mother and daughter nodes or any other of their morpho-syntactic features, if these are deemed crucial for the choice of semantic composition rule.

focus, questions and givenness

(47) for any terminal node α, ⟦α⟧𝒰 ={{}}

41

(48) for any branching constituent μ with daughters δw and δs , where δs is the metrically strong daughter by default prosody, ⟦μ⟧𝒰 is the smallest set that contains a. Prop(𝒲, 𝒮) ⋃ weakRes(⟦δw ⟧𝒪 , ⟦δs ⟧𝒪 , 𝒲, μ) if δs is metrically strong in μ b. Prop(𝒲, 𝒮) ⋃ strongRes(⟦δs ⟧𝒪 , ⟦δw ⟧𝒪 , 𝒲, μ) if δw is metrically strong in μ for all 𝒲 ∈ ⟦δw ⟧𝒰 , 𝒮 ∈ ⟦δs ⟧𝒰 Condition: If δs is weak in μ (prosodic reversal), δs is given. Note: In case (48b), δw is the/a daughter that is actually metrically strong, and 𝒲 are its unalternatives. Accordingly, δs corresponds to ω in definition (46), δw to σ and 𝒲 to 𝒮. 8

Appendix: the Relation between Givenness, Background and Deaccenting

This paper started out from the empirical generalizations that being in the background of a focus is not a sufficient condition for being deaccented; givenness is required, too. This was argued for with the help of examples like (49), repeated from section 2.2 above, in which the attempt to deaccent a non-given item in order to create a narrow focus seems to render the sentences unacceptable as an out-of-the-blue utterance. (49) a. (The store across the street sells refurbished computers, but …) # we sell NEW printers. b. (This store sells new and refurbished computers, but) … # it only sells NEW printers. The question whether the background of a focus must be given has not, to the best of my knowledge, taken center-stage in any papers on focus in English. In this appendix I will discuss those few sources in which the question is at least touched upon. Katz & Selkirk (2011)’s experimental material consists almost exclusively of cases in which a non-given element is in the background of a focus. The result of the experiments reported in that paper is clear: Non-given elements must bear regular pitch accents, even if in the background of a focus. An example is given in (50) ((3A) from their appendix).

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(50) Gary is a really bad art dealer. He gets attached to the paintings he buys. He acquired a few So he would only offer [that Modigliani]F ⏟ to⏟⏟ MoMA ⏟⏟.

Picassos and fell in love with them. The same thing happened with a Cézanne painting. non-given

I bet the Picassos would have fetched a much higher price.

Here, to MoMA is clearly in the background of the focus associated with only, yet is not (and cannot be) deaccented, confirming our generalization that deaccenting requires givenness, not just background-ness. One of the few sources to explicitly argue the opposite position is Neeleman & Szendrői (2004), which discusses the Superman sentence in (51).23 (51) Father: Mother:

What happened? (You know how I think our children should read decent books. Well, when I came home, rather than doing his homework), Johnny was reading SUPERMAN to some kid.

According to Neeleman & Szendrői (2004), (to some) kid in example (51) is deaccented because it is in the background of a contrastive focus, read SupermanF (rather than read decent books). Crucially, some kid is not given, yet deaccented. I take Superman sentences to be the exception, rather than the rule. Structurally parallel cases to Neeleman & Szendrői’s (2004) do not in general allow deaccenting of a new element, witness the very questionable status of (52) and (53). (52) (You know how I think our children should read decent books. Well, when I came home, rather than doing his homework, …)

a. # Johnny was reading SUPERMAN to some woman. b. # Johnny was reading SUPERMAN in the bathroom. (53) (I said it is important that our family doesn’t hang out with politicians. And yet, at the party, instead of staying in the kitchen,) # you introduced the MAYOR to my uncle. Arguably it is significant that the deaccented item in the original Superman sentence (51) was the noun kid (rather than woman, bathroom or uncle in (52)

23

The only other one I am aware of is Féry & Samek-Lodovici (2006:esp. pp. 137ff.), but the cases discussed there all involve some kind of symmetrical deaccenting.

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and (53)); the context does contain the word children, and clearly the speaker’s kid (and the fact that he is a kid) is salient in it.

Bibliography Beaver, D., & Clark, B. (2008). Sense and Sensitivity: How Focus Determines Meaning. Cambridge: Wiley-Blackwell. Büring, D. (2012). What’s new (and what’s given) in the theory of focus? In Proceedings of the Thirty-Fourth Annual Meeting of the Berkeley Linguistics Society (pp. 403–424). Berkeley, CA: Berkeley Linguistics Society. Büring, D. (2013/15). A theory of second occurrence focus. Language as a Cognitive Process/Language, Cognition and Neuroscience, 30, 73–87. Büring, D. (2015). Unalternative semantics. In Proceedings of SALT 25 (pp. 550–575). Büring, D. (Forthcoming). Discontinuous foci and unalternative semantics. In Proceedings of SinFonIJA 8 (p. tba). Féry, C., & Samek-Lodovici, V. (2006). Focus projection and prosodic prominence in nested foci. Language, 82, 131–150. Kadmon, N., & Sevi, A. (2011). Without focus. In B.H. Partee, M. Ginzburg, & J. Šķilters (Eds.), Formal Semantics and Pragmatics. Discourse, Context and Models. The Baltic International Yearbook of Cognition, Logic and Communication volume 6 (pp. 1–50). Manhattan, KS: New Prairie Press. Katz, J., & Selkirk, E. (2011). Contrastive focus vs. discourse-new: Evidence from prosodic prominence in English. Language, 87, 771–816. Katzir, R. (2013). A note on contrast. Natural Language Semantics, 21, 333–343. Kehler, A. (2005). Coherence-driven constraints on the placement of accent. In Proceedings of SALT 15 (pp. 98–115). Ladd, D.R. (1980). The Structure of Intonational Meaning. Bloomington: Indiana University Press. Neeleman, A., & Szendrői, K. (2004). Superman sentences. Linguistic Inquiry, 35, 140– 159. Onea, E., & Zimmermann, M. (2019). Questions in discourse: An overview. In K. von Heusinger, M. Zimmermann, & E. Onea (Eds.), Questions in Discourse. Volume 1: Semantics (pp. 5–117). Leiden: Brill. Rooth, M. (1985). Association with Focus. Dissertation University of Massachusetts Amherst. Amherst, MA. Rooth, M. (1992a). Reduction redundancy and ellipsis redundancy. In Proceedings of the Stuttgart Workshop on Ellipsis 29 (pp. 1–26). Rooth, M. (1992b). A theory of focus interpretation. Natural Language Semantics, 1, 75– 116.

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Schwarzschild, R. (1993). The contrastiveness of associated foci. Ms. Hebrew University of Jerusalem. Schwarzschild, R. (1999). Givenness, AvoidF and other constraints on the placement of accent. Natural Language Semantics, 7, 141–177. Selkirk, E. (1995). Sentence prosody: Intonation, stress, and phrasing. In J.A. Goldsmith (Ed.), The Handbook of Phonological Theory (pp. 550–569). London: Blackwell. Selkirk, E.O. (1984). Phonology and Syntax: The Relation between Sound and Structure. Cambridge, MA.: MIT Press. Stevens, J.S. (2013). Against a unified analysis of givenness and focus. In Proceedings of WCCFL 31 (pp. 438–446). Wagner, M. (2006). Givenness and locality. In Proceedings of SALT 16 (pp. 295–312). Wagner, M. (2012). Focus and givenness: A unified approach. In I. Kučerová, & A. Neeleman (Eds.), Contrasts and Positions in Information Structure (pp. 102–147). Cambridge: Cambridge University Press. Williams, E. (1997). Blocking and anaphora. Linguistics Inquiry, 28, 577–628.

chapter 3

The Scalar Particle har’i in Ngamo (West Chadic)* Mira Grubic

1

Introduction

This paper presents an analysis of the particle har(’i) in Ngamo. This particle is challenging to describe, due to its many different uses: it can be used as even, until, as far as, and already, cf. (1)–(4). (1) (Many people built a house last year.) Har Kule salko bano mano even Kule build.pfv house last.year ‘Even Kule built a house last year.’ (2) (Nono fell asleep at around 11p.m. and woke up at midnight.) Nono iko monsom har tintil beɗi. Nono do.pfv sleep until middle night ‘Nono slept until midnight.’ (3) Nono nduko har bo dumno. Nono go.pfv up.to opening door ‘Nono went as far as the door.’

* This research was conducted as part of project A5 “Focus realization, focus interpretation and focus use from a cross-linguistic perspective” of the Collaborative Research Center 632 “Information Structure”, funded by the German Science Association (DFG), and is based on a chapter of my dissertation (Grubic 2015). I would like to thank the DFG, as well as my Ngamo language consultants, and two anonymous reviewers for their helpful comments. Unless indicated otherwise, the data here stem from my own fieldwork. The following glosses are used: 1/2/3 = first/second/third person, bm = background marker, comp = complementizer, def = definite, dep = dependent pronoun, det = determiner, dub = dubitative, excl = exclamation, f = feminine, fm = focus marker, fut = future, hab = habitual, i = i/ye marker, icp = intransitive copy pronoun, indep = independent pronoun, ipfv = imperfective, irr = irrealis, link = linking morpheme, m = masculine, neg = negation, pfv = perfective, pl = plural, poss = possessive, prt = particle, rel = relative, sbjv = subjunctive, sg = singular, tot = totality extension, vent = ventive extension.

© koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004378322_004

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(4) (We were expecting rain in the evening, but it started raining now, in the afternoon.) Har a ka ham ndeyi. har 3sg.ipfv ipfv water God ‘It is already raining.’ I argue that all of these uses of har(’i) are scalar and alternative-sensitive, but not all are additive. The paper is structured as follows: section 2 presents an introduction to focus and focus-sensitivity, including a proposal for a QUD account of even in English. Section 3 introduces the relevant data concerning the realization of focus/backgrounding in Ngamo, while section 4 shows the different readings and association patterns for examples where har(’i) is translated as even. It then provides an analysis of har(’i), discussing how it differs from the proposed account for even, including the role of the notion of QUD s in this account. Section 5 shows how the analysis can be extended to also account for its other uses.

2

Focus and Focus-Sensitivity

2.1 Focus and Questions under Discussion I adopt an alternative semantic view of focus. Under this approach, focus induces alternatives on a non-truth-conditional level of meaning (Rooth 1985, 1992, 1996, see Büring (this volume) for an unalternative account of focus), cf. (5). (5) Focus indicates the presence of alternatives that are relevant for the interpretation of linguistic expressions. (Krifka 2008, p. 18) For example, (6a–b) have the same truth conditions, but differ in their focus value: (6a) indicates alternatives of the form Mary introduced X to Sue, for different X, whereas (6b) indicates alternatives of the form Mary introduced Bill to X. (6) a. Mary introduced Bill to Sue. focus value: { Mary introduced Ali to Sue, Mary introduced Bill to Sue, Mary introduced Cem to Sue, … } b. Mary introduced Bill to Sue. focus value: { Mary introduced Bill to Sue, Mary introduced Bill to Tom, Mary introduced Bill to Ute, … }

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I adopt a question under discussion approach to focus (Roberts, 1998; Büring, 2003; Beaver & Clark, 2008).1 This approach combines Roothian alternative semantics with the main function of focus: discourse management. Taking as a starting point that the goal of discourse is to share previously unshared information, the QUD theory models discourse as driven by implicit (hearer-) questions: The (eternally unreachable) goal of each new conversation is to cooperatively answer the super-question “What is the way things are?”. This question is tackled by splitting it up into subquestions, which each ask for a partial answer to the superquestion, cf. (7).2 Any new assertion answers the currently salient most specific question, the Current Question (CQ). (7)

A complete subtree of subquestions of a higher question is called its strategy. Full answers to the subquestions of a superquestion yield the answer to the superquestion. There are in principle an infinite number of strategies possible to answer the question “what is the way things are?”, which strategy is chosen depends on the other goals of the interlocutors – “goals in the real world” (Roberts, 2012, p. 7). The focus-background structure of an utterance indicates what the Current Question is. For example, in (8), the Current Question is What did she eat?: (8) A: B:

Mary ate a pear. No, she ate an appleF.

1 See also Klein & von Stutterheim (1987); van Kuppevelt (1995); Ginzburg (1996). See Onea & Zimmermann (2019, §1.4–1.5, in particular 1.4.1) and see Riester (this volume), § 8.2.1 and Onea (this volume) §6.4 for an overview) 2 I adopt the notational convention used in Büring (2003) to display the hierarchy of superand subquestions in a ‘discourse tree’, whereby the dominating nodes are superquestions, the daughter nodes subquestions, and sister nodes are in a temporal order: questions further to the right are asked or presupposed later, and will thus usually not be represented unless the tree represents a longer stretch of discourse. When the Current Question is answered, it is ‘closed’, and the next highest question will become relevant again, possibly leading to a new subquestion. See Riester (this volume) and Onea (this volume) for discussions and adaptations of the discourse tree notation.

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The focus of the declarative utterance corresponds to the part asked for in the Current Question. This is modeled by the requirement that an utterance must be relevant and congruent to the Current Question (Roberts, 1998; Büring, 2003; Beaver & Clark, 2008).3 Relevance of declarative utterances is defined via answerhood, cf. (9), (10).4 (9) Relevance of assertions (Büring, 2003, p. 518): An assertion A is relevant in a discourse tree D iff A is an answer to the Current Question CQ for A in D. (10) Answerhood (Roberts, 2012, p. 11): a. A partial answer to [a CQ] is a proposition which contextually entails the evaluation – either true or false – of at least one [of the alternatives in the CQ]. b. A complete answer [to a CQ] is a proposition which contextually entails an evaluation for each [of the alternatives in the CQ]. Relevance for assertions thus has to do with the truth-conditional content: The answer has to settle the issue raised in the question, at least partly. In addition, the assertion must be congruent to the Current Question at the time when it is uttered. Under the assumption that a question denotes a set of propositions, namely the set of possible answers to the question (Hamblin 1973, p. 48, see Onea & Zimmermann 2019, §1.2.2 for an overview of different accounts of the semantics of questions), congruence is a relation between the focus alternatives indicated by focus marking and the alternatives denoted by the Current Question. I follow Roberts (1998, p. 24), who cites von Stechow (1989, p. 36) as original reference, in assuming that the two sets are identical rather than in a

3 Büring (2003) also includes a requirement for answers to be informative. Riester (this volume), argues against relevance (§8.2.2). See also Büring (this volume § 2.3.3 and § 2.4.2.1) for conditions placed on the QUD, and Riester (this volume) on how implicit QUD s can be identified and represented. 4 For Büring, this definition of answerhood is too strong, since answers like A in (i) are possible. He thus proposes (ii). (i) Q: Will you come to the party? A: Presumably. (ii) Answerhood (Büring): A is an answer to [a CQ] if A shifts the probabilistic weights among the propositions denoted by [the CQ]. I adopt Roberts’ more strict definition of answerhood.

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subset/superset relation.5 Following Beaver & Clark (2008, p. 37), I assume that it needn’t be the whole utterance which evokes the alternatives corresponding to the CQ, but only a part of the utterance, cf. (11). (11) Congruence, adapted from Beaver & Clark (2008)’s Focus Principle: Some part of a declarative utterance should evoke a set of alternatives [corresponding to] all the Rooth-Hamblin alternatives of the CQ. For example, the focus in (12c) might indicate either a Current Question like (12a) or (12b), cf. Beaver & Clark (2008, p. 37). (12) a. Who do you think laughed? b. Who laughed? c. I think that [Mary]F laughed. Relevance and Congruence are too weak up to now, cf. example (13)6 (by Andreas Haida (p.c.)): they wrongly predict the exchange in (13) to be felicitous, since (i) it provides the desired information that Özil scored the goal, as required by Relevance, and (ii) part of the sentence evokes alternatives which correspond to those indicated by the question, as required by Congruence. (13) Q: Who scored the goal? A: #I think that Peter was on the balcony when Özil scored the goal, because he didn’t believe that the German team could still win. This suggests that a further constraint is needed, an at-issueness constraint, cf. the definition of at-issueness in (14) (by Simons et al., 2011, p. 323).7

5 For Rooth (1992) and Beaver & Clark (2008), the focus alternatives can be a superset of the CQ alternatives. Since the answer often (in a sense) creates the question, indicating what the speaker believes the Current Question to be (cf. Büring, this volume), it would however be counterintuitive to assume that the answer can involve more salient individuals than the corresponding question. 6 Thanks to Andreas Haida for pointing this out to me. 7 See also Riester, this volume §8.3.6-§8.3.7, for a more fine-grained notion of non-at-issue content.

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(14) At-issueness (Simons et al., 2011, p. 323) a. A proposition p is at-issue iff the speaker intends to address the CQ via ?p. b. An intention to address the QUD via ?p is felicitous only if: (i) ?p is relevant to the QUD, and (ii) the speaker can reasonably expect the addressee to recognize this intention. Thereby, ?p is the corresponding yes/no-question for the proposition p. One question is relevant to another iff it is part of a strategy to answer this other question, cf. (15), adapted from Büring (2003, p. 513)’s and Roberts (1998)’s definitions: (15) Relevance of questions: A question Q is relevant in a discourse tree D iff Q is part of a strategy to answer its Current Question CQ in D. The answer ‘Özil scored the goal’ in (13), is not-at-issue, because the speaker cannot expect the hearer to recognize that she wants to address the CQ with the question ‘Did Özil score the goal?’: temporal adjuncts like the when-clause in (13) are presupposition triggers, and presupposed (and other projective) parts of utterances are usually not-at-issue, and can thus usually not contain answers to the Current Question (Simons et al., 2011, p. 322).8 A declarative utterance is thus not only required to be congruent and relevant to the CQ, but the part that answers the CQ must also be at-issue. (16) is an attempt at formulating such a constraint. (16) At-issueness constraint The part of a declarative utterance U that evokes a set of alternatives corresponding to all the Rooth-Hamblin alternatives of the CQ must be at-issue with respect to the CQ.

8 Examples where the answer to an overt question is within a projective part of the utterance are only felicitous because the hearer recognizes the speaker’s intention to answer another CQ, e.g. in (i): “Why did Bob give me this amount of money?” (Simons et al. 2011, p. 320, see also Onea & Zimmermann 2019, §1.4.5 for a discussion of such examples). (i) Quentin, Ann and Bob [ate] at a restaurant where the tip is usually incorporated into the bill. Bob handed Quentin what he said was his share of the bill, then left the table. […] Quentin [(confused)]: Are we supposed to leave a tip? Ann: Bob doesn’t realize that the tip is included in the price.

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This constraint regulates the form of the answer, requiring it to be formulated in a way that the hearer can easily recognize the part that answers the Current Question. So, to sum up, the focus/background marking of an utterance serves to indicate which (possibly implicit) CQ the speaker intends to answer. The relation between the CQ and the answer is modeled using the requirements of Relevance, Congruence, and At-issueness. 2.2 Focus-Sensitivity and Questions under Discussion This section discusses how focus-sensitive operators like only, also, and even interact with the Current Question (see also Onea & Zimmermann 2019, § 1.4.2). Focus-sensitive operators are operators whose contribution to the interpretation of their containing sentence changes when the focus of the sentence changes. For example, (17a) is only felicitous in contexts in which Mary introduced somebody else to Sue, and (17b) is only felicitous in contexts in which Mary introduced Bill to somebody else. Even in (18) is said to have similar felicity constraints, with the additional condition that the other true alternatives are ranked lower on a salient scale, here possibly a scale of unlikelihood. (17) a. Mary also introduced Bill to Sue. b. Mary also introduced Bill to Sue. (18) a. Mary even introduced Bill to Sue. b. Mary even introduced Bill to Sue. Both operators thus have a presuppositional meaning component which makes reference to the alternative set introduced by focus: these other alternatives are included, making them inclusive or additive particles (König, 1991, p. 33). In addition, even is scalar, presupposing that the prejacent is high on a scale compared to other alternatives (König 1991, p. 69, Karttunen & Peters 1979, p. 33, Jacobs 1983, p. 147).9 The exact nature of the scalar meaning component of even is under debate. In some proposals, the scale is a scale of likelihood, e.g. Karttunen & Peters (1979). It has however been suggested that the scale cannot be a likelihood scale in all cases (e.g. Fauconnier 1976, p. 262, Kay 1990, p. 71, Gast & van der Auwera 2011, p. 7) – most accounts thus assume that the ordering relation of the scale is determined by the context (e.g. Fauconnier, 1976; Jacobs, 1983). 9 Note that in the literature on even, one or both of its presuppositions have also been called conventional implicatures, e.g. in Karttunen & Peters (1979, p. 12) and König (1991, p. 69).

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2.2.1 Only in a QUD Account This section presents the QUD account of only proposed in Beaver & Clark (2008); Coppock & Beaver (2013) as a prerequisite for formulating a similar account for even. Beaver & Clark (2008) take mirativity or counter-expectation marking to be the central function of exclusive particles, cf. the informal description of the meaning of exclusives in (19) (adapted from Beaver & Clark, 2008, p. 251): (19) Meaning of exclusives The lexical meaning of exclusives is exhaustively described by: Discourse function: To make a comment on the [CQ], a comment which weakens a salient or natural expectation. To achieve this function, the prejacent [i.e. the propositional complement of only] must be weaker than the expected answer to the CQ on a salient scale. Presupposition: [There is a true alternative in the CQ which is] at least as strong as the prejacent. Descriptive Content: [All true alternatives in the CQ] are at most as strong as the prejacent. The lexical entry for only is shown in (20) (from Coppock & Beaver 2013, p. 24, a version of the proposal in Beaver & Clark 2008, p. 261). Thereby, minS is defined as in (21a),10 and maxS as in (21b), where p ≥S q means “alternative p is at least as strong as alternative q on a salient scale of strength”. Since (20) makes reference to the CQ, only is classified as conventionally associating with focus, i.e. it is hard-wired in the semantic of only that it is focus-sensitive. (20) ⟦only⟧S = λp.λw: minS(p)(w). maxS(p)(w)

(21) a. minS(p)= λw.∃p’ ∈ CQS [p’(w) ∧ p’ ≥S p] b. maxS(p)= λw.∀p’ ∈ CQS [p’(w) → p ≥S p’]

According to this proposal, only is always scalar: A sentence like (22a) is assumed to answer a CQ like (22b), with alternatives like (23), ordered on a scale of strength (here: an entailment scale). Note that it is not the full sentence Only

10

This is Coppock & Beaver (2013)’s corrected version of the min operator in Beaver & Clark (2008, p. 261), which required that weaker alternatives be false, and thus made the wrong predictions for entailment scales. The presupposition in the informal version in (19) was corrected accordingly, too.

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four students left which is ordered on the scale, but only the prejacent Four students left. This is due to the fact that the CQ is (22b) rather than (22c).11 (22) a. Only four students left. b. How many students left? c. Only how many students left? (23)

The answer in (22) thus presupposes that there is a true alternative in the CQ which is at least as strong as Four students left (the min-component), and asserts that all true alternatives in the CQ are at most as strong as Four students left (the max-component). Together, they entail that the prejacent, Four students left is the strongest true alternative. This accounts for the fact that all stronger alternatives (e.g. Five students left) are truth-conditionally excluded, while weaker alternatives in this example (e.g. Three students left) are still entailed by (22b). When the sentence is negated, e.g. Not only four students left, the same QUD in (22b) and ranking in (23) are assumed. The min-component, being a presupposition, survives, leading to the presupposition that there is a true alternative in the CQ which is at least as strong as the prejacent. The max-component is however negated, leading to the assertion that there is a true alternative in the CQ which is stronger than the prejacent.12 For this reason, the prejacent gets

11

12

Beaver & Clark analyze only as a sentential operator (but cf. Coppock & Beaver, 2013, for a compositional analysis of only). The focus alternatives are evoked by (some part of) the proposition in its scope (cf. Congruence above). This is due to the following equivalences: (i) a. ¬∀x∈A, P(x) ⇔ ∃x∈A, ¬P(x), therefore: ¬[∀p’ ∈ CQS p’(w) → p’ ≥S p] ⇔ ∃p’ ∈ CQS ¬[p’(w) → p’ ≥S p] b. ¬[p → q] ⇔ p∧¬q, therefore: ∃p’ ∈ CQS ¬[p’(w) → p’ ≥S p] ⇔ ∃p’ ∈ CQS [p’(w) ∧ ¬[p’ ≥S p]]

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excluded as a candidate for the strongest true alternative: it is true, but not the strongest true answer. Similarly, in a sentence like (24b) with CQ (24a), where Ali, Ben and Cem are salient individuals, alternative answers are ranked on a scale. Like in (22), the ranking criterium for the scale is entailment, cf. (25). Answer (24b) presupposes that there is a true alternative at least as strong as the prejacent, excluding all those alternatives which do not entail the prejacent (in gray) as candidates for the strongest true alternative. The assertion then excludes all propositions stronger than the prejacent, leaving the prejacent as the strongest true alternative. When the sentence is negated, as in (24c), the same CQ in (24a) and scale in (25) are assumed, and the presupposition survives, so that the same candidates remain as with the positive sentence. The assertion excludes the prejacent as a candidate for the strongest true alternative, leaving all alternatives which entail the prejacent as candididates. (24) a. Who smokes? b. Only Ali smokes. c. Not only Ali smokes. (25)

In entailment-scale examples like (22) and (24), the prejacent is still entailed when the sentence is negated. The reason for this is the assertion that a stronger alternative is true: since the alternatives are ranked on an entailment scale, the strongest true alternative, no matter which one it is, will entail the prejacent. There are however other, evaluative examples of only, where the prejacent does not survive when the sentence is negated. For example, (26b), as an answer to the CQ in (26a) expresses that being a PhD student is ranked lower on a salient scale of occupations than other more important or prestigious occupations. Here, “academic rank” is the ranking criterium rather than entailment, cf. (27). (26) a. What is Amy’s job? b. Amy is only a PhD student. c. Amy isn’t only a PhD student. ↛ Amy is a PhD student.

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(27)

Again, only triggers a presupposition that the strongest true alternative is at least as strong as the prejacent. The positive sentence (26b) asserts that the prejacent is the strongest true alternative. The negative sentence in (26c) asserts that a stronger alternative is true instead. Since the strength relation here is not entailment but academic rank, the alternatives mutually exclude each other. The strongest true alternative, no matter which it is, will therefore exclude the prejacent as a true alternative. Beaver & Clark (2008)’s account thus easily explains the behaviour of the prejacent in negative only-sentences. Before turning to a proposal for a QUD-account of even, the min-component of (20) merits further discussion. It is an unusual kind of presupposition, a socalled discourse presupposition: it indicates what the speaker believes the QUD to be like.13 Compare (24b) with the exchange in (28) without the particle only. The range of candidate answers after accommodation of the presupposition in (24b) is much more restricted than in (28). There are several ways how the range of candidates can be tested. For example, when a test sentence with only is negated, and the CQ is posed again, only stronger alternatives are possible answers to the CQ, cf. (29). Another test, shown in (30) (adapted from Umbach, 2004, p. 165), sets up a contrast between the test sentence and another alternative, and involves asking for more information about this other alternative. With only, the contrasting alternative has to be a stronger alternative (e.g. In the past, Ali and Cem smoked), whereas without only, it can be any other alternative. (28) CQ: Who smokes? A: Ali smokes.

13

See also Büring, this volume §2.4, for arguments that the QUD need not be contextually salient, see in particular § 2.4.1, discussing that with “only”, the backgrounded part need not be given; see Riester (this volume), §8.3.2 for the opposite view.

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(29) It’s not the case that … a. … only Ali smokes. b. … Ali smokes. Who smokes? (30) Some things have changed. a. Now, only Ali smokes. b. Now, Ali smokes. How were things in the past? The min-component is also responsible for the ‘salient or natural expectation’ above, i.e. the mirative or counter-expectation marking (cf. also Zeevat, 1994, 2009; Roberts, 2011, i.a.): the speaker indicates that of the set of expected answers, the prejacent is the weakest.14 The mirative meaning component survives embedding under negation, e.g. (29a) still conveys that more people were expected to smoke. 2.2.2 Even in a QUD Account The focus-sensitive particles even and also are only briefly discussed in Beaver & Clark (2008). Without providing a concrete proposal for the meanings of even and also, they provide suggestions on the interaction of the particles with the CQ. First, they propose that the particles conventionally associate with the focus, i.e. they make direct reference to the CQ in their lexical entries. For an additive-scalar operator like even, Beaver & Clark suggest that its discourse function, like that of only, is mirative: where only corrects an overly strong expectation, even corrects an overly weak expectation Beaver & Clark (2008, p. 71) – I will assume that this amounts to something like (31). (31) Meaning of scalar additives The lexical meaning of scalar additives is exhaustively described by: Discourse function: To make a comment on the Current Question (CQ), a comment which strengthens a salient or natural expectation. To achieve 14

A reviewer noted that the notion of counter-expectation or mirativity is not sufficient to account for the discourse function of only. For example, in (i), it was expected by speaker and addressee that four students hand in their homework. It seems to be enough if stronger alternatives are under discussion. The reviewer pointed out that it is thus desirable that no notion of (un)expectedness is built into the semantics of only. See also Grubic (2015a, §5.3.2, §7.4.2) for arguments that the speaker needs to independently keep track of the (un)expectability of the different focus alternatives. (i) As we expected, only four students handed in their homework.

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this function, the prejacent must be stronger than the expected answer to the CQ on a salient scale. Presupposition: The strongest true alternatives in the CQ are at most as strong as the prejacent. Descriptive Content: The prejacent is a true answer to the CQ. Note that there is no additive presupposition in (31).15 I propose the following lexical entry for even to capture Beaver & Clark (2008)’s intended meaning.16 (32) ⟦even⟧S = λp.λw: maxS(p)(w).p(w) To sum up, this section discussed Beaver & Clark (2008)’s QUD account for English only, and presented a proposal for a QUD account for even. The remainder of this paper discusses the Ngamo counterpart of even, har(’i). It will be shown that har(’i) is more versatile, also being used as until, as far as, and already, and that har(’i) does not interact with the CQ in the same way as even does.

3

Focus/Background Marking in Ngamo

This section discusses the marking of the focus/background distinction in Ngamo. Like in many African languages (Fiedler et al., 2010), there is a subject/ non-subject asymmetry in focus/background marking in Ngamo. For nonsubject term focus, there are three structural ways of realizing the same focus structure: (i) entirely unmarked (even prosodically) (33a), (ii) insertion of a morphological marker =i/ye in canonical word order (33b), (iii) non-canonical word order, with =i/ye (33c). For subjects, only the third option is available (34).17 Predicate focus, i.e. focus on verbs, VPs, TAMs, Verum or the whole sentence, usually remains unmarked (35). 15

16 17

There are other proposals in the literature which also do not assume an independent additive meaning component, but rather assume that the additivity follows from the interaction of the assertion and the presupposed scalar component (Horn, 1969; Fauconnier, 1976; Gast & van der Auwera, 2011). This will be further discussed in section 4.4. This formalization does not entirely account for all relevant data, and is refined in chapter 4.4. Even though preverbal subjects were sometimes accepted in answers to subject whquestions, evidence from association of yak’i (= “only”) with focus shows that yak’i cannot associate with a preverbal subject. Since there is evidence that yak’i, in contrast to har’i, needs to have a focused constituent in its scope, preverbal subjects are proposed to be

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(33) (What did Kule build in Potiskum?) a. Kule salko bano a Potiskum. Kule build.pfv house at Potiskum b. Kule salko=i bano a Potiskum. Kule build.pfv=i house at Potiskum c. Kule salko a Potiskum=i bano. Kule build.pfv at Potiskum=i house ‘Kule built a house in Potiskum.’ (34) (Who built a house?) Salko bano=i Shuwa. build.pfv house=i Shuwa ‘Shuwa built a house.’ (35) (What did Shuwa do to the house?) Salko (te). build.pfv 3sg.f ‘She built it.’ In Schuh (2005, p. 93), the apparent morphological focus marker was classified as a background marker (Schuh, 2005). Schuh notes that background marking is an areal feature: whereas other languages at the eastern edge of the West Chadic region use similar syntactic focus marking strategies, only the languages spoken in the Potiskum region make use of a morphological marker of this kind (Schuh, 2005, p. 93).18 These morphological markers all stem from the definite determiner and are related to similar morphological markers marking temporal adverbial clauses and conditionals, cf. table 1, adapted from Schuh (2005).19

18

19

out-of-focus in Grubic (2015a), corroborating earlier claims in Schuh (2005, pp. 92–93). A further possibility, pointed out by a reviewer, is that only bound focus needs to be marked – note however that yak(’i) can associate with unmarked non-subject terms. Truckenbrodt et al. (2008) argue that there is a morphological marker [-n], sometimes realized as an empty mora [-μ], in Shongom Tangale, a language outside the Potiskum region, but it bears no relation to the determiner system. I included ye and the when-clause marker ɗo in Ngamo, and the Ngizim background marker nən as a variant of -n (for nən, cf. Schuh, 1972, p. 210). Note that the origin of the Karekare na marker is unclear. Schuh (2005, pp. 93–94) tentatively suggests that it may either be related to the when-clause marker ma, or to the Ngizim -n/nən.

59

the scalar particle har’i in ngamo (west chadic) table 1

det bm if/when when

Yobe State languages: morphological markers

Ngamo

Bole

Karekare

Ngizim

def: -i[/ye] -i[/ye] na … (-i[/ye]) [ɗo … (-i/ye)]

def:yê ye bàa … (ye) ye

def:yi, dem:âm nà … ye/ya … (ma)

dem:tənu, def:-gu -n[/nən] -n/nən … (tənu/ngum)

Both the definite determiner =i/ye (m.), and the marker of conditionals =i/ye scope leftward (36), as do some other functional elements, e.g. the negation (37), providing some support to the claim that =i/ye in focus constructions marks the background to the left, rather than the focus to the right. (36) a. bi ye room det.m ‘the (previously mentioned) room’ b. Na iko ham ye, banono nzere. if do.pfv water i house=1sg.poss leak.hab ‘If/When it rains, my house leaks.’ (37) a. bano bu house neg ‘not a house’ Apart from the formal similarity to the definite determiner, there are other properties of the background marker that support an analysis of =i/ye as a background marker rather than a focus marker: First, in contrast to languages with morphological focus marking (e.g. Yom, Oti-Volta, (38), from Fiedler (2006)), the background marker in Ngamo does not occur in short answers to whquestions (39). (38) Yom (Oti-Volta), cf Fiedler (2006) Q: Who is eating bananas? A: béséŕwá =rà. girl =fm ‘The girls.’

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(39) Ngamo: Q: Who answered? A: (*I/*Ye) Jajei. bm Jajei ‘Jajei.’ Second, =i/ye can occur twice in a clause with only one focus. For example, (40) shows a second ye marker following the focused constituent.20 In example 40, the final ye’e cannot be a definite determiner, since Potiskum takes the feminine determiner s/se/se’e (41). (40) Kule salko =i bano a Potiskum ye’e. Kule build.pfv bm house at Potiskum bm ‘Kule built a house in Potiskum.’ (41) Potiskum =se Potiskum det.f ‘the Potiskum’ In contrast to marked focus/background constructions in many other languages, =i/ye background marking does not lead to a stronger exhaustivity inference: In =i/ye-marked constructions, just like in unmarked constructions, the exhaustive inference is a conversational implicature. This can be seen in examples like (42): =i/ye marking in the first sentence does not trigger an exhaustivity presupposition to the extent that nobody else built a house, or assert exhaustivity, otherwise cancellation of the exhaustive inference by the second sentence would not be possible. (42) Salko bano=i Dimza, Umar ke salko bano. build.pfv house=bm Dimza Umar also build.pfv house ‘Dimza built a house, and Umar also built a house.’ To sum up, non-subject focus can remain unmarked in Ngamo, while focused subjects are inverted. The background can be marked by a morphological marker =i/ye (for a discussion of =i/ye as a kind of topic marker, see Onea & Zimmermann 2019, §1.4.1.2). This marked construction does not yield a stronger exhaustive interpretation. 20

The form of the =i/ye marker varies depending on its environment: here it is ye’e because it is sentence-final and the preceding word ends with a consonant (cf. Grubic, 2015a, p. 74).

the scalar particle har’i in ngamo (west chadic)

4

61

Har(’i) as even

This section first shows the syntactic positions that the particle har(’i) in its use as even can occur in, the kinds of constituents it can associate with, and the different readings it can have. Then, an analysis of har(’i) in its use as even is proposed, which will be extended to its other uses in the further chapters. 4.1 Possible Positions Har(’i) can associate with a preverbal subject, either adjacent, preceding or following the subject, or from a distance. Har’i is the post-focal form, and har the pre-focal form.21 (43) (Many people built a house last year) (Subj) (Har) Kule (har/har’i) salko bano (har’i) mano (har’i). even Kule even build.pfv house even last.year even ‘Even Kule built a house last year.’ When associating with a direct object, the particle har(’i) can occur preceding or following the subject, immediately preceding or following its associate, or in clause-final position, cf. (44). The same is true for association with indirect objects and adjuncts, cf. e.g. (45) for an example of association with an IO. (44) (Kule built many things last year) (DO) (Har) Kule (har) salko (har) bano (har’i) mano (har’i). even Kule even build.pfv even house even last.year even ‘Kule even built a house last year.’ (45) (Mammadi gave a watch to many people yesterday) (Har) Mammadi (har) onko agoggo (har) ki Abu (har’i). even Mammadi even give.pfv watch even to Abu even nzono (har’i). yesterday even ‘Mammadi even gave a watch to Abu yesterday.’

(IO)

Har(’i) can associate with the verb or VP from a sentence-initial or -final position, or when immediately preceding or following the VP. It cannot immediately follow the focused verb, however, cf. (48). 21

Note that har can immediately follow a preverbal subject without being in its post-focal form har’i.

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(46) (Kule made many changes to his house last year) (V) (Har) Kule (har) shuɗanta bano=s (har’i) mano (har’i). even Kule even paint.pfv house=def.det.f even last.year even ‘Kule even painted the house last year.’ (47) (Baba bought a car last year) (Har) Baba (har) salko bano (har’i) mano (har’i). even Baba even build.pfv house even last.year even ‘Baba even built a house last year.’ (48) (Kule made many changes to his house last year) *Kule shuɗanta har’i bano=s mano. Kule paint.pfv even house=def.det.f last.year (intended:) ‘Kule even painted the house last year.’

(VP)

(V)

Har(’i) was considered to be marginal in sentences in which it associates with =i/ye marked focus. Examples (49)–(51) show the grammatical but only marginally felicitous possible positions for har(’i) in canonical word order with =i/ye marking – there are no subject examples, since the =i/ye marker is ungrammatical sentence-initially, and thus cannot precede the subject in canonical word order. (49) (Kule built many things last year) (DO) (?Har) Kule (?har) salko=i (?har) bano (?har’i) mano even Kule even build.pfv=bm even house even last.year (?har’i). even ‘Kule even built a house last year.’ (50) (Mammadi gave a watch to many people yesterday) (IO) ? ? ? ? ( Har) Mammadi ( har) onko agoggo=i ( har) ki Abu ( har’i) even Mammadi even give.pfv watch=bm even to Abu even nzono (?har’i). yesterday even ‘Kule even gave a watch to Abu yesterday.’ (51) (Kule built houses in many places last year.) (ADV) (?Har) Kule (?har) salko bano=i (?har) a Potiskum (?har’i) even Kule even build.pfv house=bm even at Potiskum even

the scalar particle har’i in ngamo (west chadic)

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mano (?har’i). last.year even ‘Kule even built a house in Potiskum last year.’ Examples (52)–(55) show the (marginally) possible positions for non-canonical word order. (52) (Many people built a house last year) (Subj) ? ? ? ? a. ( Har) salko bano=i ( har) Kule ( har’i) mano ( har’i). even build.pfv house=bm even Kule even last.year even b. (?Har) salko bano mano=i (?har) Kule (?har’i). even build.pfv house last.year=bm even Kule even ‘Even Kule built a house last year.’ (53) (Kule built many things last year) (DO) ? ? ? ? ( Har) Kule ( har) salko mano=i ( har) bano ( har’i). even Kule even build.pfv last.year=bm even house even ‘Kule even built a house last year.’ (54) (Mammadi gave a watch to many people yesterday) (IO) ? ? ? ( Har) Mammadi ( har) onko agoggo nzono=i ( har) ki even Mammadi even give.pfv watch yesterday=bm even to Abu (?har’i). Abu even ‘Mammadi even gave a watch to Abu yesterday.’ (55) (Kule built houses in many places last year.) (ADV) (?Har) Kule (?har) salko bano mano=i (?har) a Potiskum even Kule even build.pfv house last.year=bm even at Potiskum (?har’i). even ‘Kule even built a house in Potiskum last year.’ Association with focus in marked constructions is thus dispreferred, although it isn’t as consistently rejected as would be predicted for semantically exhaustive constructions. As section 3 showed, =i/ye constructions merely have an exhaustivity implicature, they are not semantically exhaustive. The non-occurrence of har(’i) in this construction is thus a puzzle.22 22

In Grubic (2015a), I argue for the additive particle ke(’e) that its infelicity in =i/ye construc-

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To sum up, this section has shown that har(’i) can either associate from a distance or be adjacent to its associate, and it can follow or precede the associate. In the following discussion, I will assume that both har and har’i can adjoin to the TP (e.g. when sentence-initial or -final and associating from a distance), to the VP (e.g. har immediately following the subject), or to NPs/DPs (e.g. har’i immediately following the subject, or har immediately preceding the direct object). 4.2 The Meaning Contribution of Sentences with har(’i) A har(’i)-sentence like (56) has at least the following entailments: the prejacent, i.e. the sentence without the particle, an additive meaning component, and a scalar meaning component. Following the literature on even in English, the former is predicted to be asserted, whereas the two latter entailments are predicted to be projective. In the following, it is however shown that only the scalar component survives embedding in a nonveridical context, leading to the conclusion that har(’i) is scalar, but not obligatorily additive. In section 4.4, the additive inference of the particle har(’i) is analyzed as arising only when the alternatives are ranked on a special scale, similar to the prejacent inference of only (cf. Beaver & Clark (2008)). (56) Har Dimza salko bano. → Dimza built a house → Other people built a house → It is surprising that Dimza built a house

(prejacent) (additive) (scalar)

In nonveridical contexts like (57) and (58), it can be seen that the prejacent, as predicted by its status as an asserted meaning component, does not survive. The scalar meaning component however survives, cf. (58). The additive inference however doesn’t survive (57)–(58). Its negation also does not follow, suggesting that this is not an asserted meaning component, but rather that sentences like Kule har salko bano are not obligatorily additive. (57) A bo ndalti=no ka na Kule har salko bano. at mouth wish(?)=1sg.poss comp.irr Kule even build.pfv house ‘I wish that Kule had even built a house.’ tions is due to the fact that the =i/ye-marked background is anaphoric: it needs to be about the same situation as its antecedent, which clashes with the meaning of the additive particle, which requires the situation to be different. For har(’i), no such meaning is assumed, which makes it unclear why it should be infelicitous in such contexts.

the scalar particle har’i in ngamo (west chadic)

65

→ Kule didn’t build a house. ↛ He built other things (Comment: not necessary that he built other things) (58) Ka na Kule har salko bano, ka Njelu ina kuyu. If.irr Kule even build.pfv house irr Njelu do.sbjv happiness ‘If Kule had even built a house, Njelu would have been happy.’ → Kule didn’t build the house ↛ He built other things → Building a house is something important/difficult (Comment: Maybe he built other things, maybe he didn’t build other things.) Testing for projection in negative sentences was complicated by the fact that har doesn’t seem to take scope below the negation. Thus (59) means “Even Dimza didn’t build a house”, rather than “Not even Dimza built a house”.23 (59) Har Dimza salko bano bu. → Dimza didn’t build a house → Others didn’t build a house → It is surprising that Dimza didn’t build a house

23

Har seems to be what Gast & van der Auwera (2011) call a beyond operator: it does not occur in scale-reversing contexts, i.e. contexts where the associate of the particle is considered to be more likely than its alternatives, rather than less likely, cf. (i). Instead, the har-sentences in (i) were accepted in the context in (ii), which doesn’t involve scale reversal. (i) (Jajam is grandmother’s favorite grandson. So she thought that at least he would visit her, but he didn’t come, just like the other grandchildren.) a. Ne nda ka la lei/#har Jajam a ndutu ba. 1sg want comp.irr dub even Jajam 3sg.sbjv go.sbjv.vent indeed ‘I wish at least Jajam had come.’ b. Ka la na lei/#har Jajam na ndino=i, ka dikati ka irr dub if even Jajam if go.pfv.vent=i irr grandmother irr a ina kuyu. 3sg.fut do.fut happiness ‘If at least Jajam had come, the grandmother would have been happy.’ (ii) Jajam lives in New Zealand, he rarely comes to Nigeria anymore. Grandmother invited him, but didn’t expect him to come – and he really didn’t come, the flight was too expensive.

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4.2.1 The Nature of the Scale Like only, English even can associate with entailment scales as well as scales leading to a rank-order reading. With rank-order readings, even is not additive anymore, cf. e.g. (60), in contrast to the parallel example with additive too/also. Wagner (2014) suggests for English that there are two even operators: a nonadditive one attached to the VP, and an additive one when attached to an NP. (60) (Susan is a master student.) Mary is even/#also a Ph.D. student. In Ngamo, these kinds of non-additive readings seem to be available, too, cf. (61)–(62). (61) Abu la makaranta, Bah me (har) malum (har’i). Abu child school Bah but even teacher even ‘Abu is a student, Bah is even a teacher.’ (Consultant comment: Bah is not a student. Can be used e.g. if they are age-mates, and Bah went to school earlier, but Abu is just starting now.) (62) Kule kaja mato, Gizo har salko bano. Kule buy.pfv car Gizo even build.pfv house ‘Kule bought a car, Gizo even built a house.’ (Consultant comment: har refers to building a house: it is more difficult to build a house. Does not indicate whether other people built a house.) The evaluative readings of har(’i) will be analyzed, on a par with the evaluative readings of only in English, as involving rank-order scales, while the additive readings involve entailment scales. Note that not all entailment scale examples lead to an additive reading. For example, har can associate with a universal quantifier, e.g. (63).24 This is predicted to be odd if the particle always has an additive presupposition, because the antecedent should be something that isn’t entailed by the current utter-

24

The scalar particle har(’i) often co-occurs with a further particle ma(’i), e.g. (i), cf. also the section below on scale-reversing contexts. In Bura (Central Chadic), ma is an additive marker that marks the scope for the additive presupposition (Malte Zimmermann, p.c.). (i) Har Asabe ma esha ne’e. even Asabe prt call.pfv 1sg ‘Even Asabe called me.’ Unfortunately, I don’t have sufficient data to attempt an analysis of the Ngamo particle.

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ance. Nevertheless, the prejacent all of them came entails the alternative some of them came, i.e. the scale involved is an entailment scale. (63) (We invited Hadiza’s classmates, but expected that only some of them would come. We were wrong: all children came.) Har shapsu ma ndano! even all.of.them prt go.pfv.pl.vent ‘Even all of them came.’ To sum up, with har(’i), alternatives can be ranked on entailment scales, or on rank-order scales. Additive readings are a certain subtype of entailment scale examples, ones where the prejacent does not entail its antecedent, but the prejacent together with the antecedent entails the antecedent. 4.2.2 Placement on the Scale A further issue in the discussion of additive-scalar particles is whether the prejacent must always be the highest element on the scale (Fauconnier, 1976), or just high on a scale (Kay, 1990). Kay presents the following example (Kay, 1990, p. 89), suggesting that even is not required to mark an absolute endpoint of a scale, because the natural end of the scale in this case would be the finals, not the semi-finals. (64) Not only did Mary win her first round match, she even made it to the semi-finals. Schwenter (2003) and Schwenter & Vasishth (2001) show that some additivescalar particles mark such an absolute end of scale, whereas others are like even in that they can also mark relative ends of scales: (65), from Schwenter (2003, p. 127f.), shows that the associate of hasta needs to be the absolute endpoint of a scale (here: ‘finals’), whereas for incluso it is enough if it is higher on a scale than its alternatives. (65) (Did Marta win in the third round?) A: ¡Pues claro! ¡Incluso ganó la final/semifinal! A’: ¡Pues claro! ¡Hasta ganó la final/#semifinal! ‘Of course! She even won in the finals/semifinals!’

It seems, however, that it is not additive, since the particle also occurs in non-additive examples like example (63).

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Har is like English even in that its associate need not be an absolute endpoint on a scale, cf. (66). (66) (Lakka and Bomato are talking about Tida’s tennis tournament.) L: Did Tida win in the third round? B: O’o, har si tutkok yo nem ki tekteke=ni ma’i. yes even 3sg.m eat.pfv.tot rel near to end=3sg.m prt ‘Yes, he even won in the semifinals!’ This is also shown in example (67), based on a similar example in Schwenter (2003); Schwenter & Vasishth (2001): here, we can see that har can be used with an alternative that is not the endpoint on an absolute scale, because it is followed up with a further, even less likely alternative. (67) (Angito and Burba are talking about a wedding that Burba attended.) A: Did Nono come to the wedding? B: Nono yak’i bu, har Jajam ma ndino ke har Hasha Nono only neg even Jajam prt go.pfv.vent also even Hasha ma ndino. prt go.pfv.vent ‘Not only Nono, even Jajam came, and even Hasha came.’ To sum up, whereas har(’i) can interact with alternatives ordered on different kinds of scales, it does not require that the constituent it associates with is an absolute endpoint on the scale. 4.3 Conventional or Free Association with Focus Beaver & Clark (2008) propose a taxonomy of focus-sensitive operators, depending on their association behaviour. They propose that some focus-sensitive operators in English conventionally associate with focus, i.e. their interaction with focus is part of their lexical meaning. According to them, the English particles only, even, too are such conventionally associating operators (Beaver & Clark, 2008, §3). Beaver and Clark’s proposal for only and the corresponding proposal for even, discussed in section 2.2 above, therefore encode the focussensitivity of these particles in their lexical entry, by direct reference to the CQ. Other operators, e.g. quantificational adverbs like always, freely associate with focus. These operators contain a free variable which receives its value from the context. Beaver & Clark (2008, p. 52) explain that since such free variables pick up “recoverable material”, they tend to be sensitive to backgrounded material. Importantly, this is not obligatory: these operators can also associate with

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non-focused constituents. This section shows that har(’i), unlike even, does not conventionally associate with focus, and discusses whether an account of free association with focus is on the right track.25 In order to show this, the particle is compared to the conventionally focus-sensitive particle yak(’i) (= “only”). Yak(’i) can occur in the same syntactic positions as har(’i), i.e. sentenceinitially or -finally, following the subject, and immediately preceding or following the focused constituent. It can associate with focus independent of the presence or absence of the =i/ye marker, cf. (68)–(69). (68) (Kule wanted to build a house and a granary last year, but:) (DO) (Yak) Kule (yak) salko (yak) bano (yak’i) mano (yak’i). only Kule only build.pfv only house only last.year only ‘Kule only built a house last year.’ (69) (Kule wanted to build a house and a granary last year, but:) (DO) (Yak) Kule (yak) salko=i (yak) bano (yak’i) mano (yak’i). only Kule only build.pfv=bm only house only last.year only ‘Kule only built a house last year.’ Interestingly, it cannot associate with a preverbal subject, cf. (70),26 instead, the subject needs to be inverted to a position following the direct object (preceding or following any IO or adverbial), cf. (71).

25

26

A third class, according to Beaver and Clark, is the group of quasi-associating operators. Since this class, by definition, only contains non-veridical operators, and har(’i) is veridical, it will be ignored here. There is one exception: an immediately following yak’i can associate with a preverbal subject (i). However, as (ii) shows, the preverbal subject in these cases is not in its standard position, but topicalized. (i) (Context: Gambo and Abare were supposed to give a watch to Bah) Abare yak’i onko agoggo ki Bah. Abare only give.pfv watch to Bah ‘Only Abare gave a watch to Bah.’ (ii) (Context: Shuwa and I, we both wanted to build a house) a. Ne’e yak’i ne salko bano. 1sg.indep only 1sg.dep build.pfv house b. *Ne yak’i salko bano. 1sg.dep only build.pfv house ‘Only I built a house’ Malte Zimmermann (p.c.) pointed out to me that the German conventionally associating

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(70) (Context: Shuwa and Kule wanted to build houses.) (SBJ) (#Yak(’i)) Shuwa (#yak) salko (#yak(’i)) bano (#yak(’i)) mano only Shuwa only build.pfv only house only last.year (*yak/#yak’i). only (intended:) ‘Only Shuwa built a house last year.’ (71) (Kule and Shuwa wanted to build a house) (SBJ) a. (Yak) salko bano=i (yak) Kule (yak’i) mano (yak’i). only build.pfv house=bm only Kule only last.year only b. (Yak) salko bano mano=i (yak) Kule (yak’i). only build.pfv house last.year=bm only Kule only ‘Only Kule built a house last year.’ A comparison between yak(’i) and the quantificational adverbial lei ki tomiya (“always”) shows exactly the same contrast between them as Beaver and Clark found between only and always.27 For example, yak(’i), like only, cannot associate with a topicalized constituent, while always and lei ki tomiya can, cf. (72) (from Beaver & Clark, 2008, p. 165) and (73). (72) a. Fishsticks, I believe Kim always buys. (Can mean: I believe that whenever Kim buys something, she buys fishsticks) b. Fishsticks, I believe Kim only buys. (Cannot mean: I believe that the only thing that Kim buys is fishsticks) (73) a. Hawwa=s, ne moishe Daho lei ki tomiya a Hawwa=def.det.f 1sg see.hab Daho always 3sg.hab esha. call.hab

27

particle nur can also associate with topics in certain restricted cases, e.g. Alle Kinder jokes like (iii), where the hanging topic mein Enkel is taken up by a resumptive pronoun. (iii) Alle Kinder haben Ohren, nur mein Enkel, der hat Henkel. all children have ears only my grandson 3sg has handles ‘All children have ears, only my grandson, he has handles.’ The question of why yak’i can occur in these examples cannot be solved here, and is left for further research. Further examples of this kind are left out for reasons of space. For the full set of tests showing that yak(’i) behaves like only in English in that it conventionally associates with focus, see Grubic (2015a, §6.2).

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‘Hawwa, I think Daho always calls (nobody else).’ (Can mean: I think that whenever Daho calls somebody, she calls Hawwa) b. Hawwa=s, ne moishe Daho a esha Hawwa=def.det.f 1sg see.hab Daho 3sg.hab call.hab=bm yak’i. 3sg.f only ‘Hawwa, I think Daho only calls (she doesn’t do anything else).’ (Cannot mean: I think that the only person that Daho calls is Hawwa) Since yak(’i) thus conventionally associates with focus, the fact that it cannot associate with a preverbal subject confirms Schuh (2005)’s observation that focused subjects invert in Ngamo, while focused non-subjects can stay in their canonical position. Therefore, the ease with which har(’i) associates with preverbal subjects is a first indication that har(’i) does not conventionally associate with focus. Further evidence that har(’i) is not a conventionally associating particle comes from association with unfocusable pronouns (cf. Krifka, 1998; von Fintel, 2004, i.a. for this test). In English, it is such a pronoun (74) (Beaver & Clark, 2008, p. 151): (74) Sally likes only him/*it. In Ngamo, nominal indirect objects follow direct objects (75a). Pronominal IOs, however, are incorporated into the verb (75b), and thus precede direct objects. Emphasized pronominal IOs are however not incorporated, but appear within a PP following the DO (76). (75) a. Tamko ne’e ki Gaboye. show.pfv 1sg.indep to Gaboye ‘(She) showed me to Gaboye.’ b. Tam=ni te. show.pfv.3sg.m.dep 3sg.f.indep ‘(s)he showed her to him.’ (76) A: B:

(Why are you wearing this watch? Kule gave it to your son!) A’a, onko=i ki ne’e. no give.pfv=bm to 1sg ‘No! He gave it to me!’

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B’:

A’a, ono. no, give.pfv.1sg ‘No! He gave it to me!’ (Consultant comment: [B] emphasizes that definitely, the watch was given to him)

The conventionally associating particle yak(’i) cannot associate with dependent, incorporated pronouns, cf. (77). It can however associate with the corresponding IO-PP, cf. (78). (77) Q: A:

Did Kule give a watch to Dimza and Jajei? O’o, Kule (#yak) onto (*yak’i) agoggo (#yak’i). No Kule only give.pfv.3sg.f only watch only (intended:) ‘No, Kule only gave a watch to her.’ (Consultant comment for the #-marked examples: ‘Jajei is expecting a watch and other things’ [i.e. association with the DO])

(78) Q: A:

Did Kule give a watch to Dimza and Jajei? O’o, Kule (?yak) onko agoggo=i ki te (?yak’i). No Kule only give.pfv watch=bm to 3sg.f only ‘No, Kule only gave a watch to her.’ (Consultant comment: difficult to tell who ‘te’ refers to, it is better if there is intermediate discussion about Jajei.)

In contrast, har(’i) can associate with incorporated IOs (79). (79) Kule onko agoggo=i ki Shuwa, ke har ono. Kule give.pfv watch=bm to Shuwa and even give.pfv.1sg.dep ‘Kule gave a watch to Shuwa, and he even gave (one) to me.’ This indicates that, in contrast to the exclusive particle yak(’i), and in contrast to its English counterpart even, har(’i) is not semantically restricted to associate with focus. According to the taxonomy proposed by Beaver and Clark, it would thus be classified as a freely associating operator. The following section will present an analysis of har(’i), including whether it should be analysed as a freely associating operator. 4.4 The Analysis of har(’i) as even In this section, I will argue that har(’i) is inherently scalar, presupposing that a (contextual) implication of the utterance is ranked high on a salient scale.

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Additivity is not a part of the meaning of har(’i), but arises in special entailment scale cases. In the following, first the notion of contextual implication is discussed, then the proposal for the core meaning of har(’i) is presented. I will argue here, following Gast & van der Auwera (2011)’s analysis of even, that for har’i, it is often the relation between a contextual implication of the utterance and its alternatives that plays a role. A contextual implication of an utterance is an entailment of the utterance together with its context (Wilson & Sperber, 2004; Gast & van der Auwera, 2011), i.e. it follows from the Common Ground as soon as it is updated with the new utterance’s assertion and presupposition. Assume, for example, that Kule built a shed and a barn is in the CG, and that somebody utters (80). After (80) is added to the CG, it follows from the CG that Kule built a house, a shed, and a barn. I will assume that in the additive reading of (80), it presupposes a scale as in (81), with this contextual implication of the utterance ranking higher on an entailment scale than its alternative(s). Here, only one alternative is important: the alternative that was in the CG before. The mirative meaning component is modeled by assuming that the true alternative is at the endpoint of the range of alternatives considered. This yields the interpretation that the true alternative is unexpectedly strong compared to its alternative(s).28 (80) Kule har salko bano. Kule even build.pfv house ‘Kule even built a house.’ (81)

The scale can however also be rank order scale. Then example 80 is not additive, i.e. it does not follow that Kule built other things. Instead, there is just an evaluative component, that building a house is in some way more impressive, or costly, or complicated, than building something else. The corresponding scale is just like the rank order scales for only, with the difference that the prejacent (or a contextual implication of it) is ranked high on the scale, cf. e.g. (82). Note that Gast & van der Auwera (2011) assume only entailment scales for English even, i.e. they would assume the scale in (83) for the evaluative use. However, 28

Again, as in the case of only discussed in section 2.2 above, it might be of advantage to separate the mirative meaning component from the endpoint-marking, to introduce a separate requirement that this alternative is stronger than expected.

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since the range of possible scales seems very similar to the scales assumed for only in Beaver & Clark (2008)’s account, which are not all entailment scales, I do not adopt their assumption. (82)

(83) How important was the building that Kule built?

Har(’i) is proposed to be a scalar particle with the core meaning in (84):29 A sentence with har(’i) asserts the prejacent, and presupposes that an implication or contextual implication of the prejacent is ranked high on a salient scale. I define a notion (C-)impl (85), a relation which holds between two propositions q and p, iff q follows from the Common Ground after it was updated with p.30 This relation also holds between q and p when p directly entails q, allowing e.g. for cases in which it is the prejacent itself that ranks high on a salient scale, and thus q = p, as e.g. in (82). (84) ⟦har(’i)TP⟧ = λp.λw: ∃q[(C-)impl(q)(p) ∧ ∀q’ ∈ ALT(q) [q’(w) → q ≥ q’]. p(w) (85) (C-)impl = λq⟨s,t⟩ .λp⟨s,t⟩ .[CG ↛ q & [CG ∪ {p}] → q]

Har(’i), like even under the standard view, does not contribute anything to the truth-conditional meaning of the sentence.31 With respect to its non-truthcon29

30

31

The presupposition of har(’i) is very similar to the max component above. If har(’i) were conventionally focus-sensitive (as Beaver & Clark (2008) suggest for English even) and would always presuppose a ranking of the prejacent on a salient scale, this would be equivalent to (i), cf. the proposal in §2.2 above. (i) λp.λw: max S(p)(w). p(w) The proposition q is assumed to follow from the set of propositions CG (the set of propositions mutually know to the discourse participants) iff q is true in all worlds in which all propositions in the CG are true (cf. logical consequence, Kratzer, 1981, p. 43), i.e. if q is true in all worlds in the context set. Schwarz (2005) assumes an analysis for einmal/auch nur, i.e. the two kinds of German NPI

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ditional meaning component, the account here however differs from other proposals for additive-scalar particles in several ways. First, it differs from most accounts (e.g. Horn 1969, Karttunen & Peters 1979, Rooth 1985, König 1991, Wilkinson 1996, Schwenter & Vasishth 2001, i.a.) in the fact that it doesn’t assume an additive meaning component. In this respect, it thus follows Fauconnier (1975, 1976); Krifka (1992); Rullmann (1997); Gast & van der Auwera (2011), who do not assume an additive meaning component for even.32 Second, the account presented here does not assume a fixed kind of scale, i.e. neither a scale of likelihood, as assumed e.g. in Karttunen & Peters (1979), nor an entailment scale, as assumed e.g. in Fauconnier (1976); Kay (1990). Rather, like with only in Beaver & Clark (2008)’s account, the scale can either be a rankorder or an entailment scale. Third, following Gast & van der Auwera (2011), it is not the prejacent but its (contextual) implication that ranks high. This has the advantage of allowing for a semantic entailment scales like (81) rather than resorting to rules which state that ‘Kule built a house’ entails its lower-ranked alternatives, e.g. ‘Kule built a barn’.33 The current theory seems empirically adequate, because in scales like (81), where the highest-ranking alternative is an actual contextual implication of the prejacent, the example needs Kule built a shed and a barn to be in the CG. In the scale in (82), where the highest-ranking alternative is the prejacent itself, there is no such requirement on the context. The two different kinds of scales also explain why in scales like (81), the lower-ranked alternatives are true, whereas in scales like (82), the lower-ranked alternatives are false. Fourth, with respect to the question of whether the highest-ranking alternative needs to be a scalar end-point, as suggested in Fauconnier (1976), and dismissed for even by e.g. Kay (1990); Schwenter & Vasishth (2001); Schwenter (2003), this analysis again borrows heavily from the analysis of only in Beaver &

32

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even, under which they have a truth-conditional effect that the particle sogar, which can occur in positive contexts, does not have: they entail that the other considered alternatives are false. He notes that, as far as he knows, there is only one other account, namely Lycan (1991), which proposes a truth-conditional impact of additive-scalar particles (Schwarz, 2005, p. 127). A reviewer pointed out to me that this analysis predicts that a har’i sentence like (80) can directly answer a wh-question like What did Kule build?. This is indeed the prediction I make, as long as this answer or a contextual entailment of it is an unexpectedly strong answer to the question. Unfortunately, I do not have the data yet to show that this is the case. As formulated in Kay (1990, p. 64) and, implicitly, in Fauconnier (1975, p. 361).

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Clark (2008): it assumes that it outranks all considered alternatives, but not necessarily all possible alternatives. This means that the set of alternatives yielded by alt in (84) is constrained at least by relevance and expectability. Fifth, due to the fact that har(’i) does not associate with focus conventionally (Beaver & Clark, 2008), the alternatives referred to in the lexical entry for har(’i) above need not be the focus alternatives – they can be any salient alternatives. This will be discussed in the next section. Since har(’i) can take VP or NP complements, it is necessary to formulate lexical entries for VP- and NP-har(’i), cf. (86)–(87), which are arrived at via the Geach rule (Coppock & Beaver, 2013). While the VP-variant can associate with the subject (see footnote 21 above), the NP-variant seems to only associate with its NP argument. For this reason, following Coppock & Beaver (2013)’s similar constraints for exclusives, an additional presupposition constraining the kinds of admissible alternatives is added in (87): it requires the alternatives to differ with respect to the quantificational NP argument.34 (86) ⟦har(’i)VP⟧S = λP⟨e,⟨s,t⟩⟩ .λx.⟦har(’i)TP⟧ (P(x))

(87) ⟦har(’i)NP⟧S = λQ⟨⟨e,⟨s,t⟩⟩,⟨s,t⟩⟩ .λP⟨e,⟨s,t⟩⟩ .⟦har(’i)TP⟧ (Q(P)), defined iff ALT = ?Q[Q(P)] This leads to the desireable result that the following three sentences, with har(’i) at different positions, receive the same denotation. During the derivation of a sentence with harVP or harNP, there is an intermediate step at which harTP is applied to the prejacent (marked in bold font in (88)–(89)). The result is therefore the same as in the harTP-example in (90). (88) ⟦Kule har salko bano⟧ = ⟦harVP⟧ (⟦salko bano⟧)(⟦Kule⟧) = [λP⟨e,⟨s,t⟩⟩ .λx.⟦har(’i)TP⟧ (P(x))] (λx.λw.x built a house in w) (Kule) = ⟦har(’i)TP⟧ (λw.Kule built a house in w) (89) ⟦[har bano] 1 Kule salko t1⟧g = ⟦harNP⟧ (⟦bano⟧)(⟦1 Kule salko t1⟧g) = [λQ⟨⟨e,⟨s,t⟩⟩,⟨s,t⟩⟩ .λP⟨e,⟨s,t⟩⟩ .⟦har(’i)TP⟧ (Q(P))] (λR.λw.∃x[house(x)(w) & R(x)(w)]) (λx.λw.Kule built x in w) = ⟦har(’i)TP⟧ (λR.λw.∃x[house(x)(w) & R(x)(w)](λx.λw.Kule built x in w)) 34

In Coppock & Beaver (2013), this is a requirement on the current QUD, but since har(’i) is not conventionally focus-sensitive, this is formulated as a requirement on the form of the scalar alternatives here, without requiring that these are focus alternatives and thus correspond to the current QUD.

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= ⟦har(’i)TP⟧ (λw.∃x[house(x)(w) & Kule built x in w]) ≈ ⟦har(’i)TP⟧ (λw.Kule built a house in w) (90) ⟦Har Kule salko bano⟧ = ⟦harTP⟧ (⟦Kule salko bano⟧) = [λp.λw: ∃q[(C-)impl(q)(p) ∧ ∀q’ ∈ ALT(q) [q’(w) → q ≥ q’].p(w)] (λw’.Kule built a house in w’) = λw.Kule built a house in w defined iff ∃q[(C-)impl(q)(λw.Kule built a house in w) ∧ ∀q’ ∈ ALT(q) [q’(w) → q ≥ q’] In (81) and (82) above, two common kinds of scales for even examples were presented: entailment scales and ranking scales. While I believe that additive har(’i)-examples always involve entailment scales, there are entailment scales that do not involve additivity. For example, (91) is not additive, i.e. it does not presuppose that anybody else came apart from all of the classmates. Nevertheless, the strongest true alternative (All of them came) entails the expected alternative(s) (e.g. Some of them came), so that the scalar strength would be entailment. (91) (We invited Hadiza’s classmates, but expected that only some of them would come. We were wrong: all children came.) Har shapsu ma ndano! even all.of.them prt go.pfv.pl.vent ‘Even all of them came.’ A further kind of example are those cited in the literature which aim to show that alternatives are not ranked on a scale of unexpectedness, e.g. (92) from Fauconnier (1976). Fauconnier observes that (92) can be felicitously uttered even if George’s drinking of armagnac is not more surprising than his drinking of rum, the French particle même (= “even”) just marks that the sum or range of drinks that George had was surprisingly large.35 The same was found for Ngamo, cf. example (93). I assume for this case, following Kay (1990, p. 72), that the relevant proposition ranked high on the salient scale is the whole sentence, and that the considered lower-ranking alternatives are ones in which Nono ate less, e.g. Nono ate goat meat, sheep meat, and cow meat.36 35 36

Kay (1990) seems to suggest that the same holds for the English translation. A reviewer pointed out to me that the question of how to treat these examples depends on their syntactic analysis: if these examples involve elided sentences rather than NP conjuncts, they would be exactly like example 80.

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(92) Georges a bu un peu de vin, un peu de cognac, un peu de rhum, un peu de calva, et même un peu d’armagnac. ‘George drank a little wine, a little brandy, a little rum, a little calvados, and even a little armagnac.’ (93) (Nono ate a lot yesterday.) Ha’akok lu oshi, lu temshi, lu kom, kerwo, har ki eat.pfv.tot meat goat meat sheep meat cow fish even with lu yabi. meat chicken ‘She ate goat meat, sheep meat, cow meat, fish, and even chicken.’ (Comment: not surprising that she is eating chicken, it just means that it is additional, in addition to the other things that she ate) Examples (91) and (93) are thus examples where the salient scale is an entailment scale, but there is no additive meaning component: the prejacent itself ranks high on the scale and entails its alternatives, no additional information from the context is needed, only the host sentence itself. The following section briefly discusses the association behaviour of har(’i). 4.5 Free Association with Focus? In Beaver & Clark’s QUD-account of only and their discussion of even and too, these particles are assumed to conventionally associate with focus because they provide a comment on the CQ. Only indicates that the strongest true answer to the CQ is surprisingly weak, while even indicates that it is surprisingly strong (Beaver & Clark, 2008, p. 71). Also, too and other additive particles indicate that the CQ has been partially answered before (Beaver & Clark 2008, p. 73, Zeevat 2014, p. 84). In the discussion above, it has been assumed that har(’i) resembles even in that it relates to one or several weaker alternatives. Recall however that har(’i) does not conventionally associate with focus (cf. §4.3). This subsection briefly discusses different kinds of non-conventional association with focus. In Beaver & Clark’s taxonomy, har(’i), since it is a veridical operator, but does not obligatorily associate with focus, would be classified as a freely associating operator. These are operators which introduce a free variable which receives its value from the context. As Beaver & Clark (2008, p. 52) write, the connection with focus is indirect: the free variable and the backgrounded material interact since they are both in some sense anaphoric. I want to argue here that there are however at least two further options for alternative-sensitive particle which do not conventionally associate with

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focus. For example, German stressed auch was proposed to associate with contrastive topics in Krifka (1998), who cites Altmann (1976); Jacobs (1983); Koktová (1987) for similar observations. Contrastive topics are marked by a rise in German, and indicate a whole strategy rather than merely a CQ with a multiple wh-superquestion, split up in subquestions (Büring, 2003). For example, in (94) (from Krifka, 1998), a strategy as in (95) is indicated. Stressed auch then indicates that the focused constituent is non-distinct in the two answers. German auch is thus assumed to be ambiguous between a unstressed variant which (conventionally) associates with focus, and a stressed variant which associates with contrastive topics. (94) I know that Pia visited the exhibition. But what did Peter do? Péter hat die Ausstellung àuch besucht. ‘Péter visited the exhibition, tòo.’ (95)

In addition, there are additive particles like ke(’e) in Ngamo (Grubic, 2015a) and dA in Turkish (Göksel & Özsoy, 2003), which can connect answers to two adjacent, related QUD s in which the focus is not the same, cf. (96) for an Ngamo example and (97) for Turkish (Göksel & Özsoy, 2003, pp. 1160–1161).37 (96) Q: A:

What did Kule and Hawwa do? Hawwa kaja mato, Kule ke salko bano. Hawwa buy.pfv car Kule also build.pfv house ‘Hawwa bought a car, and Kule built a house.’

(97) Deniz tiyatro-ya git-ti. Ahmet de arkadaş-lar-ı-yla Deniz theatre-dat go-p Ahmet dA friend-pl-3sg.poss-com sinema-ya git-ti. cinema-dat go-p ‘Deniz has gone to the theatre. And Ahmet, (he) went to the cinema with his friends.’

37

In several languages, the additive particle can also be used as a sentence connector. König (1991, p. 65) mentions Latin et, Greek kaí, Russian i, Norwegian og(så), Lezgian -ni, Manam -be, Zulu na-, Sesotho le, and Malayalam -um.

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For ke(’e) in Ngamo, there is evidence that it requires that the sentences which it connects are answers to different QUD s, i.e. they may not be partial answers to the same QUD. For example, the focus can be identical in both sentences, but the background must differ (98)–(99). The comment in (99) suggests that the respective QUD s must at least be asked about different situations or times. (98) Salko bano=i Kule, kaja mato=i ke Kule. build.pfv house=bm Kule buy.pfv car=bm also Kule ‘Kule built a house, and Kule also bought a car.’ (99) ??Salko bano=i Hawwa, (ke) salko bano=i (ke) Kule. build.pfv house=bm Hawwa also build.pfv house=bm also Kule (intended:) ‘Hawwa built a house, and Kule also built a house.’ (Comment: this is possible if it means ‘it is Hawwa that built the house and then Kule built a house’, not at the same time.) This means that whereas the lexical entry of ke(’e) does make reference to the CQ, it requires the CQ to be different instead of the same. Even though there is this interaction with the CQ, this particle does not conventionally associate with focus. This is thus a further way in which particles can associate with alternatives without being conventionally focus-sensitive. A further possibility would be that the relevant alternatives are provided by a secondary QUD. Some more complex focus examples seem to involve additional sets of alternatives apart from the CQ, which can be formalized as secondary QUD s. This certainly includes cases where QUD s appear to be nested, so that the full answer to an overt QUD also fully answers an implicit QUD, cf. (100) (from Kadmon & Sevi (2011, p. 7/p. 37), cf. also the discussion of this example in Büring, this volume). In this example, there is one set of alternatives corresponding to the possible answers to the overt QUD, and another set of alternatives with which only interacts: possible answers to the QUD “Who does granny’s dog like?”. (100) Q: A:

What’s peculiar about granny’s dog? She only likes John.

In addition, supplemental QUD s are assumed e.g. in Riester & Baumann (2013) for foci within not-at-issue parts of the utterance (see also Onea & Zimmermann 2019, §1.4.4), e.g. in appositives. It might be that any conventionally scalar element obligatorily introduces alternatives – which might be modelled as supplemental or secondary QUD s – in order to generate the scalar alternatives,

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without necessarily requiring these alternatives to be congruent to the CQ. This is, tentatively, the approach chosen here. To sum up, this section showed that har(’i), in its reading as even, takes propositional, VP- or NP-complements, and introduces a presupposition that a (contextual) implication of the prejacent is ranked high on a salient scale, compared with its alternative(s). Har’i is not inherently additive. In contrast to even, har(’i) is not conventionally focus-sensitive. This final subsection discussed ways in which particles can non-conventionally associate with focus. In the following, a further use of VP-har(’i) is presented, which uses special kinds of scales on which alternatives are aligned e.g. with times.

5

Other Uses of har(’i)

This section briefly presents a description and analysis of three further uses of har(’i), which are analyzed as scalar, too. The first use, as already, receives a scalar analysis following Krifka (2000)’s analysis of schon in German. The other two uses, until and as far as, are not commonly assumed to be scalar (but cf. Grubic 2012a,b for a scalar analysis of kapa (= ‘even’, ‘until’, ‘as far as’) in Ngizim). 5.1 Har(’i) as already Har(’i) can be used as already, cf. (101)–(102).38 (101) Ba’ano sanito (har) baɗ (har’i). my.daughter age.her already five already ‘My daughter is already five years old.’ (102) Kule (har) a ka monsom (har’i). Kule already 3sg ipfv sleep already ‘Kule is already sleeping.’ (Comment: you are expecting him not to be asleep, it is too early for him to sleep)

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Note that har was also used together with the temporal adverbial kaiso (= ‘now’) to mean still – this will however be treated as an instance of the usual scalar ‘even’ use. (i) Kule har kaiso a monsom. Kule even now 3sg sleep ‘Kule is still sleeping.’

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Har was not accepted as already in negative sentences, compare (103) to (104). In counterfactual contexts, however, it is visible that the mirative meaning component (“surprisingly early”) survives, cf. (105). (103) (We were expecting rain in the evening, but it started raining now, in the afternoon.) Har a ka ham ndeyi. already 3sg.ipfv ipfv water God ‘It is already raining.’ (104) (We are expecting rain in the evening. Now, it is afternoon and isn’t raining.) #Har a ka ham ndeyi bu. already 3sg.ipfv ipfv water God neg (intended:) ‘It is not yet raining.’ (Consultant comment: This means ‘it was not even raining’. You have to say instead ‘Dongo a ham ndeyi bu.’ [Dongo = not yet, according to Schuh et al. (2009, p. 23)]39) (105) Ka na har a ham ndeyi, ka ne komɗinno. if.irr already 3sg water God irr 1sg get.wet.icp (offered translation:) ‘If it were raining (earlier than expected), I would get wet.’ To sum up, har(’i) can receive an interpretation as already, indicating that the event described takes place earlier than expected. In section 4.4, this will be analyzed as a further scalar use of har(’i), with the difference that the alternatives are ordered on a temporal scale (Krifka, 2000). 5.1.1 The Analysis of har(’i) as already Krifka (2000)’s focus-sensitive analysis of German schon (= “already”) is adopted and adapted,40 in order to formulate a unified analysis for the different uses of har(’i). Krifka proposes that schon is a focus-sensitive operator which triggers the presupposition that all other considered alternatives are ranked lower on a salient scale than the expressed alternative. For examples similar to 39

40

An anonymous reviewer pointed that this translation cannot be entirely accurate in this example, since the example contains a negation, and suggested that dongo may just mean “yet”. Thanks to Anne Mucha (p.c.) for pointing out the relevance of this paper to me.

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(106), Krifka notes that the salient scale is as in (107). Like in the proposal for the even readings above, this ranking accounts for the mirative meaning component, i.e. the inference that a lower-ranked alternative was expected to be true. (106) Ba’ano sanito (har) baɗ (har’i). my.daughter age.her already five already ‘My daughter is already five years old.’ (107)

There are two differences between Krifka’s account and the one used here for har(’i): First, Krifka assumes that the focused constituent and its alternatives are ranked on a salient scale, rather than propositions, as the har(’i) account suggests. Second, Krifka adopts the suggestion of Löbner (1989); Michaelis (1996) that the mirative component, e.g. the inference that in (106) that five years is older than expected, is a conversational implicature. In the account I assume for har(’i), the mirative meaning follows from the fact that the true alternative is on the border of the range of considered alternatives. The mirative component is thus predicted to be projective, and non-cancellable. The corresponding German examples with schon (= ‘already’) are already acknowledged in the literature as focus-sensitive uses (Löbner, 1989, p. 184, i.a.). Krifka however proposes that examples like (108) are focus-sensitive too, with the focus being on the polarity of the sentence, and the alternatives thus being {p, ¬p}. These alternatives are temporally aligned, with the negative alternative preceding and thus being ranked lower than the positive alternative, cf. (109).41 (108) Kule (har) a ka monsom (har’i). Kule already 3sg ipfv sleep already ‘Kule is already sleeping.’

41

Krifka notes that Löbner (1999) also calls this type of schon a “sentence focus particle”.

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(109)

Like in other har(’i) uses, the higher-ranked alternatives, i.e. Kule’s sleep or awakeness at later times, are simply not considered. The lower-ranked alternative is considered, but is not the strongest true alternative. There is no requirement that the lower-ranked alternatives be true, i.e. (108) is compatible with contexts in which there was no previous interval of Kule being awake. Krifka notes that this is desireable in the light of examples like (110) (Mittwoch, 1993), where there is no previous interval of A’s husband not being an American citizen, cf. (111) for the same example in Ngamo. (110) A: B: A:

I’ve applied for American citizenship. Is your husband also applying? He is already American, for he was born in America.

(111) Asabe knows that Hadiza is applying for an American citizenship, and asks whether her husband is also applying. Hadiza answers: Si har ɗeinni ngoi Amurika – Si 3sg.m already sit(?).icp person=link America 3sg.m le’i=s Amurika. birth=def.det.f America ‘He is already American – he was born in America.’ (Comment: possible even if he had no other citizenship.) Krifka’s analysis also predicts something else: the expectation that the prejacent will hold at some later time (König, 1977; Ippolito, 2007). The alternatives in the examples discussed here are aligned on a temporal scale.42 For example, in (106), the age of the daughter is naturally aligned with time, since she is e.g. four before she is five. In (108), the two alternatives are also aligned with time, so that the alternative Kule isn’t sleeping is earlier than Kule is sleeping. When e.g. (108) is negated, the prejacent Kule is sleeping is negated. Because there are

42

There are other examples for German schon where the alternatives are aligned with something else than time, e.g. “degrees of membership or prototypicality” (Umbach, 2009, p. 6), e.g. (i) (from König (1977, p. 183)). Whether har(’i) is possible in these contexts was not conclusive. (i) Paul ist noch gemäßigt. Peter ist schon radikal. ‘Paul is still moderate. Peter is already radical.’

the scalar particle har’i in ngamo (west chadic)

85

only the two polar alternatives, we thus know that the other, more expected, alternative Kule isn’t sleeping is true. The presupposed scale in (109) with its temporal order Kule isn’t sleeping < Kule is sleeping however survives negation. The expectation that Kule will sleep sometime in the near future follows from this presupposed salient scale (cf. also Krifka’s discussion of not yet / noch nicht, the negated form of already/schon – he however analyses this expectation as an implicature). In the elicited examples, har(’i) always takes a VP complement, i.e. the VPhar(’i) defined above can be used.43 For instance, example (108) is calculated as follows, with q then being the prejacent Kule is sleeping, ranked higher on a salient scale than its alternative Kule isn’t sleeping. (112) ⟦Kule har a ka monsom⟧ = ⟦harVP⟧ (⟦a ka monsom⟧)(⟦Kule⟧) = [λP⟨e,⟨s,t⟩⟩ .λx.⟦har(’i)TP⟧ (P(x))] (λx.λw.x is sleeping in w) (Kule) = ⟦har(’i)TP⟧ (λw.Kule is sleeping in w) = [λp.λw: ∃q[(C-)impl(q)(p) ∧ ∀q’ ∈ ALT(q) [q’(w) → q ≥ q’].p(w)] (λw’.Kule is sleeping in w’) = λw.Kule is sleeping in w, defined iff ∃q[(C-)impl(q)(λw.Kule is sleeping in w) ∧ ∀q’ ∈ ALT(q) [q’(w) → q ≥ q’] To sum up, when har(’i)VP is used with an already reading, the only effect of har(’i) is a presupposition that a (contextual) implication of the prejacent ranks high on a salient scale. In the cases considered, the alternatives are aligned with times, so that lower-ranked alternatives are earlier alternatives. This presupposition yields two inferences which are also projective: (i) the mirative inference (“This is happening surprisingly early”), which is argued to be due to the endpoint position of the true alternative on the scale, and (ii) the future actualization inference (“This will hold at some future time”) that is visible especially in non-veridical contexts. The latter is due to the presupposed temporal alignment of alternatives, which reflects the expectations of the discourse participants, and is not found with any other scales,44 while the mirative inference is expected to occur with all uses of har(’i).

43

44

A reviewer asked whether my analysis predicts a double occurrence of har(’i), as already and even, to be redundant. I do not have such data, but I would predict this to be nonredundant, since it involves different scales: with hareven, the scale can be an entailment or rank-order scale, with haralready, the scale is temporal. For this reason, accounts that write this inference into the lexical entry of already as a

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5.2 Har(’i) as until and as far as In addition to its use as even, har(’i) can also be used as until or as far as.45 It expresses so-called durative until (Karttunen, 1974; De Swart, 1996; Giannakidou, 2002, 2003; Condoravdi, 2008), i.e. it is used in sentences describing a state or activity that continues until the point in time indicated by the until-phrase, and possibly even further. As the felicity of (113) in the context in (114) shows, the inference that the activity stops at the time indicated is just a conversational implicature, and does not arise in all contexts. (113) Nono fell asleep at around 11p.m. and woke up at midnight. Nono iko monsom har tintil beɗi. Nono do.pfv sleep until middle night ‘Nono slept until midnight.’ (114) Nono fell asleep at around 11p.m. When we left, at midnight, she was still sleeping. Possibly she slept the whole night. The fact that the state or activity need not ever end is evidence for the fact that this is a durative use of until: for example, (116) has the same meaning as (115), there is no inference that Njelu got married at or shortly after the time of his death. If this were the so-called punctual use of until, this inference would arise, and (116) would be odd, just as it is in the English translation of (116).

45

presupposition (e.g. König, 1977; Ippolito, 2007) need to assume something different for marginality uses of already, since there is no such inference in this case, cf. (i) and (ii). (i) Subcompact cars are already dangerous. → Subcompact cars will be dangerous in the future. (ii) If subcompact cars were already dangerous, I would buy a compact car. ↛ Subcompact cars will be dangerous in the future. Crosslinguistically, this seems to be relatively common. Gast & van der Auwera (2011) mention the following European languages in which an additive-scalar operator either means “until” or “as far as” in addition, or originates from an expression meaning “until” or “as far as”: Welsh hyd yn oed (“as far as, up or down to (and including), even”), Polish nawet (originally “as far as”), Spanish aun (originally “until” < Lat. adhuc), Spanish hasta, (“as far as”, “until”), Swedish till och med (“up to and including”, “until”), and Russian/Bulgarian daže (originally “until”). In their typology, these operators are either “universal” or “beyond”, meaning that they can either be used in all contexts, or are restricted to veridical/PPI contexts. In addition, there is Italian perfino (originally “until” according to Visconti (2005, p. 239)), and Greek mexri (durative “until”, can sometimes be used as “even”, cf. Giannakidou (2007, p. 46)); French jusqu’à, Romanian pîna si (“until”, “even”), Czech dokonce (“(up) to the end”), and Arabic hatta (“until, as far as, up to, even”), (König, 1991, pp. 165– 166). The latter is suggested to be the source of har in the languages of this region, e.g. by Ziegelmeyer (2008, p. 11), cf. also the discussion in Schuh & Gimba (In preparation, p. 16, in the chapter on quantifying and contrastive prepositions and conjunctions).

the scalar particle har’i in ngamo (west chadic)

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(115) Njelu ɗeiko sompor har matunni. Njelu stay.pfv bachelor until die.icp ‘Njelu remained a bachelor until he died.’ (116) Njelu iko mandu bu har matunni. Njelu do.pfv wife neg until die.icp ‘Njelu remained a bachelor until he died.’ (lit. ‘??Njelu didn’t marry until he died.’) There are two readings described in Condoravdi (2008) for the interaction between durative until and negation, both of which occur with har: (i) the notthroughout reading, under which the state or activity ends earlier than the time indicated by the until-phrase, and (ii) the throughout-not reading, under which there is no such state or activity within the considered interval. According to Condoravdi, the negation scopes above the until-phrase in the first case, and below it in the second. In Ngamo, this is confirmed by the different position of the negation, which only follows, and thus takes scope over, the adverbial in the first reading. (117) (Nono fell asleep at around 11p.m., but then woke up again at 11:43 and stayed awake for the rest of the night.) Nono iko monsom har tintil beɗi bu. Nono do.pfv sleep until middle night neg ‘Nono didn’t sleep until midnight.’ (not-throughout) (Consultant comment: Her sleeping didn’t reach up to midnight.) (118) (Nono went to bed at around 11p.m. and tried to sleep but couldn’t. When we left, at midnight, she was still trying to fall asleep. Perhaps she didn’t manage to sleep all night.) Nono iko monsom bu har tintil beɗi. Nono do.pfv sleep neg until middle night ‘Nono didn’t sleep until midnight.’ (throughout-not) Thus, whereas the har-sentence in (118) is also felicitous in a context where Nono didn’t sleep before midnight, and then fell asleep at midnight, which would license punctual until, it crucially is also felicitous in contexts like (118), which only allow for durative until. As (119) shows, har also has locative uses as as far as, used in sentences describing a motion towards and reaching a location specified by the harphrase.

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(119) Nono nduko har bo dumno, kai, har nduko hena. Nono go.pfv up.to opening door excl even go.pfv outside ‘Nono went as far as the door, in fact, she even went outside!’ Like in its until meaning, the inference that the motion stopped at the location contributed by the har-phrase is a conversational implicature, and can be cancelled. 5.2.1 Analysis of har(’i) as until/as far as I discuss these readings together, since they are very similar. In both cases, the particle acts as a preposition, taking either a nominal or a clausal complement. In the until example in (120), the relevant (contextual) implication is one where the state or durative eventuality expressed by the verb is indicated to hold from an implicit startpoint to the point indicated by the until-phrase. The alternatives ranked lower on a scale in this case are intervals with the same startpoint, but earlier ending times.46 The scale in these cases is an entailment scale, cf. (121). The alternatives to the (contextual) implication are all of the form ‘Nono slept from tstart to X’. Note that, again, stronger (i.e. later) alternatives are not truth-conditionally excluded, they are simply not considered. This means that (120) is compatible with a context where Nono slept longer, but not with a context in which she woke up before midnight. (120) Nono iko monsom har tintil beɗi. Nono do.pfv sleep until middle night ‘Nono slept until midnight.’ (121)

With the as far as interpretation, the considered alternatives are closer alternatives. For example, in (122), the alternatives are of the form ‘Nono went from lstart to X’, with the considered answers ranked on an entailment scale, cf. (123). (122) Nono nduko har bo dumno. Nono go.pfv up.to opening door ‘Nono went as far as the door.’ 46

See also a similar analysis for the particle kapa in Ngizim in Grubic (2012a,b).

the scalar particle har’i in ngamo (west chadic)

89

(123)

When the sentence is negated, there are two different interpretations, depending on whether the negation is inside or outside the scope of the har(’i)phrase.47 In (124a), the negation scopes higher than har(’i). I assume that the alternatives, in this case, are all positive (i.e. of the form Nono slept from tstart to X), and are ranked as assumed above. The effect of the negation is that the truth of the prejacent is negated, i.e. the strongest considered alternative is asserted to be false. Weaker, lower-ranking alternatives are still under consideration, leading to the inference that Nono slept up to a point in time preceding midnight. In (124b), the negation is in the scope of the until-phrase. I assume that here, the alternatives are of the form Nono didn’t sleep from tstart to x, for different x. (124) a. Nono iko monsom har tintil beɗi bu. Nono do.pfv sleep until middle night neg ‘Nono didn’t sleep until midnight.’ ≈ Nono slept from tstart to a time preceding midnight. (not-throughout) b. Nono iko monsom bu har tintil beɗi. Nono do.pfv sleep neg until middle night ‘Nono didn’t sleep until midnight.’ ≈ From tstart to midnight, Nono didn’t sleep. (throughout-not) To account for these uses of har(’i), it however appears that har(’i) needs to have a truth-conditional contribution as a preposition as well. A unified proposal, under which har(’i) would merely introduce a presupposition, would predict that a sentence like 120 and 122 would be felicitous without the particle har’i, albeit possibly with a different meaning (at instead of until). This was not tested for Ngamo, but there are very few examples of temporal and 47

In Ngamo, the scope of the negation is more transparent than in English. Condoravdi (2008) assumes the following scope for the different readings: (i) Nono didn’t sleep until midnight. a. Not-throughout: Past(Not((Until(12))(Nono-sleep))) b. Throughout-not: Past(Until(12)(Not(Nono-sleep)))

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locative adverbials without any prepositions in the available data, so I consider this very unlikely. Instead, I propose a different, but related, analysis of har’i in its until/as far as reading. Under this analysis, har’i is a preposition, with a truth-conditional meaning contribution. It takes two complements: one denoting a (temporal) interval or (locative) region, and one denoting a proposition, and states that the proposition holds for all subintervals or subregions from an implicit startpoint to the specified interval/region (125). This use of har(’i) is the most constrained: like the use of NP-har(’i) above, it places a requirement on the admissible alternatives. In addition, again following Coppock & Beaver (2013)’s account of exclusive particles, the fact that this adverbial use of har(’i) only occurs with entailment scales can be written into its lexical entry in form of a presupposition. (125) ⟦har(’i) Adv⟧ = λt.λQ⟨s,t⟩ .λw.⟦har(’i)TP⟧(λw.∀t’[tstart ≤ t’ ≤ t] at(Q(w),t’)) defined iff (i) and (ii) both hold: (i) entailment(≥). (Entailment scale requirement) (ii) alt ⊆?t[λw.∀t’[tstart ≤ t’ ≤ t] at(Q(w),t’)]] (alt ⊆ Until when did Q hold?) Har(’i) as until/as far as thus has a truth-conditional meaning contribution, but is also related to the other har’i uses above in being scalar, ranking a proposition (in this case the prejacent) high on a scale.

6

The Conclusion

To sum up, har(’i) can take TP, VP or NP complements, and presupposes that a (contextual) implication of the prejacent is the highest-ranking considered alternative on a salient scale. The alternatives often, but not necessarily, correspond to the alternatives in the CQ, i.e. the particle does not associate with focus conventionally. The admissable scales, like in the yak(’i) examples, seem to be entailment or rank-order scales. The scale is relative rather than absolute, in the terminology of Schwenter & Vasishth (2001); Schwenter (2003), i.e. the scale in principle allows for the existence of stronger alternatives, but they are not considered. The mirative meaning component of har(’i) is due to the fact that the (contextual) implication is on the borderline of the considered alternatives. The use of har(’i) as already shows that the scales can also be more complex: in these cases, VP-har(’i) is used, and the scales are alternatives aligned with times. Apart from this difference in scale, the same har(’i) meaning can

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the scalar particle har’i in ngamo (west chadic) table 2

Summary of har’i variants

Form

Cat.

har’iTP har’iVP har’iNP har’iCP/DP

TP VP NP CP/DP

Type of the complement

Question

Strength

⟨s, t⟩ – ⟨e, ⟨s, t⟩⟩ – ⟨⟨e, ⟨s, t⟩⟩, ⟨s, t⟩⟩ –

i/r

– – – Up to where/when does Q hold? entailment

be used in these cases. The available data does not show whether TP- and NPhar(’i) can associate with alternatives aligned on such scales. Finally, in the case of har(’i) as until/as far as, there is a further kind of complement that har(’i) takes, namely temporal intervals or locative regions. The relevant contextual implication is one where a state, durative eventuality or motion continues up to the endpoint indicated by the har(’i)-phrase. The other considered alternatives, in this case, are alternatives in which it continues up to an earlier or closer endpoint. The alternatives are ranked on an entailment scale, and seem to allow only for a certain kind of alternatives, namely those that answer until when? or up to when?-questions. The different har’i variants are summarized in table 2. Again, I assume that VP-, and NP-har(’i) can in principle be derived from TP-har(’i) by type-shift. CP/DP-har’i, with the until/as far as meaning, however seems to warrant its own lexical entry: it has a different, but related meaning.

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Schuh, R.G., Dole, J.A.J., Goge, U.M., & Gashinge, I.A. (2009). Ngamo-English-Hausa dictionary. Potiskum: Ajami Press. Schuh, R.G., & Gimba, A.M. (In preparation). Bole reference grammar. Ms. University of California, Los Angeles, CA. Retrieved from http://aflang.humnet.ucla.edu/bole/ bole.html. Schwarz, B. (2005). Scalar additive particles in negative contexts. Natural Language Semantics, 13, 125–168. Schwenter, S.A. (2003). Additive particles and scalar endpoint marking. Belgian Journal of Linguistics, 16, 119–134. Schwenter, S.A., & Vasishth, S. (2001). Absolute and relative scalar particles in Spanish and Hindi. Berkeley Linguistic Society, 26, 225–233. Simons, M., Tonhauser, J., Beaver, D., & Roberts, C. (2011). What projects and why. In Proceedings of Semantics and Linguistic Theory 20 (pp. 309–327). von Stechow, A. (1989). Focusing and backgrounding operators. In Arbeitspapiere der Fachgruppe Sprachwissenschaft 6 (pp. 37–84). Konstanz: Universität Konstanz. Truckenbrodt, H., Zimmermann, M., Danja, B.A., & Grubic, M. (2008). Focus and word order in Tangale (West Chadic). Talk presented at Syntax of the World’s Languages III, Free University of Berlin. Umbach, C. (2004). On the notion of contrast in information structure and discourse structure. Journal of Semantics, 21, 155–175. Umbach, C. (2009). Comparatives combined with additive particles: The case of German noch. In Proceedings of Sinn & Bedeutung 13 (pp. 1–15). Stuttgart. Visconti, J. (2005). On the origins of scalar particles in Italian. Journal of Historical Pragmatics, 6, 237–261. Wagner, M. (2014). Even and the syntax of focus sensitivity. Talk presented at the conference ‘Focus Sensitive Expressions from a Cross Linguistic Perspective’, at Bar Ilan University, Tel Aviv, 3.2.2014. Wilkinson, K. (1996). The scope of even. Natural Language Semantics, 4, 193–215. Wilson, D., & Sperber, D. (2004). Relevance theory. In L.R. Horn, & G. Ward (Eds.), Handbook of contemporary pragmatic theory (pp. 607–632). London: Wiley-Blackwell. Zeevat, H. (1994). Applying an exhaustivity operator in update semantics. In H. Kamp (Ed.), Ellipsis, Tense and Questions. (pp. 233–267). Amsterdam: University of Amsterdam, ILLC. Zeevat, H. (2009). Only as a mirative particle. Sprache und Datenverarbeitung, 33, 179– 196. Zeevat, H. (2014). Language production and interpretation: Linguistics meets cognition. Leiden: Brill. Ziegelmeyer, G. (2008). Aspects of adverbial subordination in Kanuri. Maiduguri Journal of Linguistic and Literary Studies, 10, 91–105.

chapter 4

Question-Answer Pairs in Sign Languages* Annika Herrmann, Sina Proske and Elisabeth Volk

1

Introduction

Natural languages comprise both spoken and sign languages across the world and research in the past decades has proven without doubt that languages of the oral-auditory and the visual-gestural modality are equally complex and exhibit similar underlying linguistic structures. In the following, we concentrate on so-called question-answer pairs, which have been reported for several sign languages. As presented in the following example of German Sign Language (DGS) in (1), a question-answer pair consists of a question (both noon#meal cook what) and an answer (soup), both articulated by the same signer. Question-answer pairs in sign languages should therefore not be confused with the established term in conversation analysis, which refers to separate utterances complementing each other at the discourse level. (1)

both

noon#meal

cook

what

soup [DGS]

‘What the two of them cook for lunch is soup.’ With regard to the well-studied language American Sign Language (ASL), question-answer pairs are usually analyzed as a syntactic device for focus marking * This paper would not have been possible without our Deaf informants, who offered us an invaluable insight into German Sign Language. We send a big thank you to all of them. Furthermore, we are particularly grateful to Klaus von Heusinger, Roland Metz, Liona Paulus, Markus Steinbach, and an anonymous reviewer for their constructive comments and discussions. We are also greatly indebted to Edgar Onea and Malte Zimmermann for inviting us to the Questions in Discourse Network Meeting in Göttingen and we thank the audience of that workshop for their helpful feedback.

© koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004378322_005

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(cf. Petronio 1991, Wilbur 1994, 1996, Petronio & Lillo-Martin 1997). Accordingly, the question provides background information and the focused answer new information. Caponigro & Davidson (2011) also associate them with a pragmatic function in terms of the Question Under Discussion (QUD) framework arguing that they might be applied to make an implicit sub-QUD explicit and subsequently provide the answer. The specific syntactic structure of questionanswer pairs, however, is still under debate. Traditionally, question-answer pairs are interpreted as a rhetorical question followed by an answer, both representing separate sentences (cf. Baker & Cokely 1980, Hoza et al. 1997, Neidle et al. 2000, Valli et al. 2005). Other approaches emphasize their grammatical properties, such as restrictions on wh-words and the possible embedding of question-answer pairs, which strongly indicate to treat question-answer pairs as a sentential unit (cf. Petronio 1991, Wilbur 1994, 1996, Davidson et al. 2008, Caponigro & Davidson 2011). In this paper, we elaborate on the latter and discuss two opposing syntactic accounts: the wh-cleft analysis brought forward by Wilbur (1996) and the analysis of question-answer pairs as complex declarative clauses argued for in Caponigro & Davidson (2011). Furthermore, we present new data from DGS investigating the grammatical structure of question-answer pairs in general and the position of wh-words in wh-questions and question-answer pairs in particular. Thereby, we confirm a treatment of question-answer pairs as a sentential unit. In addition, we rule out Wilbur’s (1996) account for DGS and support a pragmatically modified version of Caponigro & Davidson’s (2011) analysis.

2

Focus Marking in Sign Languages

The aim of this paper is to investigate question-answer pairs in sign languages and in particular to present DGS data on the use of wh-words in wh-questions and question-answer pairs. Since question-answer pairs are analyzed as an information packaging structure, specifically as a kind of focus construction (cf. Petronio 1991, Wilbur 1994, 1996, Petronio & Lillo-Martin 1997), we start with a brief description of focus marking strategies in sign languages, which cover morphological, prosodic, and syntactic means. Basically following an account of alternative semantics (cf. Rooth 1985, 1992, Büring 1997, 2007), focus is defined as indicating “the presence of alternatives that are relevant for the interpretation of linguistic expressions” Krifka (2007:18). In addition, focus is often discussed in terms of a twofold distinction between focus and background information whereby focus represents the new

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information, even though this is not a prerequisite in all cases. In the literature on focus marking, various focus types are identified that can be categorized as two major subtypes (Zimmermann & Onea 2011), namely information focus and contrastive focus. Information focus offers new information to the discourse by providing the answer to a wh-question, for instance. Contrastive focus, however, requires a closed set of alternatives to be explicitly mentioned or implicitly present in the previous discourse. But see Büring (2019) for an account of focus inherently being contrastive in terms of unalternative semantics. Research on focus marking in sign languages reveals that there is an interaction between focus and stress as observed for spoken languages.1 The focused constituent receives primary stress and Wilbur (1994, 1999) argues that phrasal stress in ASL appears in sentence final position.2 She follows the typology of Vallduví (1991) and claims that focus realization in ASL is [-plastic]. While stress in spoken languages is expressed by higher pitch, greater loudness, and longer duration, stress in sign languages is marked by manual and nonmanual articulators. The term manual refers to the use of the signer’s hands and stress is usually realized by larger movement of the hands, a higher velocity of the movement, and a longer duration of the sign (cf. Wilbur 1999). Nonmanual components for focus marking include facial expressions as well as head and body movements, such as brow raise, wide eyes, and mostly forward body and head positions. Lillo-Martin & de Quadros (2008) categorize three different focus types for ASL and Brazilian Sign Language: information focus, contrastive focus, and emphatic focus. These focus types are realized by morphological, prosodic, and syntactic means, but for the purpose of this paper it suffices to say a few words about morphological marking via focus particles and concentrate on prosodic and syntactic strategies of focus marking. The existence of focus particles is confirmed for ASL (Wilbur 1994), Sign Language of the Netherlands (van der Kooij et al. 2006, Herrmann 2013), DGS

1 Focus marking in sign languages is well-studied for ASL (Wilbur 1994, 1996), Brazilian Sign Language (Lillo-Martin & de Quadros 2008, Nunes & de Quadros 2008), the Sign Language of the Netherlands (Crasborn & van der Kooij 2013, Kimmelmann 2014), Russian Sign Language (Kimmelmann 2014), and DGS (Waleschkowski 2009, Herrmann 2013, 2015). For an overview of information structure in sign languages, see Wilbur (2012) and Kimmelmann & Pfau (2016). 2 Accounts of how to detect sentence boundaries in sign languages are presented in Crasborn (2007), Hansen & Heßmann (2007), and Herrmann (2010).

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and Irish Sign Language (Herrmann 2013). Herrmann (2013) compares focus particles in DGS, Sign Language of the Netherlands, and Irish Sign Language and shows that the restrictive particle only and the additive particle also are manually expressed in all three sign languages. Most particles appear to be best analyzed as adverbs (cf. Jacobs 1983, Büring & Hartmann 2001, Reis 2005, Herrmann 2013); however, interesting distributional patterns can be observed pertaining to the use of the DGS focus particle ONLY, for instance. Both in (2) and (3) (cf. Happ & Vorköper 2006; Herrmann 2013:249), ONLY is realized sentence-finally, but the relevant focus constituent that the particle refers to is prosodically marked. (2) tim F book buy only ‘Only Tim has bought the book.’

[DGS]

(3) tim book F buy only ‘Tim has bought only the book.’ With respect to prosodic focus marking, various nonmanual means such as brow raise and a change of head position are identified (Aarons 1994, LilloMartin & de Quadros 2008, Crasborn & van der Kooij 2013, Kimmelmann 2014, Schlenker et al. 2016). For Sign Language of the Netherlands, also mouth actions are described to be involved in focus marking (Crasborn & van der Kooij 2013). Furthermore, body leans may signal affirmation or refusal and fulfill the function of a contrastive marker (Wilbur & Patschke 1998, van der Kooij et al. 2006, Crasborn & van der Kooij 2013).3 Since all of these nonmanual markings can interact and overlap, Crasborn & van der Kooij (2013) did not find a clear difference between nonmanual markings used for information or contrastive focus and argue for mixed prosodic properties. In addition to prosodic means, there are also syntactic focus marking strategies in sign languages. Hence, the focused constituent can move leftward to the clause initial position, which Neidle (2002) and Lillo-Martin & de Quadros (2008) identify as SpecFocP. The canonical SVO word order for ASL is presented

3 Furthermore, Kimmelmann & Pfau (2016) point out that opposite localization of referents in signing space can be used to mark contrast resulting in a phenomenon called ‘dominance reversal’ (Frishberg 1985). Usually, one hand functions as the active main articulator (dominant hand) whereas the other hand rather stays passive (nondominant hand). However, in case of dominance reversal, the former passive hand may become active, thus indicating contrast.

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in (4), whereas (5) and (6) (Lillo-Martin & de Quadros 2008:169 f.) show a leftward movement for information focus and contrastive focus.4,5 (4) S1: what you read? ‘What did you read?’ S2: i read book stokoe ‘I read Stokoe’s book.’

[ASL]

I-focus (5) S2: book stokoe i read ‘I read [Stokoe’s book]F.’ (6) S1: you read chomsky book? ‘Did you read Chomsky’s book?’ C-focus S2: no, book stokoe i read ‘No, I read [Stokoe’s book]F.’ In the above examples, focus is marked both syntactically and prosodically. However, in the case of information focus, prosodic marking is sufficient, as can be seen in (7). (7) S1: what you read? ‘What do you read?’ I-focus S2: i read book stokoe ‘I read [Stokoe’s book]F.’

[ASL]

4 The on- and offset of the line above the glosses indicates the scope of the nonmanual markers. I- and C-focus represent a specific nonmanual marking accompanying the focused constituent. With regard to information focus, Lillo-Martin & de Quadros (2008:169) indicate the same nonmanual marking previously referred to as ‘tm1’ by Aarons (1994) including brow raise, widened eyes, and sometimes a back and sideward head tilt or a down and forward head movement. 5 Wilbur (1997:96f.) argues for the possibility of a contrastive topic depending on the previous context. Accordingly, she analyzes mary in (i) as marked for contrastive focus, while (ii) includes a topic followed by a comment. C-focus (i) john not-like jane. mary he loves ‘John doesn’t like Jane. It’s MARY he loves.’ Top (ii) mary jim love tease [ASL] ‘As for Mary, Jim loves to tease her.’

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A further syntactic strategy used for focus marking is doubling. Doubling is a common phenomenon in sign languages where a sentence initial or internal element is doubled so that it also occurs in sentence final position. Among the elements that can be doubled are modals as in (8), quantifiers, verbs, and whwords (cf. Petronio 1993).6 (8) john can read can ‘John really [can]F read.’

[ASL]

Since doubling is a marker of emphasis (cf. Wilbur 2012), Lillo-Martin & de Quadros (2008) analyze it as emphatic focus. However, Wilbur (2012:474) makes a distinction between focus and emphasis. Both have in common that some element receives more attention or weight, but the two categories are grammatically independent. Not all emphasized elements have to be focused and focused elements can but do not need to be emphasized. In sum, focus in sign languages is mainly marked prosodically by different and often overlapping nonmanuals, but also syntactically based on movement operations and phenomena such as doubling. Moreover, so-called questionanswer pairs are a further syntactic strategy that is used to foreground new information. In the following section, we will elaborate on the specifics of question-answer pairs and address competitive analyses concerning their syntactic structure in ASL.

3

Question-Answer Pairs in ASL

Questions and answers are usually assumed to constitute distinct structures, which are used in dialogues of different individuals as means of interpersonal knowledge exchange, i.e. common ground updates and management (see also Onea & Zimmermann 2019 for an overview of semantic theories of questions and their functions in discoure). Nonetheless, in a way similar to wh-clefts in 6 Doubling is not restricted to declaratives and also occurs in interrogatives. Moreover, sign languages differ in terms of the elements that can be doubled (Petronio 1993, Zeshan 2004, Šarac Kuhn et al. 2007). In polar questions, for instance, it is often the subject pronoun that may occur twice (‘subject pronoun copy’, cf. Padden 1988). The fact that also wh-words may be doubled in wh-questions in sign languages lead to a debate regarding the syntax of whquestions in ASL. Petronio & Lillo-Martin (1997) argue that sentence final wh-elements are base-generated in C∘ and associated with a focus position while the other wh-element moves leftward to SpecCP. However, Neidle et al. (2000) claim that wh-movement is rightward and the second wh-element a base-generated topic.

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spoken languages, sign languages such as ASL and DGS also display questionanswer pairs, which are complex units expressed by only one signer to make a statement. As demonstrated in the DGS example (9), a question-answer pair starts out with a question (shepherd boy there task what), but instead of expecting the addressee to reply, the same signer immediately provides the answer herself (sheep take-care).7 Although the first part of the questionanswer pair in (9) resembles a wh-question, it exhibits a distinct nonmanual marking and some differences in the grammatical structure. Following Davidson et al. (2008), we call this part of the construction the question constituent. The second part, on the other hand, is labeled the answer constituent. (9)

shepherd

boy

there

task

what

sheep

takecare [DGS]

‘The shepherd’s boy’s task is to take care of the sheep.’ Crucially, the question constituent of a question-answer pair is not directed at the addressee to ask for new information, but is used as a device to foreground the answer constituent (cf. Petronio 1991, Wilbur 1994, 1996, Petronio & LilloMartin 1997, Davidson et al. 2008, Caponigro & Davidson 2011).8 Accordingly, the subsequent answer is assumed to be the focused constituent providing new information. For the purpose of a first classification of question-answer pairs,

7 The DGS example in (9) is taken from the annotated DGS data set of five of the Echo fables, in this case The shepherd’s boy and the wolf, which were re-narrated by Deaf DGS signers in the SignLab of the University of Göttingen. The translation of question-answer pairs is tied to the problem that it already implies a specific interpretation. Accordingly, different translations appear in the literature, each reflecting a designated theoretical approach. For instance, Hoza et al. (1997) translate question-answer pairs as independent sentences interpreting the question part as a separate rhetorical question and Wilbur (1996) chooses a translation as wh-clefts. In the following, we adopt the terminology of Davidson et al. (2008) and translate question-answer pairs as English copular sentences. 8 Hoza et al. (1997) adopt a deviating approach by assuming no systematic differences between question and answer constituents in question-answer pairs and their related independent variants. As will be demonstrated below, this view cannot be maintained, as it is inconsistent with the empirical evidence.

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we offer a preliminary definition in (10) before going into detail about the specific properties of questions-answer pairs. (10) Question-answer pairs (version 1) A question-answer pair is a complex unit consisting of a. a question constituent and b. an answer constituent aiming at foregrounding the answer constituent to indicate information focus. Question-answer pairs are reported for several different sign languages such as ASL (cf. Baker & Cokely 1980:137; Petronio 1991; Aarons 1994:131–136; Neidle et al. 2000:190; Valli et al. 2005:130), Australian Sign Language (cf. Johnston & Schembri 2007:210), and DGS (cf. Pfau 2008:56). However, detailed analyses only relate to ASL so far (cf. Wilbur 1994, 1996, Hoza et al. 1997, Davidson et al. 2008, Caponigro & Davidson 2011). Furthermore, both in terms of the data basis and the respective interpretations, these analyses differ strikingly, so that there is no consensus yet regarding the syntactic, semantic, and pragmatic constitution of signed question-answer pairs. In the following, we describe the main properties of question-answer pairs as they are presented in the literature on ASL and introduce two opposing analyses: one analysis brought forward by Wilbur (1996) and another presented in Caponigro & Davidson (2011). 3.1 Grammatical Structure of Question-Answer Pairs As mentioned above, question constituents of question-answer pairs may resemble a wh-question, but they usually display notable deviations especially concerning the nonmanual marking and the distribution of wh-words. Most investigated sign languages so far exhibit brow furrow (‘bf’) as the main nonmanual strategy to mark a wh-question (cf. Cecchetto 2012:302).9 As opposed to this, question constituents in ASL are reported to be marked primarily by brow raise (‘br’) (cf. Baker & Cokely 1980:137; Wilbur 1996:209; Hoza et al. 1997:8; Neidle et al. 2000:190; Davidson et al. 2008:108; Caponigro & Davidson 2011:334).10 In ASL and other sign languages, this particular nonmanual marking usually

9

10

In ASL and DGS, for instance, an additional forward body lean is possible (cf. Valli et al. 2005:128; Herrmann & Steinbach 2013). Moreover, Austrian Sign Language and Croatian Sign Language use an upward movement of the chin (‘chin up’) as a primary marker of wh-questions (cf. Šarac Kuhn & Wilbur 2006:164). Valli et al. (2005:130) also mention an additional forward head tilt and a slight headshake.

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accompanies several structures such as polar questions as in (11a) (cf. Davidson et al. 2008:111), topicalization (11b) (cf. Aarons 1994:147), relative clauses (11c), and conditional clauses (11d) (cf. Wilbur & Patschke 1999:9,12). br (11) a. i laugh ‘Was I laughing?’ br b. vegetable john like corn ‘As for vegetables, John likes corn.’ br c. [dog chase cat] bark ‘The dog that chased the cat barked.’ br d. [suppose/if rain tomorrow] we can go-to movies ‘If it rains tomorrow, we can go to the movies.’

[ASL]

As a consequence, the function of the nonmanual marker brow raise is a controversial issue that has become a matter of much debate. Material marked by brow raise is sometimes interpreted as general background information sitting in the left periphery (cf. Coulter 1978). Others choose a purely syntactic analysis indicating nonmanuals as spell-outs of syntactic features (cf. e.g. Aarons et al. 1992, Petronio & Lillo-Martin 1997, Wilbur & Patschke 1999, Neidle et al. 2000). Wilbur & Patschke (1999:18) argue, for instance, that the nonmanual marker brow raise appears in A’-positions which are linked to operator features that are [-wh]. As opposed to this, parallels are drawn with characteristics of intonation in spoken languages, thus analyzing brow raise as part of the prosodic system and assuming a compositional semantic and pragmatic account (cf. e.g. Padden 1990, Reilly et al. 1990, Nespor & Sandler 1999, Dachkovsky & Sandler 2009). Accordingly, Dachkovsky & Sandler (2009) relate brow raise to the meaning of high tones (H) in spoken languages and argue that they signal continuation and a dependency relation in Israeli Sign Language. Another difference between wh-questions and question constituents of question-answer pairs relates to the position of wh-words. ASL, being a language with an unmarked SVO word order, has a comprehensive paradigm of wh-words at its disposal, which may appear in situ (12a), sentence finally (12b), or doubled in wh-questions (cf. Cecchetto 2012:297). In line with the doubling structures mentioned in Section 2, wh-doubling is possible in situ and final as in (12c) or sentence initial and final as in (12d) (cf. Davidson et al. 2008:112). (12) a. john buy what yesterday b. john buy yesterday what

[ASL]

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c. john buy what yesterday what d. what john buy yesterday what ‘What did John buy yesterday?’ In question-answer pairs, on the contrary, wh-words seem to be generally preferred at the right edge of the question constituent as in (13a) (cf. Wilbur 1996:216f.; Davidson et al. 2008:108). Crucially, the doubling of wh-words as in (13b) appears to be prohibited, or at least highly constrained in the context of question-answer pairs (cf. Wilbur 1996:218; Davidson et al. 2008:112). Only Hoza et al. (1997:8) refer to examples of question-answer pairs like (13c) that apparently include two wh-words. br (13) a. john buy what book ‘The thing John bought was a book.’ br b. *what john eat what pasta ‘The thing John ate was pasta.’ br c. who tell bill “what” mary ‘The girl who told Bill was Mary.’

[ASL]

The sign “what” at the right edge of the question constituent in (13c) is articulated either with one or both open palms of the hands facing upwards and moving horizontally from side to side. According to Hoza et al. (1997:4), “what” is used to convey different question meanings and therefore may correspond to the same argument as the initial sign who in (13c). Hoza et al. (1997) further argue for the possibility of wh-doubling in question-answer pairs on these grounds. However, the sign “what” seems to be best characterized as a general question particle and its occurrence in question-answer pairs as in (13c) therefore appears not to be a typical case of wh-doubling. In line with this, Hoza et al. (1997) only provide examples of wh-doubling including the question particle, while they do not discuss the possibility of doubling other wh-words. So far, only such question constituents were mentioned, which include whwords. Interestingly, Hoza et al. (1997) and Caponigro & Davidson (2011) also provide examples, in which the question constituent structurally resembles a polar question as in (14) (cf. Caponigro & Davidson 2011:331). The question constituent is again marked nonmanually by brow raise and the answer constituent is realized by manual signs such as yes and no or rather only nonmanually by head nods and headshakes.

106 br (14) john have motorcycle no ‘John doesn’t have a motorcycle.’

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[ASL]

Wilbur (1996), however, only counts structures as question-answer pairs if they contain a wh-word. At the same time, she refers to examples such as in (15), which she describes as polar questions in a rhetorical function (cf. Wilbur 1996:212). Although the negative headshake (‘hs’) is interpreted as an answer to the preceding question, Wilbur (1996) does not classify the whole utterance as a question-answer pair and therefore translates it as two individual sentences. br hs (15) finish ‘Are we/you finished? NO!’

[ASL]

In line with Wilbur (1996:225), one crucial difference between examples such as in (15) and question-answer pairs as in (13a) constitutes the relationship between the question and the answer constituent. Accordingly, questionanswer pairs contain a question providing an open proposition with a variable x, which is conveyed in terms of the respective wh-word. The answer, on the other hand, fills in the missing information. Since Wilbur (1996) does not assume such a relationship for examples as in (15), which do not include a whword, she separates them from question-answer pairs. When following Wilbur’s (1996) approach, not only question constituents are excluded, which resemble a polar question, but also answer constituents, which represent a clausal phrase and, as a consequence, do not exclusively provide the missing information. However, while Caponigro & Davidson (2011:336) note the higher frequency of short answer constituents, they also mention the possibility to optionally realize whole clauses as in (16), which provide the relevant answers to the relating questions (cf. a similar example in (9) from DGS). Hoza et al. (1997:12) assume that no syntactic relationship between the question and answer is needed, so that the appropriateness of the answer may solely be evaluated on the basis of the previous discourse and shared knowledge. br (16) a. john buy what (he buy) book [ASL] ‘The thing John bought was a book.’ br b. john have motorcycle no (he not have motorcycle) ‘John doesn’t have a motorcycle.’

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As opposed to Hoza et al. (1997), both Wilbur (1996) and Caponigro & Davidson (2011) point out that question-answer pairs can be embedded as the complement of a predicate, thus constituting a complex sentential unit. Caponigro & Davidson (2011:337) further explain this embedding only to be possible with predicates such as hope and think in (17a), which select a declarative clause. Predicates such as ask in (17b), on the other hand, are considered as unacceptable. Therefore, Caponigro & Davidson (2011) assume predicates selecting interrogative clauses to block the embedding of question-answer pairs. br (17) a. those girls hope [their father buy what car] [ASL] ‘Those girls hoped that the thing their father bought was a car.’ br b. *those girls ask [their father buy what car] ‘Those girls asked whether the thing their father bought was a car.’ Hoza et al. (1997:20–22) choose a different interpretation of instances like in (17a). Their ASL informants judged them to be grammatical, but in their own production they usually added a short head nod (‘hn’) on the predicate as in (18), while longer pauses or eye blinks were possible between the predicate and the following question-answer pair. Since Hoza et al. (1997) analyze these nonmanual markings as clause boundaries, they assume a realization of reported speech, as suggested by the translation in (18). However, Caponigro & Davidson (2011:338) indicate that the co-reference between the matrix subject those girls and the possessive pronoun of the embedded subject their in (17a) rules out reported speech in this case. In a direct quotation reading, the possessive pronoun our would be expected. hn br (18) mary think throw apple who john ‘Mary thinks: “Who threw the apple? John.” ’

[ASL]

In sum, there are two main opposing approaches to the grammatical structure of question-answer pairs in ASL. Hoza et al. (1997) adopt the traditional view, also expressed by Baker & Cokely (1980), Neidle et al. (2000) and Valli et al. (2005), characterizing question-answer pairs as composed of separate sentences, which do not share a coherent syntactic structure. To support this claim, they argue that the first part of a question-answer pair shares all basic properties of true questions and, for instance, also allows wh-doubling, while the second part might be realized as whole sentences. Based on the specific nonmanual marking of the question constituent, the apparent restrictions on

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wh-doubling, and especially the possibility to embed a question-answer pair as the complement of a predicate, Wilbur (1996) and Caponigro & Davidson (2011) adopt an alternative approach, analyzing question-answer pairs as complex sentential units. However, they hold diverging views particularly with regard to the possibility of question constituents resembling polar questions and of answer constituents realized as clausal phrases. As a consequence, Wilbur (1996) and Caponigro & Davidson (2011) develop different syntactic analyses of question-answer pairs, which will be presented in the following in more detail. 3.2 Analysis as Wh-clefts (Wilbur 1996) Wilbur (1996) assumes that question-answer pairs represent a syntactic, prosodic, and semantic unit used to mark the answer part as the focus constituent. Concerning the syntax of question-answer pairs, Wilbur (1996:209) draws a parallel to wh-clefts, as they can be found in spoken languages like English and German. Concerning wh-clefts as in (19), the copula verb be is assumed to connect a free relative clause (what John bought) with a certain constituent (a book) that is marked as focus accordingly. (19) What John bought was a book. Moreover, this focus constituent functions as the subject and the free relative clause as the predicate of a small clause, which is selected by the copula verb as a complement (cf. Wilbur 1996:241). Applying this analysis to question-answer pairs, Wilbur (1996:238) analyzes the question constituent as a free relative clause and the predicate of the small clause. The answer constituent, however, receives focus marking and represents the subject. Since sign languages such as ASL do not display copula verbs, Wilbur (1996) suggests a related operator λ selecting the small clause. For the syntactic structure of ASL, Wilbur (1996) assumes Spec,CP to be on the left and C0 to be on the right as already proposed by Petronio & Lillo-Martin (1997). The underlying syntactic structure of question-answer pairs such as (20a) can thus be illustrated as in (20b). The related surface structure, which is generated by raising the subject (the answer constituent) to Spec,IP and moving the predicate (the question constituent) to Spec,CP, is given in (20c) (cf. Wilbur 1996:247). The focus feature [+F] is located in I0 with the result that the answer constituent receives focus marking via spec-head agreement. (20) a. i dislike what john his tie ‘What I dislike is John’s tie.’

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b.

c.

3.3

Analysis as Complex Declarative Clauses (Caponigro & Davidson 2011) In accordance with Wilbur (1996), Caponigro & Davidson (2011) suppose that question-answer pairs represent a clausal unit and are used to mark focus. More specifically, they assume that question-answer pairs are used to make an implicit sub-QUD explicit and answer it within a single sentence. In line with this approach, Caponigro & Davidson (2011:363) argue, for instance, that question-answer pairs cannot be uttered out of the blue without a presumed main QUD. Additionally, the question constituent of a question-answer pair cannot repeat a question, which was already signed explicitly. The dialogue in (21) includes Signer A who overtly signs a sub-QUD related to the main QUD ‘What did each person buy?’. However, Signer B cannot sign a question-answer pair repeating the sub-QUD, as it is no longer implicit at this point. For more

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general information on QUD see Onea & Zimmermann (2019) and for a detailed account of potential questions and their influence on discourse structure also consider Onea (2016, 2019). (21) Scenario: main QUD ‘What did each person buy?’ Signer A: john buy what? ‘What did John buy?’ Signer B: #john buy what book ‘The thing John bought is a book.’

[ASL]

As an alternative to Wilbur’s (1996) wh-cleft analysis, Caponigro & Davidson (2011) argue for question-answer pairs as complex declarative clauses. One important argument that they mention refers to the use of wh-words. Caponigro & Davidson (2011) state that question-answer pairs have the same range of wh-words as wh-questions. Wh-clefts, however, typically only license a certain set of wh-words. Therefore, when included in wh-clefts, wh-words such as how, which, and how much result in ungrammatical sentences as in (22). By contrast, the relating question-answer pairs of ASL in (23) are rated as fully acceptable (cf. Caponigro & Davidson 2011:365). (22) a. *How he drove here was really fast. b. *Which book John bought was that one. c. *How much the car cost was $20,000. (23) a. john drive how very-fast b. john buy book which that c. car cost how-much $ 20,000

[ASL]

Furthermore, the association of the question constituent with a free relative clause, which is a prerequisite for the wh-cleft analysis, gives rise to discrepancies. On the one hand, Caponigro & Davidson (2011) expect question constituents to be possible that resemble a polar question and therefore do not contain a wh-word. On the other hand, relative clauses in ASL seem to always be bound by a head noun and thus cannot appear freely (cf. Caponigro & Davidson 2011:331). Finally, Caponigro & Davidson (2011) also refer to the possibility of clausal answer constituents, which cannot be maintained with a wh-cleft analysis. As mentioned above, only such answer constituents are predicted by Wilbur (1996), which solely contain the missing information to complement the open proposition provided by the question constituent. Caponigro & Davidson (2011) interpret question-answer pairs as complex declarative sentences, which serve as the matrix clause of an embedded inter-

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rogative clause representing the question constituent and an embedded declarative clause representing the answer constituent. As the question constituent always displays the nonmanual marking brow raise and wh-doubling appears to be prohibited, Caponigro & Davidson (2011) argue for its embedded structure. Embedded wh-questions also receive a special nonmanual marking in ASL and exclude wh-doubling as demonstrated in (24) (cf. Caponigro & Davidson 2011:333). For a discussion of embedded questions in spoken languages, see also Roelofsen et al. (2019). (24) *he ask [ john buy what yesterday what] ‘He asked what John bought yesterday.’

[ASL]

With reference to the possible embedding of the whole question-answer pair, Caponigro & Davidson (2011:336) assume the answer constituent to be embedded as well. Furthermore, the answer constituent is supposed to be realized as a declarative clause obligatorily containing the new information, while the rest of the clause may be optionally omitted. As already shown in (16a), repeated here as (25), the answer constituent obligatorily contains the sign book, whereas the rest of the clause (he buy) may be dropped causing an elliptical realization. br (25) john buy what (he buy) book ‘The thing John bought was a book.’

[ASL]

The syntactic structure of question-answer pairs in ASL as proposed by Caponigro & Davidson (2011:340–342) is illustrated in (26). The question-answer pair as a whole is interpreted as a complex declarative clause and corresponds to the highest IP, while the covert copula verb in V0 takes an interrogative CP (the question constituent) as its subject and an IP (the answer constituent) as its complement. Since the answer constituent is associated with an IP, it is generally interpreted as a declarative clause, which can be realized elliptically. (26)

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Drawing on theoretical approaches applied to spoken languages, Wilbur (1996) provides the first comprehensive account of the syntactic structure of question-answer pairs in ASL and analyzes them as wh-clefts, which are specifically used as a focus marking strategy. In this way, she defines quite restrictive but clear conditions with regard to the syntax and semantics of questionanswer pairs. Caponigro & Davidson (2011), however, report on empirical data partly contradicting these conditions and therefore propose an alternative account. Their model has the advantage that the structure of the question constituent is not restricted to wh-questions, but also allows for polar questions. Furthermore, it accounts for the fact that the answer may be realized either by a whole clause or elliptically, i.e. only containing the new information. The above-presented analyses of question-answer pairs mainly take into consideration ASL. In the following section, we present new data to address the question, in which way question-answer pairs are realized in DGS. Based on an empirical investigation, we discuss various aspects such as nonmanual markings, wh-word positions, question constituents resembling polar questions, and embedding.

4

Question-Answer Pairs in DGS

As mentioned above, different syntactic analyses have been proposed for the specific properties of question-answer pairs in ASL. Here, we introduce two studies investigating question-answer pairs in DGS. Our main interest, however, concerns the position of wh-words in wh-questions and question-answer pairs, as this is still a controversial issue both in DGS and other sign languages. The unmarked word order of DGS is assumed to be SOV (Glück & Pfau 1998, Rathmann 2003; Happ & Vorköper 2006:120). In wh-questions, the wh-word can occur sentence initially, sentence finally, or it can be doubled in sentence initial and final position, but it is still unclear whether specific syntactic restrictions exist (Happ & Vorköper 2006:324; Grin 2014). The first study presented in Section 4.1 is a pilot study considering the general structure of question-answer pairs in DGS. The second study discussed in Section 4.2 is an empirical questionnaire study and concentrates on the position of wh-words both in wh-questions and questions-answer pairs. We describe the methodology and report on the results. Section 4.3 concludes with a discussion and elaborates on further implications with respect to the analyses offered by Wilbur (1996) and Caponigro & Davidson (2011).

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4.1 Pilot Study on Question-Answer Pairs in DGS In this initiating pilot study, we elicited 18 target sentences involving questionanswer pairs as in (27). We used a translation task with a linguistically trained Deaf early DGS informant, followed by a thorough post-elicitation data discussion.11 Caponigro & Davidson (2011:359) mention that question-answer pairs are much less preferred when signed out of the blue, so we always added a context with clearly defined and controlled preparatory sentences. (27) Max comes home after work. He immediately begins to clean the kitchen and the bathroom. Why does he clean his apartment? His girlfriend wants to visit him. Our informant translated the last two sentences of (27) as a question-answer pair positioning the wh-word at the end of the question constituent as shown in (28). Moreover, the question constituent was signed with brow raise, while the answer constituent included a final head nod on the verb. In the following discussion, our informant explained that wh-questions are usually interpreted as clear information seeking questions expecting an answer rich in content and are thus accompanied by brow furrow. Question-answer pairs on the other hand do not imply an expectation of an answer from the addressee, but are often used in the course of storytelling and are marked by brow raise instead. Concerning the wh-word position, the informant stated that in DGS, wh-words usually occur at the end of a wh-question. On the other hand, wh-words could also be positioned sentence initially or be doubled, but this would increase the information seeking character of the question. Although the informant accepted wh-words at the beginning of the question constituent, wh-doubling was generally rejected in question-answer pairs. (28)

he

11

clean

br why

his

girlfriend

hn visit [DGS]

Throughout the text, ‘Deaf’ refers to the cultural identity of individuals, while ‘deaf’ refers to the biological condition of being deaf.

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As already mentioned in Section 2, both Wilbur (1996:217) and Caponigro & Davidson (2011:337) argue, that it is possible to embed the whole questionanswer pair as a complement of predicates such as think and hope, which select a declarative clause. On the contrary, a predicate like ask, which selects an interrogative clause, should block the embedding. To test these predictions for DGS, we also discussed examples such as (29) and (30) with the informant. (29)

l-i-s-a

hope

[her

father

buy

br what

car

new] [DGS]

‘Lisa hopes that the thing her father bought is a new car.’ br (30) *lisa ask [her father buy what car new] ‘Lisa asks if her father bought a new car.’ The embedded structure in (29) was accepted by our informant, whereas (30) was clearly rejected, thus providing further support for Wilbur’s (1996) and Caponigro & Davidson’s (2011) analysis. A predicate such as hope allows an embedding of the whole question-answer pair as in (29), but it is not possible to embed the question-answer pair as a complement of the predicate ask as shown in (30). Regarding the position of wh-words within the embedded structure, our informant accepted final wh-words as in the above examples. The doubling of wh-words was again rejected, while initial wh-words were judged to be possible, but very unusual. While Wilbur (1996:212) only argues for question-answer pairs involving question constituents with a wh-word, Caponigro & Davidson (2011:330) also claim question constituents to be possible, which resemble a polar question. To further obtain evidence for either analysis, we also integrated examples like (31) into the pilot study. (31) Tina and Marie are going shopping after school. Tina wants to buy a dress and Marie new shoes. Does Tina find a dress? Yes. In the translation task, the last two sentences were again realized as a questionanswer pair, which is presented in (32), and our informant considered the nonmanual marking to be the same as in question-answer pairs including a

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wh-word. Hence, brow raise accompanied the question constituent, whereas a final head nod occurred on the answer constituent. Moreover, our informant also accepted the embedding of question-answer pairs as in example (33), which involves a question constituent resembling a polar question. As described above, the embedding was only possible with a predicate selecting a declarative clause. Although both (32) and (33) were accepted, our informant judged question constituents involving wh-words as more common. (32)

t-i-n-a dress ‘Tina found a dress.’

br find

hn yes

[DGS]

br (33) tim think [he competition win yes] ‘Tim thinks that he will win the competition.’ In a nutshell, our pilot study demonstrated that question-answer pairs are possible in DGS with the question constituent marked by bow raise, syntactically either resembling a wh-question or a polar question. Additionally, both variants of question-answer pairs can be embedded under a predicate selecting a declarative clause. There seems to be a preference for final wh-words in question-answer pairs, whereas initial wh-words are marginally acceptable and wh-doubling is rejected. Doubling, as described in Section 2, is a common way of marking emphasis in sign languages and our informant considered initial and doubled wh-words to be markers of emphatic structures. We assume an emphatic marking through doubling to be possible in the context of wh-questions, but inappropriate for question-answer pairs. To what extent these assumptions can be reproduced empirically is demonstrated in the following section presenting the methodology and the results of our second study. 4.2 Empirical Study on Question-Answer Pairs and Wh-questions in DGS In addition to the pilot study on several aspects of question-answer pairs in DGS, the follow-up questionnaire study empirically scrutinizes the issue of wh-word positioning in more detail. Based on the above-presented analyses

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of question-answer pairs in ASL and the DGS data based on the pilot study, we predicted that wh-questions and question-answer pairs differ in terms of their syntactic restrictions on the wh-word position in DGS. More specifically, we hypothesized the following: 1) wh-questions do not impose any syntactic restrictions on the wh-word position, 2) wh-words are only acceptable at the end of the question constituent of question-answer pairs, and 3) doubled whwords are prohibited in question-answer pairs. 4.2.1 Methodology We collected data of six native and three early Deaf DGS signers (two women and seven men at the age of 16 to 70 years, mean age 50.1) in the SignLab of the University of Göttingen.12 The study comprised two parts. First, the participants were asked to judge 36 DGS sentences in a rating questionnaire. As a second step, further qualitative data was elicited in a semi-structured interview. For the first task, we used stimulus sentences created in collaboration with a linguistically trained Deaf early DGS informant. The stimulus material consisted of six context constructions including wh-questions as illustrated in (34) and six context constructions including question-answer pairs as in (35). Based on the pilot study, we decided to realize wh-questions with the nonmanual marker brow furrow, whereas the question constituents of questionanswer pairs were signed with brow raise. Moreover, the answer constituent always included a single noun phrase. In addition, note that wh-questions were realized in role shift (Lillo-Martin 2012); role shift is a phenomenon, where the signer slips into the role of a character reporting utterances and thoughts (called quotation role shift), and actions (called action role shift or constructed action) from that character’s perspective. This is usually indicated by a change of body and head positions as well as eye gaze shifts from the actual addressee to the reported addressee (cf. Herrmann & Steinbach 2012).13

12

13

Native signers are deaf children of deaf parents. Since only few deaf children have deaf parents, the situation of sign language acquisition is special in comparison to spoken languages. We therefore also included early signers who acquired DGS before the age of six, regularly use DGS, and consider themselves fluent DGS signers. It is crucial for question-answer pairs that the answer of the question is given by the signer himself. In order to maintain the condition of having only one signer in the videos, the whquestions were realized in role shift. The marker ‘< >’ indicates the scope of the role shift. The preceding number shows from whose perspective the utterance is reported (in (34) from Marie’s perspective as indicated by 3b). ‘ix’ stands for a pointing sign (index; usually an extended index finger). Subscript numbers or letters refer to different locations in the signing space associated with different discourse referents (numbers) or places (letters).

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(34) l-e-a ix3a m-a-r-i-e ix3b cinema ixA meet. l-e-a two ticket buy. [DGS]

3b
3a bf she3b ask we-both sit where ‘Lea and Marie meet at the cinema. Lea buys two tickets. She asks: “Where do we sit?”’ (35) afternoon four children meet. they soccer play.

br they soccer play where sports#field ‘In the afternoon four children meet each other. They play soccer. Where they play soccer is at the sports field.’ Both wh-questions and question-answer pairs included six wh-words as illustrated in Figures 4.1–6: what, where, who, when, how-much, and whereto.14 Furthermore, each target sentence was modified in terms of the wh-word position and thus realized with an initial, final, and doubled wh-word. The resulting 36 videos were divided into three randomized lists, so that each participant was confronted with twelve different videos. As indicated in (34) and (35), we used controlled contexts. A context consisted of three sentences: the first sentence introduced a particular situation and/or place, the second sentence described the activity of the individuals involved, and the last sentence represented the wh-question or questionanswer pair. To keep variation between the different contexts as minimal as possible, the following criteria were applied: 1) a maximum of two explicit ref14

All of these wh-words are simple signs in DGS. Complex signs such as whose or towhom, which are composed of the sign who and a possessive pronoun or the agreement marker pam, were excluded (cf. Pfau & Steinbach 2007).

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figure 1

what

figure 2

where

figure 3

who

figure 4

when

figure 5

how-much

figure 6

where-to

erents with frequent and short German names, 2) present tense, 3) only one verb or event per sentence, 4) only plain verbs excluding agreement verbs, classifier verbs, and auxiliaries,15 6) basic word order, and 7) omission of specific nonmanual markings (e.g. negation, aspect marking, or topicalization). To further clarify the task, we edited the videos and inserted a white circle on the right edge of the picture, which appeared directly at the beginning of a wh-question or question-answer pair. Figure 7 represents a corresponding still. Thus, the white circle signaled the start of the critical sentence and stayed there for 1.5 seconds. The participants were asked to rate the signing from the moment the white circle appeared. In this way, we aimed at focusing their attention to the critical sentence instead of taking the full context into consideration. Ratings were based on a five-point scale, which was printed for each of the videos on a paper and pencil questionnaire. Instead of numbers, we used thumbs illustrations as can be seen in Figure 8.

15

According to Padden (1988), verbs are classified with regard to their agreement patterns in sign languages. While spatial verbs and agreement verbs show agreement by modification of the sign’s path movement or finger orientation, plain verbs are lexically specified and do not agree with locations in the signing space.

question-answer pairs in sign languages

figure 7

video

figure 8

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rating scale

In a second step, we conducted a semi-structured interview. This was carried out in DGS by DGS competent hearing instructors (in some cases with two participants at a time).16 In the interview session, we first discussed the participants’ judgments while reviewing each of the videos. Second, with the help of prepared questions based on the pilot study, different aspects were discussed in detail concerning the position of wh-words, the possibility of wh-doubling, nonmanual marking, and the structure of question-answer pairs in general. The interviews were video recorded for further analysis. 4.2.2 Results In addition to the first results of our pilot study on question-answer pairs in DGS, the second study (judgment task and interview session) aimed at a broader empirical data discussion offering the participants the opportunity to reflect on their own judgments. We thus examined whether the clear statements of our pilot informant could be reproduced by other signers. To concentrate on the qualitative analysis, we kept the number of context constructions purposely low. The duration of the interviews ranged from 25:30 to 51:42 minutes. We first briefly summarize the results we gained from the questionnaire and then turn to the interviews. To back up our results pertaining to the interviews, we discussed the responses with a further Deaf early DGS informant. In the end of this section, we also report on this final data discussion. 4.2.2.1 Questionnaire Nine DGS signers performed acceptability judgments for twelve videos each, resulting in a data set of 108 judgments in total, 54 for wh-questions and 54 for question-answer pairs. We considered the position of wh-words (final, ini-

16

The presence of hearing researchers may have had an influence on the participant’s sign language use especially concerning word order and the use of mouthings. For the analysis, these possible influences were taken into account.

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graph 1

The position of wh-words in wh-questions (n = 54)

graph 2

The position of wh-words in question-answer pairs (n = 54)

tial, and doubled) and the choice of wh-words (what, where, who, when, how-much, and where-to) to be crucial variables for the evaluation of the questionnaire. As Graph 1 illustrates for wh-questions, all videos were mostly rated as either ‘very good’ or ‘good’ regardless of the wh-word position. Moreover, it appears that no main difference between the judgments of final and initial wh-words was made. The judgments of doubled wh-words, however, shifted to some extent from ‘very good’ to ‘good’. In contrast to our predictions based on the literature on ASL and the results of our pilot study, the rating of question-answer pairs displayed a quite similar pattern as the rating of wh-questions (illustrated in Graph 2). Most videos received a judgment as ‘very good’ or ‘good’, while more videos were rated as ‘very good’. Between the judgments of final and initial wh-words almost no difference occurred. Although not as clear as for wh-questions, there is also a shift away from ‘very good’ to less positive levels concerning the judgments of doubled wh-words. Taking into account the choice of wh-words, Graph 3 illustrates that whquestions including the wh-words what and how-much were rated the best. On the other hand, the wh-word who received rather mixed ratings. Several participants explained during the interview, however, that the reason for these more negative ratings mainly originated in the corresponding context that included some lexical peculiarities for them (e.g. dialectal variation).

question-answer pairs in sign languages

graph 3

The choice of wh-words in wh-questions (n = 54)

graph 4

The choice of wh-words in question-answer pairs (n = 54)

121

As Graph 4 shows for question-answer pairs, all wh-words were mostly rated as ‘very good’. Therefore, there was no wh-word being generally ruled out in this context. Interestingly, question-answer pairs, which contained the wh-word what, were rated as ‘very good’ by all participants. Taking the questionnaire as a basis, we assume that neither the position nor the choice of wh-words played a decisive role for judging the videos. However, the interviews give rise to interesting observations concerning the strategies how to perform acceptability judgments in general and the perception of the properties that wh-questions and question-answer pairs in DGS exhibit in particular. 4.2.2.2 Interviews In this section, we report on the results of the interviews that we conducted with regard to the position of wh-words and the structure of question-answer pairs. In addition, we conclude this section with a validation of these findings by a Deaf early DGS informant. As explained above, the interviews were initiated by reviewing the videos together, so that the participants could refer back to the questionnaire and explain their previous judgments. Although, prior to the experiment, we asked the participants not to take their respective dialect of DGS into consideration, we found that lexical variants of specific signs, e.g. summer, cinema, and zoo, were repeatedly mentioned as a reason for a less positive judgment. In addition, further signs, such as solution and family,

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were also seen as problematic. One signer did not recognize the sign solution and therefore did not fully understand the content of the relating wh-question. Another signer explained, that he would strictly avoid using the variant of family displayed in the video, as it is a borrowed sign from ASL. Dialectal variation therefore played a decisive role and should always be taken into consideration when creating a questionnaire for DGS signers. Most participants explained that they did not realize the questionnaire was about the position of wh-words. During the interview, however, all of them were able to make quite explicit statements especially with respect to whquestions. Five signers preferred wh-words at the end of the wh-question and labeled it as the more usual variant. The other four signers noted that there is actually no difference between initial and final wh-words in wh-questions and that they could not tell which position they usually use. However, two of them intuitively produced several wh-questions during the interview and always realized the wh-word either sentence finally or doubled. Four signers noted additionally, that initial wh-words may further emphasize the question. The use of wh-doubling in wh-questions was claimed by four signers to be dependent on the specific situation; hence, it was described as not always needed, so that a question including wh-doubling may sometimes appear as odd. Two of the younger participants even mentioned, that they generally avoid wh-doubling and that this is a structure merely used by older signers. Yet, when producing a wh-question during the interview, one of them unconsciously applied wh-doubling. Finally, several signers stated that wh-doubling marks the importance of the question and occurs deliberately to receive a fast answer, often combined with a stronger facial expression. Concerning question-answer pairs, it was rather difficult for most of the participants to clearly reflect on this specific structure. In general, questionanswer pairs were seen as fully acceptable and frequently used in DGS. Interestingly and most convincingly, many signers did not recognize that questionanswer pairs actually contain a question and an answer part. However, there were three signers who mentioned several observations. One signer explained, that wh-doubling intuitively seemed odd in the context of question-answer pairs without providing clear reasons. Another signer pointed out, that she would always place the wh-word at the end of the question part. The realization at the beginning of the question was judged as strange, but still possible, and wh-doubling as the least acceptable variant. As already noticed for wh-questions, she similarly claimed wh-doubling to generally emphasize the question. She further argued that the signer already knows the answer to a question-answer pair, so that the addressee is not expected to respond and the question does not need to be stressed. Concerning the whole question-answer

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123

pair, another signer explained that it represents a structure, which is used in specific contexts as a stylistic device attracting the attention of the addressee. Moreover, the whole question-answer pair was interpreted as one closely connected unit. As already mentioned above, we asked a Deaf early DGS informant to evaluate the findings of the interview sessions. Concerning wh-questions, she shared the intuition that wh-words at the end of a wh-question seem to occupy the default position, while there might be an increasing emphasis on the question with initial wh-words and even more with wh-doubling (see also Grin 2014 for similar results from an evaluation of corpus data). Moreover, she emphasized that wh-doubling is commonly used with wh-questions and is purposely applied to receive a fast answer. Question-answer pairs, on the other hand, mostly display wh-words at the end of the question part, while there are less occurrences with initial wh-words and again less with wh-doubling. Yet, she judged all three variants as acceptable structures, so that wh-doubling is not completely ruled out for question-answer pairs in DGS. In sum, our informant confirmed that our results generally reflected her intuitions. 4.3 Discussion With reference to our two studies on wh-questions and question-answer pairs, we discovered how Deaf DGS signers perceive several aspects of the DGS grammar. We briefly summarize these findings, apply them to the above presented analyses of question-answer pairs in ASL, and add a revised version of the definition of question-answer pairs in sign languages given in Section 3. Based on the pilot study, we expect question-answer pairs in DGS to allow question constituents either resembling wh- or polar questions. Moreover, both variants of question-answer pairs may be embedded as a complement of predicates selecting a declarative clause. Concerning the nonmanual marking, the question constituent is marked by brow raise, while a short head nod is frequently used on the answer constituent. The pilot study further suggested, that wh-words are usually placed at the end of the question constituent, whereas initial and doubled wh-words mark the question for emphasis and are thus less common. In fact, wh-doubling in question-answer pairs was rejected. The questionnaire study revealed that all three realizations of wh-word placement were generally accepted for both wh-questions and question-answer pairs. While no main difference between the judgments of initial and final wh-words appeared, wh-doubling received a slightly more negative rating both with regard to wh-questions and question-answer pairs. Furthermore, the questionnaire did not indicate any restrictions on the choice of wh-words. The interviews, however, suggest an unmarked final wh-word position, whereas

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initial wh-words result in a more marked word order. Finally, wh-doubling was claimed to be an indication of emphasis and therefore not appropriate in the context of question-answer pairs that structurally already convey focus marking. Still, wh-doubling was not rated as completely ruled out or ungrammatical in question-answer pairs, but rather as not matching the signer’s intention. In addition to dialectal variation, there might be another reason that could explain the different results of the questionnaire and the interviews. DGS, as well as other sign languages across Europe, was faced with a long-lasting tradition called oralism or the ‘German Method’ establishing an education system that considered sign languages a primitive communication system, while spoken languages were seen as the more advanced, superior development. As a consequence, the use of sign languages was largely banned at schools for the deaf and exclusively replaced by speech articulation and lip reading (McBurney 2012). Although DGS is acknowledged as a legally recognized language in Germany by now, it is still not self-evident that DGS is used and its grammar being taught in educational settings. Deaf DGS signers therefore are not accustomed to provide judgments on their language, although they do have clear intuitions about the use of DGS. It is possible that our participants were more liberal in their judgments due to these circumstances and it was clearly easier for them to formulate their intuitions in a more relaxed interview situation. Both Wilbur (1996) and Caponigro & Davidson (2011) argue that questionanswer pairs in ASL represent a semantic, prosodic, and syntactic unit that is also confirmed for DGS based on our data. For ASL, they list the special nonmanual marking, the prohibition of wh-doubling, and the possibility to embed the whole sequence under verbs selecting declaratives as specific properties of question-answer pairs. Crucially, Wilbur’s (1996) analysis does not include question constituents, which resemble polar questions. Moreover, the analogy to wh-clefts suggests only a restricted set of wh-words to be possible in question-answer pairs. As explained above, these restrictions cannot be confirmed by our data, as DGS allows polar questions in question-answer pairs and shows no restrictions with respect to the choice of wh-words. Wilbur’s (1996) approach therefore seems to be inappropriate for DGS. Another argument against a cleft-analysis is the fact that DGS allows sentential answer constituents (cf. example (9) above). In general, the data rather support Caponigro & Davidson (2011), whose analysis mostly accounts for our findings. However, they argue for wh-doubling to be ungrammatical in question-answer pairs due to the underlying embedding of the question constituent in ASL. Strikingly, this prohibition of wh-doubling is not reflected in our results. Instead, wh-doubling

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125

only appears as the least preferred, but still acceptable variant that is bound to specific contexts and therefore less acceptable in combination with questionanswer pairs. As mentioned in Section 2, wh-doubling qualifies as a marker of emphasis (Wilbur 2012). Separating emphasis and focus, we do not argue on the grounds of syntactic constraints, but assume a pragmatic clash in case the question constituent is marked for emphasis via wh-doubling, while the answer constituent is marked for information focus, hence evoking less acceptable judgments. Based on these assumptions, we revise our previously given definition of question-answer pairs and include, as a pragmatic constraint, the tendency to avoid question consituents that are emphatically marked: (36) Question-answer pairs (version 2) A question-answer pair is a complex unit consisting of a. a question constituent and b. an answer constituent aiming at foregrounding the answer to indicate information focus. Thus, an additional emphatic marking of the question constituent, e.g. via wh-doubling, is avoided, as it clashes on the pragmatic level. Obviously, more data concerning embedded interrogatives in DGS would be needed to fully account for the syntactic specification of the question constituent. Our studies mainly took into consideration the position of wh-words. Based on the pilot study, we assumed and used a specific nonmanual marking of question-answer pairs and kept their realization constant for the subsequent study. Moreover, the answer constituent generally included only a single noun phrase. In this way, we decreased the variability of the videos, so that differences should be mainly attributed to the specific placement and choice of whwords. Crucially, these aspects such as the variability of nonmanual marking and the possibility of sentential answers still need to be examined to complete the picture. For future research on question-answer pairs, it would also be illuminating to include production studies and corpora analyses investigating the use of question-answer pairs.

5

Conclusion

In this paper, we discussed a common structure in sign languages – so called question-answer pairs – and presented new data from DGS. Previous research mostly considered them in terms of information structure of sign languages

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and it has been argued that question-answer pairs are used as a focus marking strategy. Moreover, different competing analyses were proposed concerning the syntactic structure of question-answer pairs in ASL. While Wilbur (1996) considers question-answer pairs to be wh-clefts, Caponigro & Davidson (2011) analyze them as complex declaratives with an underlying embedded structure. Empirical data from DGS comparing the position of wh-words in wh-questions and question-answer pairs showed that final wh-words might occupy the unmarked position in DGS, while initial wh-words result in a more marked word order. Wh-doubling, on the other hand, is commonly applied, but bound to specific contexts, as it is used for emphasis. In contrast to ASL, wh-doubling is not ruled out for question-answer pairs in DGS, but represents a possible though least preferred variant of realizing the question constituent. We therefore suppose, that the position of wh-words in question-answer pairs is not directly linked to syntactic, but rather to pragmatic constraints. Since questionanswer pairs are used to highlight the answer as new information in the discourse, additional emphasis marking on the question constituent in form of wh-doubling gives rise to a pragmatic clash, hence leading to a decreased acceptability. Due to the facts that (i) our pilot study indicated polar questions to be possible in question-answer pairs and (ii) we could not find any restrictions on the choice of wh-words in question-answer pairs, we argue against Wilbur’s (1996) wh-cleft analysis and support the claims presented in Caponigro & Davidson (2011), providing a pragmatically modified version of their analysis. Still, further research on question-answer pairs is needed to fully account for their specific syntactic structure.

5.1

Notational Conventions

sign s-i-g-n (sign) sign#sign sign-sign ix3

regular sign fingerspelled sign optional sign compound sign one single sign described by more than one word in the glosses pointing sign (usually an extended index finger) used for localizing referents and locations in the signing space

The on- and offset of the line above the glosses indicates the scope of the accompanying nonmanual markers.

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3a< >3b Scope of a role shift; the indices refer to the shifted referents. br br = brow raise bf bf = brow furrow hn hn = head nod hs hs = headshake ht ht = head tilt

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chapter 5

Inferring Meaning from Indirect Answers to Polar Questions: the Contribution of the Rise-Fall-Rise Contour* Marie-Catherine de Marneffe and Judith Tonhauser

1

Introduction

Polar questions like (1Q) can be given direct answers, such as (1A1) or (1A2), or indirect answers, such as (1A3) from Sperber & Wilson 1986, 56. (1) Q: A1: A2: A3:

Do you want some coffee? Yes. No. Coffee would keep me awake.

A yes or no answer to a polar question ?p entails p or ¬p, respectively (assuming, e.g., Krifka’s 2013 anaphoric analysis of response particles). Following Groenendijk & Stokhof 1984, we take a polar question ?p to partition the context set (the set of worlds compatible with the propositions in the common ground of the interlocutors) into two cells: one cell consists of worlds in which p is true, i.e., for (1Q), worlds in which the proposition that the addressee wants some coffee is true, and the other cell consists of worlds in which ¬p is true, i.e., for (1Q), worlds in which the proposition that the addressee does not want some coffee is true. (For alternative analyses of polar questions see AnderBois’ contribution in this volume and references therein.) Yes and no are direct answers to polar questions (as are responses that lexicalize the content of p or ¬p) because they entail a unique cell of the context set without providing additional information.

* For helpful feedback on this research, we thank the participants of Speerlab at The Ohio State University, the audiences at CUNY 2013, at the Questions in Discourse workshop in Stuttgart in 2013, at the University of Munich in 2014 and at the MXPRAG workshop in Berlin in 2015, as well as two anonymous reviewers. We are grateful to Julie McGory and Mike Phelan for recording the stimuli, to Lauren Squires for helpful discussion of the stimuli, and to The Ohio State University for financial support.

© koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004378322_006

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We assume that a response to a polar question ?p addresses the polar question if and only if the response entails or conversationally implicates either p or ¬p. We furthermore assume that a response to a polar question is judged to be acceptable if and only if the response addresses the polar question. The direct answers in (1A1) and (1A2) are thus predicted to be judged to be acceptable in response to the polar question in (1Q) because they entail p and ¬p, respectively. (For an overview on the semantics of questions and answers see Onea & Zimmermann’s contribution in volume 1.) The response in (1A3) does not entail p or ¬p since it is possible to follow (1A3) up with … and I (therefore) would like some coffee as well as with … and I (therefore) wouldn’t like some coffee. If the listener can take the speaker who produced (1A3) in response to the question in (1Q) to be cooperative, then the listener draws the inference that (1A3) must conversationally implicate either p or ¬p. As discussed in the literature on indirect answers (e.g., Clark 1979, Hobbs & Robinson 1979, Hirschberg 1985, Green & Carberry 1992, 1994, 1999, de Marneffe et al. 2009), listeners rely on a variety of cues to draw inferences about whether the intended meaning of the indirect answer to the polar question is a positive one (i.e., ‘yes, I want some coffee’) or a negative one (i.e., ‘no, I don’t want some coffee’). One cue comes from the discourse goals and plans of the interlocutors, as well as their mutual beliefs and shared knowledge. For instance in (1), if it is mutual knowledge to Q and A that A has an interview early in the morning, (1A3) is likely to be interpreted as a negative answer. However, if Q and A have to finish an important job and it is already late in the day, (1A3) is likely to be interpreted as a positive answer. Another cue comes from utterances subsequent to the indirect answer, as discussed in Green & Carberry 1992, 1994, 1999. For instance, if A elaborates on (1A3) with I have an important meeting tomorrow, the listener would conclude that A intended a negative response to the question, but a continuation such as We need to work a few more hours would be taken to indicate a positive response. Green & Carberry (1999, fn. 34) also suggest that the prosodic realization of the indirect answer may provide a cue when they state that “it is an interesting question for future research whether it [prosodic information, MCdM & JT] can help in recognizing the speaker’s intentions”. However, the role of prosody in the interpretation of indirect answers has not yet been systematically explored.1 In this paper, we start to fill this gap by presenting the results of an experiment designed to identify whether and how the prosodic realization

1 See Goodhue & Wagner (2014) on the role of prosody in the interpretation of ‘yes’ and ‘no’ answers to polar questions.

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of an indirect answer to a polar question influences the inference that listeners draw from the indirect answer. The experiment explored American English listeners’ interpretations of indirect answers with scalar adjectives, such as (2B), in response to polar questions with semantically stronger adjectives, such as (2A). The indirect answers were realized either with a neutral contour (H* LL%)2 or with the rise-fall-rise contour (L*+H L-H%), with the pitch accents of the contours realized on the stressed syllable of the adjective. (Both of these contours are explained in section 3.) (2) A: B:

Is your sister beautiful? She’s attractive.

Since beautiful is the stronger scalemate of attractive in the ⟨beautiful, attractive⟩ scale, a listener may infer from B’s answer, by standard Gricean reasoning, that B intended to convey that her sister is attractive but not beautiful, i.e., a negative response. To explore whether prosody influences the interpretation of indirect answers, we exploit the fact that a scalar implicature may arise from indirect answers like that in (2): our experiment was designed to explore whether and how the prosodic realization of the indirect answer with the weaker scalar adjective influences a listeners’ degree of belief in the scalar implicature, i.e., whether the implicature is more or less likely to arise. We chose the rise-fall-rise contour for our investigation since it has been documented extensively with indirect answers and even described to be particularly natural with indirect answers, as opposed to direct answers. Ward & Hirschberg (1985, 769), for example, state that the rise-fall-rise contour “occurs precisely when speakers cannot, or do not wish to, commit themselves to direct responses”. The contour is also ideally suited to our investigation because it is generally taken to conventionally contribute meaning to the utterance on which it is realized (e.g., Ward & Hirschberg 1985, Büring 1997, 2003, Wolter 2003, Constant 2012, Wagner 2012, Wagner et al. 2013). In the next section, we provide relevant empirical and theoretical background on scalar implicatures, including the influence of prosody on scalar implicature generation. Section 3 presents the experiment we conducted and

2 In Tone and Break Indices (ToBI) annotation (Beckman & Ayers Elam 1997), a H* is a high tone pitch accent aligned with the stressed syllable and L*+H is a complex pitch accent made up of a low tone aligned with the stressed syllable and an immediately following high tone. A low intermediate phrase accent that is followed by a low intonational phrase boundary tone is indicated by L-L% and one that is followed by a high intonational phrase boundary tone is indicated by L-H%.

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section 4 discusses the implications of our findings for analyses of the risefall-rise contour and in the context of previous research on prosody and scalar implicatures. Section 5 concludes the paper.

2

Empirical and Theoretical Background on Scalar Implicatures

Scalar implicatures are inferences that listeners may draw from utterances with expressions that form a scale with stronger expressions (e.g., Gazdar 1979, Horn 1972, 1989). For example, the determiners some and all form a so-called Horn scale, represented by ⟨all, some⟩, with all the stronger expression since all X are Y entails some X are Y, but not vice versa. If a speaker chooses to make a statement that contains the semantically weaker expression rather than a statement that contains the semantically stronger expression, the speaker can be taken to implicate that she does not believe that the statement with the stronger expression is true. Thus, a listener who hears an utterance with some may infer that the speaker intended to convey the scalar implicature ‘some but not all’ under the assumption that the speaker had reasons to not use the stronger expression all, for instance because that stronger statement would have been false. For example, a listener who hears an utterance of (3a) may infer that the speaker intended to convey not just the literal meaning of (3a) given in (3b), but rather the meaning in (3c), which is the literal meaning enriched with the scalar implicature. (3) a. I like some tango orchestras. b. I like some (and possibly all) tango orchestras. c. I like some but not all tango orchestras. Gradable adjectives also form scales. For instance, the adjectives beautiful and attractive that were featured in example (2) form the scale ⟨beautiful, attractive⟩ since beautiful is stronger than attractive. (We present two diagnostics for identifying pairs of adjectives that stand in this strength relationship in section 3.2.1.) Given that the two adjectives form a scale, it follows that a listener who hears B’s response to A’s question in (2), repeated below for convenience, may infer that B intended to convey the scalar implicature ‘attractive but not beautiful’, for example because a stronger statement (e.g., Yes or She’s beautiful) would have been false. (2) A: B:

Is your sister beautiful? She’s attractive.

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Scalar implicatures do not arise obligatorily. In fact, a hallmark of scalar implicatures is that they are cancelable. Thus, B in (2) could follow up her utterance with … and, yeah, in fact, she’s beautiful, without contradiction. Recent research shows that several factors are at play in whether an utterance with a weaker scalar expression gives rise to an implicature. One of these factors is the scalar expression itself. Comparisons across different types of scalar expressions reveal that quantificational determiners like some are much more likely to give rise to scalar implicatures than scalar adjectives (Doran et al. 2012, van Tiel et al. 2016); scalar implicature rates for adjectives in these studies are as low as 4 %. Other factors include what the listener believes the speaker’s knowledge state to be (Goodman & Stuhlmüller 2013), the form of the scalar expression (e.g., some versus some of versus sm; Thorward 2009, Degen 2015), the experimental paradigm (Geurts & Pouscoulous 2009, Degen & Goodman 2014), and whether the scalar expression is realized with a pitch accent or as part of the focus of the utterance (e.g., Chevallier et al. 2008, Thorward 2009, Zondervan 2010, Schwarz et al. To appear). Since the prosodic realization of the utterances that give rise to scalar implicatures is of direct concern to this paper, we review these studies in more detail. Chevallier et al. (2008) and Schwarz et al. (To appear) focused on the disjunction ‘or’ in French and English, respectively. In Chevallier et al.’s study, French participants read five-letter-strings (a word, e.g., ‘TABLE’ or a non-word, e.g., ‘JAMIS’) and would hear a disjunctive or a conjunctive statement about the letters in the string (e.g., ‘There is an A or a B’ or ‘There is an A and a C’, translated from French). In some of these utterances, the ‘or’ or ‘and’ received “contrastive stress” (p. 1747). (Chevallier et al. do not give further information about the prosody.) Participants were asked to judge whether the statement was true or false. In Schwarz et al.’s study, participants heard English sentences such as Mary will invite Fred or Sam to the barbecue in which a contrastive pitch accent (L+H*) was realized either on the auxiliary (will) or the disjunction or. All content words were uttered with a H* accent. Participants were presented in writing with two interpretations (‘Mary will invite Fred or Sam but not both’ and ‘Mary will invite Fred or Sam or possibly both’) and were asked to select the right one. Both Chevallier et al. (2008) and Schwarz et al. (To appear) found that the disjunction is more often interpreted as exclusive (‘A or B, but not both’) rather than inclusive (‘A or B, and possibly both’) when it is realized with a pitch accent. Zondervan (2010) explored the hypothesis that scalar implicatures only arise when the scalar expression is part of the information focus of the sentence (van Kuppevelt 1996, van Rooij 2002). He examined the scalar expression ‘or’ in Dutch. One of his experiments manipulated information focus marked by

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prosody as well as context. Participants read a context, then heard a target sentence (containing the disjunction), which they had to judge as true or false. Context varied between the focus and non-focus conditions. The location of the pitch accent differed from Chevallier et al. 2008 and Schwarz et al. To appear: in the focus condition, the two elements of the disjunction received a pitch accent (H*), but not the scalar expression itself (e.g., ‘Paola took an APPLE or a PEAR from the fruit section’ translated from Dutch); in the non-focus condition, the subject of the sentence received a pitch accent (H*) (e.g., ‘PAOLA took an apple or a pear from the fruit section’ translated from Dutch). In line with previous results, Zondervan found a higher implicature rate in the focus condition. Thorward (2009) investigated how pitch accent interacts with implicature in the case of English some. In her experiment 2, participants watched the experimenter move 3 or 4 (out of 4) animals over a fence in a barnyard. A puppet then described the scene, e.g., Some cats jumped over the fence, and participants were asked to judge whether the puppet’s utterance was an accurate description of the scene. The location of the pitch accent varied in the target sentence: either the determiner some received a pitch accent (H* or L+H*) or the noun describing the animal received a pitch accent (L+H*). For the scenarios in which all the animals jumped over the fence, adults rejected the puppet’s utterance more often when some was realized with a pitch accent than when it was not, confirming that pitch accent plays a role in implicature generation. These studies show that scalar implicature generation is sensitive to prosody. Specifically, they show that scalar implicature generation is sensitive to whether the weaker scalar expression is realized with a pitch accent or as part of the focus. Building on these results, the experiment we describe in the next section explored whether and how the prosodic realization of indirect answers with weaker scalar expressions influences the interpretation of the indirect answer. .

3

Experiment

The experiment was designed to explore how the response that listeners infer from an indirect answer to a polar question is influenced by the prosody of the indirect answer. 3.1 Participants 63 individuals recruited on Amazon’s Mechanical Turk platform participated in the experiment. We removed the data of 2 participants who did not consent,

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of 2 participants who did not self-identify as speakers of American English, of 1 participant who did not give a response to all dialogues, and of 1 participant who gave wrong answers to two of the three control dialogues. We analyzed the data of the remaining 57 participants (30 female, 26 male, 1 undeclared; ages: 18–68, median age: 31.5). 3.2 Materials Stimuli in the experiment consisted of spoken, two-turn dialogues between two individuals, Mike and Julie. In each dialogue, Mike asks Julie a polar question formed from a copula clause with an adjective and Julie responds with a copula clause. The target stimuli were formed from sixteen pairs of adjectives with the following two properties: i) the adjectives were interpreted on the same scale and ii) one adjective was semantically stronger than the other one. In the target stimuli, Mike’s question realized the stronger adjective (e.g., Is your sister beautiful?) and Julie’s indirect answer realized the weaker adjective (e.g., She’s attractive). 3.2.1 Norming Studies for the Selection of Adjectives We used two diagnostics to identify suitable pairs of adjectives. The first diagnostic is the ‘even’ diagnostic: two adjectives W (‘weaker’) and S (‘stronger’) are interpreted on the same scale, with S stronger than W, if and only if a sentence containing W can be followed up with ‘even S’ and a sentence containing S cannot be followed up with ‘even W ’. The ‘even’ diagnostic is applied in (4) to the pair ⟨beautiful, attractive⟩: (4) a. My sister is attractive, even beautiful. b. My sister is beautiful, #even attractive. The second diagnostic is the ‘but not’ diagnostic from Horn 1972: two adjectives W and S are interpreted on the same scale, with S stronger than W, if and only if a sentence with W can be followed up with a denial of S and a sentence with S cannot be followed with a denial of W. The ‘but not’ diagnostic is applied in (5) to the pair ⟨beautiful, attractive⟩: (5) a. Samantha is attractive, but not beautiful. b. Samantha is beautiful, #but not attractive. We ran two norming studies to identify adjective pairs that pass these two diagnostics with a set of 30 adjective pairs that a semantically trained native speaker of American English had previously judged to pass the two diagnos-

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tics.3 Appendix 6 gives the 30 adjective pairs, the carrier sentences used in the norming studies and the results of the two norming studies for each pair. All of the experiments discussed in this paper were run on Amazon’s Mechanical Turk platform. To participate, individuals had to have US IP addresses and also had to have completed at least 1,000 Human Intelligence Tasks (HIT s) with an overall approval rate of at least 97%. Participants completed a short survey about their age, their native languages and, if English was their native language, whether they spoke American English (as opposed to, e.g., Indian or Australian English). Participants were told that they would be paid regardless of how they responded to the survey questions. We only analyzed responses by participants who self-identified as native speakers of American English. 3.2.1.1 Norming Study 1 In the first norming study, we used the ‘even’ diagnostic to identify pairs of adjectives that are interpretable on the same scale, with one adjective stronger than the other. Participants. 41 individuals participated in the experiment. We discarded the data of 1 participant who did not consent, 2 participants who gave incorrect answers to more than 2 of the 5 control stimuli and 8 participants who did not provide an answer to any of the 5 control stimuli. We analyzed the data of the remaining 30 participants (11 female, 19 male; ages: 18–62, median age: 38.5). Stimuli. The written stimuli consisted of two-turn discourses in which the first speaker uttered a sentence with an adjective, and the second speaker uttered a follow-up consisting of even and the other adjective, as in Figure 1. For each of the 30 adjective pairs, we created one target stimulus where the first utterance realized the adjective that was hypothesized to be weaker and the second utter-

3 Some of the adjective pairs that we tested in the norming studies were used in previous studies on scalar items. Not all of these pairs passed both of our diagnostics. Specifically, the pairs ⟨unforgettable, memorable⟩, ⟨horrific, unsettling⟩, ⟨ridiculous, silly⟩, which were used in van Tiel et al. 2016, and the pair ⟨obnoxious, annoying⟩, which was used in Doran et al. 2009, did not pass one or both diagnostics. Furthermore, we relied on the adjective pair ⟨tight, snug⟩, used in Doran et al. 2009 and van Tiel et al. 2016, in a control stimulus in norming study 1: the sentence Jeff’s pants are snug. They’re even tight was hypothesized to be acceptable, but the corresponding stimulus was judged to be odd by 7 out of the 16 participants that judged that item. While the findings of our norming studies may in part be due to the carrier sentences we used, these observations minimally suggest it is sensible for experimental investigations of scalar implicatures to identify whether native speakers of the relevant language agree that two scalar adjectives stand in the relevant strength relationship.

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Sample stimulus and response task in norming study 1

ance realized even and the adjective that was hypothesized to be stronger, and a target stimulus with the reverse order of the adjectives. In addition to the 60 target stimuli, there were 5 control stimuli formed from clearly acceptable sentences (e.g., Blair’s room is comfortable. It’s even cozy.) and 5 that were formed from clearly unacceptable sentences (e.g., Elle’s exam scores were perfect. They were even below average). The 60 target stimuli were distributed across two lists so that each list contained one of the two target stimuli of each adjective pair. Each list had 15 target stimuli that were hypothesized to be acceptable and 15 that were hypothesized to be unacceptable. Both lists were divided into two sub-lists of 15 target stimuli (roughly half of which were hypothesized to be acceptable). Each sub-list also had five control stimuli (roughly half of which were acceptable). The stimuli in each sub-list were presented to the participants in a pseudo-randomized order. Each participant was assigned to a list, and could either complete one or both sub-lists of that list. Procedure. Participants were told that they would read small exchanges between two friends, Mike and Jack, and that Jack is the kind of guy who likes to trump whatever Mike says. They were also told that Jack doesn’t master English very well, and so he sometimes says something odd. Participants read twoturn dialogues between Jack and Mike, and were asked to judge whether Jack’s response to Mike was odd, by selecting either ‘odd’ or ‘not odd’, as illustrated in Figure 1. At the beginning of the experiment, each participant completed two training examples for which the correct answers were given. Results. Each target stimulus received between 6 and 8 judgments (median: 7). For each target stimulus, we determined whether it was judged to be acceptable or unacceptable by identifying whether the majority of judgments were ‘not odd’ or ‘odd’, respectively. For an adjective pair to pass the ‘even’ diagnos-

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tic, the target stimulus in which the stronger adjective followed even had to be judged to be acceptable, and the target stimulus in which the weaker adjective followed even had to be judged unacceptable. Of the 30 adjective pairs, 24 passed the ‘even’ test. 3.2.1.2 Norming Study 2 In the second norming study, we used the ‘but not’ diagnostic to identify pairs of adjectives that are interpretable on the same scale, with one adjective stronger than the other. Participants. 36 individuals participated in the experiment. We discarded the data of 3 participants who did not consent, 1 participant who did not indicate that (s)he was an American English speaker, and 1 participant who did not correctly answer at least 3 of the 5 control stimuli. We analyzed the data of the remaining 31 participants (14 female, 17 male; ages: 25–60, median age: 36). Stimuli. Target stimuli consisted of sentences like those in (5). For each of the 30 adjective pairs, we created one target sentence where the adjective that was hypothesized to be weaker was followed by but not and the adjective that was hypothesized to be stronger, as in (5a), and a target sentence with the reverse order of the adjectives, as in (5b). In addition to the 60 target stimuli, there were 5 control stimuli that were clearly non-contradictory sentences (e.g., Jeff’s mother is happy and creative.) and 5 that were clearly contradictory sentences (e.g., Jane’s blouse is new and used.). The 60 target sentences were distributed across two lists so that each list contained one of the two target sentences of each adjective pair. Each list had 15 target sentences that were hypothesized to be contradictory and 15 that were hypothesized to be non-contradictory. Both lists were divided into two sub-lists of 15 target sentences (roughly half of which were hypothesized to be contradictory). Each sub-list also had five control sentences (roughly half of which were contradictory). The stimuli in each sub-list were presented to the participants in a pseudo-randomized order. Each participant was assigned to a list, and could either complete one or both sub-lists of that list. Procedure. Participants read sentences and were asked to judge whether the sentence were contradictory or not, by selecting either ‘contradictory’ or ‘not contradictory’, as illustrated in Figure 2. At the beginning of the experiment, each participant completed two training examples for which the correct answers were given.

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Sample stimulus and response task in norming study 2

Results. Each target sentence received between 6 and 9 judgments (median: 7). For each target sentence, we determined whether it was judged to be acceptable or unacceptable by identifying whether the majority of judgments for the target sentence were ‘not contradictory’ or ‘contradictory’, respectively. For an adjective pair to pass the ‘but not’ diagnostic, the target sentence in which the stronger adjective followed but not had to be judged to be acceptable, and the target sentence in which the weaker adjective followed but not had to be judged unacceptable. Of the 30 adjective pairs, 24 passed the ‘but not’ test. 3.2.1.3 Selection of Adjective Pairs Of the 30 adjective pairs, 19 passed both the ‘even’ and the ‘but not’ diagnostic. 16 of these adjectives were used in the experiment.4 These adjective pairs are given in Appendix 7 with the carrier sentences used in the experiment. 3.2.2 Types of Stimuli and Preparation of Prosodic Stimuli The stimuli in the experiment consisted of two-turn, spoken discourses: a polar question formed from a copula sentence with an adjective and a copula sentence answer with an adjective. The stimuli were recorded in a soundattenuated booth with two native speakers of American English trained in MAE ToBI. The polar questions were all produced with a low tone pitch accent on the stressed syllable of the adjective, a high intermediate phrase accent and a high intonational phrase boundary tone (L* H-H%). In the target stimuli, the stronger adjective of a pair occurred in the polar question and the weaker adjective of the pair occurred in the indirect answer, as in (2), repeated here for convenience.

4 The adjective pairs were also used in a separate experiment designed to explore whether personal experience influences the listeners’ degree of belief in the scalar implicature. Since the relevant manipulation could not be implemented for three adjective pairs, these adjective pairs were excluded from further consideration in the experiment discussed in this paper.

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Is your sister beautiful? She’s attractive.

The answers of the target stimuli were recorded with one of two contours, resulting in a total of 32 target stimuli (two for each of the 16 pairs of adjectives). The first, ‘neutral’ contour consisted of a high tone pitch accent on the stressed syllable of the adjective, a low intermediate phrase accent and a low intonational phrase boundary tone (H* L-L%). The second, ‘rise-fall-rise’ contour consisted of a complex pitch accent made up of a low tone aligned with the stressed syllable of the adjective and an immediately following high tone, a low intermediate phrase accent and a high intonational phrase boundary tone (L*+H L-H%). The thirty adjective pairs from which the 16 adjective pairs were chosen for the experiment were all designed such that the stressed syllable of the weaker adjective was followed by at least one unstressed syllable, and therefore the weaker adjective had sufficient segmental material on which to realize this complex contour. The two contours are illustrated in Figure 3. In the filler stimuli, in contrast to the target stimuli, the weaker adjective of a pair of adjectives occurred in the polar question and the stronger adjective of the pair occurred in the answer, as in (6). Thus, there were a total of 16 filler stimuli, one for each adjective pair. (6) A: B:

Is your sister attractive? She’s beautiful.

In the six control stimuli, the adjectives realized in the polar question and the answer were antonyms, as in (7): (7) A: B:

Was your suitcase light? It was heavy.

The answers of filler and control stimuli were recorded only in the neutral contour. Since in the filler stimuli the meaning of the adjective in the answer was stronger than the meaning of the adjective in the question, we hypothesized that listeners would be able to infer a positive response solely on the basis of the meanings of the adjectives. Thus, we included the filler stimuli to distract participants from the prosody manipulation present in the target stimuli. The control stimuli, on the other hand, were included to be able to assess whether participants were paying attention to the task. The stimuli are available at https:// github.com/mcdm/QiD2017IndirectAnswerProsody/tree/master/sounds.

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Two utterances of It was strenuous with the neutral contour (upper panel) and the rise-fall-rise contour (lower panel)

For each adjective pair, there were three stimuli (two target stimuli and one filler stimulus), for a total of 48 target-or-filler stimuli. We distributed these 48 target-or-filler stimuli across three lists so that each adjective pair occurred once in each list (either as a target or as a filler stimulus). Each of the three lists thus had 16 target-or-filler stimuli: 5 or 6 target stimuli with the neutral contour, 5 or 6 target stimuli with the rise-fall-rise contour, and 5 or 6 filler stimuli. Furthermore, each list had 6 control stimuli, for a total of 22 stimuli per list. The order of the stimuli in the three lists was pseudo-randomized. We then created

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Sample stimulus and response task in the experiment

3 additional lists by reversing the order of the stimuli. Each of these 6 lists were split into two sub-lists (with roughly half of the target, filler and control stimuli of the list). A participant was assigned to a list, and could complete either one or both of the two sub-lists of that list. 3.3 Procedure Participants were told that two friends, Julie and Mike, haven’t seen each other for a while, that they are catching up over coffee and that Mike asks Julie questions to which she responds. Participants were instructed to listen to each discourse between Mike and Julie, and then to respond to a question about what Julie meant with her response; specifically, participants were asked whether she meant to convey the meaning of the adjective in Mike’s question. Participants could listen to each discourse as often as they wanted. Participants gave their response on a 7-point Likert scale labeled at four points: 1/Definitely No, 3/Perhaps No, 5/Perhaps Yes, 7/Definitely Yes. We assume that a participant’s degree of belief in the scalar implicature is stronger the lower the response is. Figure 4 illustrates a sample stimulus and response task. Since the adjectives realized in the control stimuli are antonyms, we expected the control stimuli to receive negative responses. (We took a correct answer to a control dialogue to be 1/Definitely No.) For the filler stimuli, on the other hand, we expected positive responses since the answer entails a positive response to the polar question. Given that Doran et al. (2012) and van Tiel et al. (2016) find relatively low implicature rates for scalar adjectives, we expected the target stimuli that were realized with the neutral contour to receive less positive responses than the filler stimuli but not overwhelmingly many negative responses. Finally, based on the intuitions reported to us by native speakers of American English, we expected that the target stimuli that were realized with the rise-fall-rise contour would receive more negative responses than the target stimuli with the neutral contour.

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Distribution of responses to filler and target stimuli in the experiment

3.4 Results Except for one target stimulus for which we only had 9 responses, we obtained 10 responses for each target and filler stimulus. The bar graph in Figure 5 shows how often each response option was chosen for the target stimuli with the neutral and rise-fall-rise (RFR) contours and the filler stimuli. As expected, filler stimuli received highly positive responses (mean response: 6.67) and target stimuli receive less positive responses than the filler stimuli, though still largely positive responses. This result is in line with the finding in the previous literature (Doran et al. 2012, van Tiel et al. 2016) that utterances with gradable adjectives have relatively low implicature rates compared to other scalar expressions.5 Also as expected, the target stimuli with

5 To compare the rate with which implicatures arose in this experiment with the implicature rates for scalar adjectives reported in the previous literature, we recoded the responses as a ‘1’ (implicature) if participants responded 1/Definitely No, 2 or 3/Possibly No, and as a ‘0’ (no implicature) if they responded 5/Possibly Yes, 6 or 7/Definitely Yes (responses of ‘4’ were discarded). With this recoding, we found an implicature rate of 20 % for target stimuli with the rise-fall-rise contour and of 13% for target stimuli with the neutral contour. This implicature

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the rise-fall-rise contour received less positive responses than the target stimuli with the neutral contour (mean response 4.77 versus 5.04, respectively). For the target stimuli, we fitted an ordinal mixed-effects regression analysis predicting response from contour with by-participant and by-item random intercepts and random slopes for contour, using the clmm R ordinal package Christensen (2013) (R version 2.15.2). We found a significant effect of contour: responses to target stimuli with the rise-fall-rise contour were significantly lower than responses to target stimuli with the neutral contour (β = -0.63, SE = 0.24, z = -2.60, p < .01). This finding suggests that the rise-fall-rise contour strengthens the degree of belief in the scalar implicature over the neutral contour: listeners are more likely to infer that the speaker intended a negative answer to a polar question when the speaker realized their indirect answer with the rise-fall-rise contour than with the neutral one. Thus, in our dialogues, the prosodic realization of an indirect answer to a polar question affected its interpretation, with the rise-fallrise contour leading listeners more toward negative answers than the neutral contour. 3.5 Discussion Our experiment investigated the interpretation of indirect answers with scalar adjectives in response to polar questions with semantically stronger adjectives. The result of the experiment shows that when the indirect answer is realized with the rise-fall-rise contour, a listener is more likely to interpret the answer as conveying a negative response to the polar question than when the answer is realized with the neutral contour. More generally, what these results show is that the prosodic realization of an indirect answer can indeed be a cue to the intended interpretation of the indirect answer with respect to the polar question. Our result provides evidence that a polar question ?p that is responded to with an indirect answer with meaning q that neither entails p nor ¬p may be more likely to be taken to mean ¬p when the indirect answer is realized with the rise-fall-rise contour than with the neutral contour. We have thus provided confirmation for the speculation in Green & Carberry 1999, fn34 that the prosody of an indirect answer “can help in recognizing the speaker’s intentions”. One avenue for future investigation is whether our findings generalize to pairs of questions and indirect answers that do not involve scalar adjectives.

rate is somewhat higher than that reported for gradable adjectives in van Tiel et al. 2016 but comparable to that reported in Doran et al. 2012.

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Do the two contours we have investigated lead to similar effects whenever the two contours are realized on indirect answers to polar questions, regardless of whether the indirect answer realizes a gradable adjective, or are these effects particular to the kinds of question-answer pairs we have investigated? For instance, is the indirect answer in (1A3), repeated below for convenience, more likely to be interpreted as a negative response when realized with the risefall-rise contour than with the neutral contour? (1) Q: Do you want some coffee? A3: Coffee would keep me awake. An answer to this question depends to a large extent on the answer to a question we have largely side-stepped in this paper until this point, namely the question of which meaning the rise-fall-rise contour contributes to an utterance, and how that meaning interacts with the interpretation of indirect answers. In the next section, we discuss the meaning of the rise-fall-rise contour in view of our experimental findings, and also address the contribution of our work to scalar implicature generation more generally.

4

Implications of the Experimental Finding

4.1 The Meaning of the Rise-Fall-Rise Contour The key finding of our experiment is that indirect answers are interpreted more negatively in response to polar questions when the answer is realized with the rise-fall-rise contour than when it is realized with the neutral contour. In this section, we review three analyses of the meaning of the rise-fall-rise contour with respect to whether they predict this finding.6 See Büring’s contribution in this volume for general background on the relationship between questions and focus prosody. 4.1.1 Ward and Hirschberg 1985 In their seminal work on the meaning of the rise-fall-rise contour, Ward & Hirschberg (1985) proposed that the contour conventionally implicates speaker

6 For reasons of space, we only discuss papers whose primary focus is the rise-fall-rise contour, to the exclusion of Büring 2003, Oshima 2008 and Wagner 2012. See Wolter 2003 for a proposal that the rise-fall-rise contour is licensed only on declarative utterances that fail to resolve an issue.

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uncertainty with respect to a scale evoked in the discourse (p. 765): uncertainty about whether it is appropriate to evoke a scale at all (type I uncertainty), uncertainty about which scale to choose, given that some scale is appropriate (type II), or, given some scale S, uncertainty about the choice of some value on S (type III). Ward & Hirschberg (1985) also proposed two felicity conditions for the rise-fall-rise contour (p. 747): some item in the utterance with the contour must be perceived as linked by a scalar relationship with its context, and it must be contextually plausible that the speaker is uncertain with respect to the scale or scalar value evoked. The first felicity condition is satisfied by our target stimuli since the scalar adjectives in the polar question and the indirect answers were chosen to be interpreted on the same scale, with the adjective in the question stronger than the adjective in the answer; cf., example (2). (2) A: B:

Is your sister beautiful? She’s attractive.

From the fact that the gradable adjectives in our target stimuli evoke a conspicuous scale, we conclude that it is not type I or II uncertainty that is conveyed by the rise-fall-rise contour in our target stimuli. While none of the examples discussed in Ward & Hirschberg 1985 mirror our target stimuli exactly, there are some examples that also feature a polar question with a semantically stronger expression than that realized in the indirect answer. In (8), their (25a), the expression the first chapter in the polar question is stronger than the expression the first half of the first chapter in the indirect answer. (We follow Ward and Hirschberg’s convention of annotating examples uttered with the rise-fallrise contour using \ to indicate the L*+H pitch accent and / to indicate the final rise, i.e., L-H%.) And in (9), their (61a), the expression a hundred in the polar question is stronger than the expression a ninety-eight in the indirect answer. (8) A: B:

Did you read the first chapter? I read the first \half/ of it. (Ward & Hirschberg 1985, 758)

(9) A: B:

Did she get a hundred on the midterm? She got a ninety-\eight/. (Ward & Hirschberg 1985, 767)

Example (9) is discussed in Ward & Hirschberg 1985 as illustrating type III uncertainty: “B might be uncertain about whether ninety-eight and a hundred are close enough (on a cardinal scale) for A’s purposes” (p. 767). Although Ward

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and Hirschberg do not discuss the type of uncertainty involved in example (8), it is plausible that here, too, B conveys uncertainty about whether reading the first half of the first chapter is enough for A’s purposes (see Figure 4 in Ward & Hirschberg 1985 for the scale involved in this example). Applied to our target stimuli, Ward and Hirschberg’s proposal predicts that, when B realizes their utterance with the rise-fall-rise contour, B is uncertain about the choice of the weaker adjective on the scale evoked by the two adjectives. Specifically, given the examples in (8) and (9), one possibility is that B conveys that she is uncertain about whether the weaker adjective is close enough, for A’s purposes, on the scale evoked by the adjectives to the stronger adjective. Thus, under Ward and Hirschberg’s account, B’s utterance with the rise-fall-rise contour in (2) might convey that B is uncertain whether attractive is close enough to beautiful for A’s purposes. This meaning (a conventional implicature according to Ward and Hirschberg) would be absent when B realizes their utterance with the neutral contour. Does this account predict our experimental finding? That is, when B conveys this kind of uncertainty, does that strengthen a listener’s degree of belief that B meant to deny the stronger adjective over and above what the utterance with the neutral contour conveys? It could, possibly, if we make the additional assumption that it only makes sense for B to convey this kind of uncertainty when the weaker adjective is the strongest value on the relevant scale that she is committed to. This assumption is plausible since it is implausible for a speaker to convey a lower value on a scale and uncertainty about whether that value is close enough to the higher value if the speaker was committed to the higher value and could have just uttered the stronger adjective to convey the higher value. So, in example (2), this would mean that using the rise-fall-rise contour not only conveys that B is uncertain whether attractive is close enough to beautiful for A’s purposes, but also that attractive is the strongest value on the relevant scale that B is committed to. Thus, under this additional assumption, B’s use of the rise-fall-rise contour conveys that B is not committed to the stronger adjective. There are two ways to take the implication that B conveys that she is not committed to the stronger adjective. A first possibility is to strengthen this implication to the implication that B conveys that she is committed to the stronger adjective being false (cf., Sauerland’s 2005 epistemic step). But, if this was the case, we would expect our participants to have given many negative responses to the target stimuli with the rise-fall-rise contour in our experiment (cf., Figure 5). Since that is not the case (recall that the response mean for these stimuli is 4.77), it does not seem plausible that listeners take B to convey that the stronger adjective is false. A second possibility is that the implication that

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B conveys that they are not committed to the stronger adjective is taken as just that: B may or may not be committed to the stronger adjective. But in this case we do not expect listeners to interpret B’s utterances with the rise-fall-rise contour as more negative than B’s utterances with the neutral contour, contrary to our finding. We therefore conclude that Ward and Hirschberg’s (1985) account does not predict our finding. 4.1.2 Constant 2012 Constant (2012) proposed that the rise-fall-rise contour is a focus quantifier over alternatives of the uttered sentence that remain assertable after the utterance has been made; the relevant alternatives that are quantified over are called ‘post-assertion alternatives’. Specifically, Constant proposed that the contour presupposes that there are post-assertion alternatives and conventionally implicates that the speaker cannot safely claim any of these alternatives. In (10), for instance, John is the focus of B’s utterance and alternatives to the uttered sentence are of the form X liked the movie, with X an individual from a contextually restricted set (e.g., the set consisting of B and his friends). The asserted content of (10B) is that John liked the movie and this proposition is removed from the set of alternatives to obtain the post-assertion alternatives, which is a set of propositions of the form X liked the movie, with X a friend of B other than John. By using the rise-fall-rise contour, the speaker conventionally implicates that none of the post-assertion alternatives can be safely claimed, for example because the speaker knows that the other friends didn’t like the movie, or because the speaker doesn’t know whether the other friends liked the movie. (We continue to annotate the rise-fall-rise contour using the \ / notation.) (10) A: B:

Did your friends like the movie? \John/ liked it. (adapted from Constant 2012, 414)

In Constant’s example (26a), given in (11), the rise-fall-rise contour is realized on the adjective good, which is a weaker adjective than, for instance, perfect (no context is given for this example): (11) The food was \good/. (adapted from Constant 2012, 414) According to Constant 2012, 415, the relevant alternative propositions for this example are of the form The food was X, including The food was {perfect | good | mediocre | bad}, i.e., alternatives on a scale of quality. The rise-fall-rise contour is felicitous in (11) because “the fact that the food was good doesn’t resolve a

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relevant alternative, like The food was perfect” (p. 415).7 In other words, the risefall-rise contour is felicitous in (11) because the set of post-assertion alternatives is not empty: the literal meaning of (11) does not resolve all of the relevant alternatives; only the alternatives The food was {good | mediocre | bad} are resolved. By using the rise-fall-rise contour in (11), the speaker conventionally implicates that the post-assertion alternative, here the proposition that the food was perfect, cannot be safely claimed, for example, because the speaker takes it to be false. Applied to our target stimuli, Constant’s account predicts that, when B realizes their utterance with the rise-fall-rise contour, B conventionally implicates that post-assertion alternatives cannot be safely claimed. In example (2), for instance, the relevant alternatives could be propositions of the form She is {beautiful | attractive | plain | ugly}. The literal meaning of B’s utterance of She’s attractive resolves all of the alternatives except for {She’s beautiful}, which therefore is the post-assertion alternative that B conventionally implicates cannot be safely claimed, e.g., because the speaker takes it to be false. When B realizes their utterance with the neutral contour, this conventional implicature is absent. Does this account predict our experimental finding? If the post-assertion alternative with the stronger adjective (e.g., She’s beautiful) cannot be safely claimed because it is false, we expect B’s indirect answer utterances with the rise-fall-rise contour to be interpreted by our participants as denying the stronger adjective. Instead, what we found is that B’s indirect answer utterances with the rise-fall-rise contour receive largely positive interpretations, as already mentioned in our discussion of Ward and Hirschberg’s analysis in the previous section. This observation suggests that Constant’s analysis may make too strong predictions for our target stimuli. What if, instead, the post-assertion alternative cannot be safely claimed by B because B does not know whether it is true? In that case, Constant’s analysis does not predict that B’s utterances with the rise-fall-rise contour are interpreted as more negative than B’s utterances with the neutral contour.8 We therefore conclude that Constant’s 2012 account does not predict our experimental finding.

7 According to Constant 2012, 415, a proposition p resolves a proposition q if p → q or p → ¬q. 8 The same reasoning applies when the set of post-assertion alternatives contains more than one alternative, e.g., She is {drop dead gorgeous | beautiful}, where we take drop dead gorgeous to be stronger than beautiful.

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4.1.3 Wagner et al. 2013 According to Wagner et al. (2013, 142), when a speaker utters a sentence that denotes proposition p and realizes that utterance with the rise-fall-rise contour, the speaker asserts p and considers p to be only an incomplete answer to the question under discussion. In (12), for instance, the question under discussion is the content question uttered by Q. Since A realizes their answer with the rise-fall-rise contour, A conveys that p, the proposition that John solved the problem, is a partial answer to the question under discussion, i.e., other people may also have solved the problem. Wagner and his colleagues assumed that if A had realized the utterance John did with the neutral contour (with a pitch accent on John), this would have implied that the answer was exhaustive, i.e., that “no one else but John solved the problem” (p. 142). (12) Q: A:

Who solved the problem? \John/ did. (adapted from Wagner et al. 2013, 142)

To apply Wagner et al.’s analysis to our target stimuli, we first have to determine which question under discussion the utterance with the rise-fall-rise contour might be a partial answer to. (On questions under discussion and their relation to prosody see, e.g., Roberts 2012, Büring 2003, Onea 2016, Simons et al. 2017 as well as Büring’s contribution in this volume.) In contrast to (12), where the overt interrogative is the relevant question under discussion, it is not plausible to assume that the polar question in our target stimuli (e.g., Is your sister beautiful? in (2)) is the relevant question under discussion since the indirect answer (e.g., She’s attractive in (2)) is not a partial answer to that question. We assume, instead, that the question under discussion in our target stimuli is implicit and, in particular, is a question to which the polar question is a sub-question (i.e., the implicit question under discussion entails the polar question; cf. Roberts 2012). What this means is that a complete answer to the implicit question under discussion entails an answer to the polar question, and an answer to the polar question is a partial answer to the implicit question under discussion. For instance, we assume that the implicit question under discussion for the dialogue in (2) is Is your sister datable?, with possible sub-questions as in (13). A combination of an answer to each of the sub-questions constitutes an answer to the question under discussion. We assume that both the question ‘Is your sister beautiful?’ and the question ‘Is your sister attractive?’ are part of this strategy of questions: the first is part of the strategy because it is the overt interrogative uttered by A; the second is part of the strategy because it is the question to which B’s answer is a direct answer.

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(13)

According to Wagner et al.’s analysis, when B responds to the polar question (e.g., Is your sister beautiful?) with the indirect answer (e.g., She’s attractive) realized with the rise-fall-rise contour, B conveys that their answer to the question under discussion (e.g., Is your sister datable?) is partially answered. For instance, in our running example (2), the question under discussion is partially answered because the answer She’s attractive is an answer to a sub-question of the question under discussion (namely to the implicit question ‘Is your sister attractive?’). At the same time, other sub-questions are not yet answered, thereby rendering B’s answer a partial answer to the question under discussion. When B realizes their indirect answer with the neutral contour, the implication that the answer is a partial answer to some question under discussion does not arise. Does this account predict our experimental finding? That is, does the fact that B’s use of the rise-fall-rise contour implies that the question under discussion is only partially answered strengthen a listener’s degree of belief that B meant to deny the stronger adjective over and above what the utterance with the neutral contour conveys? That does not seem to be the case: B being committed to this implication is compatible both with B being committed to the stronger adjective and with B denying the stronger adjective. Consider example (2): if B conveys, by using the rise-fall-rise contour, that the proposition that the sister is attractive is only a partial answer to the question under discussion of whether the sister is datable, then B may still be committed to the sister being beautiful or to the sister not being beautiful. Since the meaning of the rise-fallrise contour, under Wagner et al.’s analysis does not influence B’s commitment state to the meaning of the stronger adjective, we conclude that Wagner et al.’s analysis does not account for our experimental finding. 4.1.4 Summary Given our experimental finding in section 3, a fruitful avenue for future research on indirect answers is to look for cues to the interpretation of an indirect answer in the prosodic realization of the indirect answer. However, in order to study how the prosodic realization of an indirect answer may influence the interpretation of the indirect answer, it is vital to understand the contribution to meaning that a particular prosody makes. In the previous sections,

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we have reviewed three accounts of the rise-fall-rise contour with respect to the question of whether these accounts predict our experimental finding. We found that Ward and Hirschberg’s (1985) account and Constant’s (2012) account either make too strong predictions for our data or no prediction, and that Wagner et al.’s (2013) account seems to make no predictions. A full assessment of accounts of the meaning of the rise-fall-rise contour must, of course, go beyond an assessment of how these analyses account for our experimental finding. We cannot do so here for reasons of space, but conclude that, in the context of research on the meaning of the rise-fall-rise contour, our experimental finding is a novel data point on the basis of which analyses of the meaning of the contour can be assessed. 4.2 The Influence of Prosody on Scalar Implicature Generation Our experiment built on prior research on the contributions of prosody to scalar implicature generation. As discussed in section 2, prior literature has already established that whether a listener takes an utterance with a weaker scalar expression to give rise to a scalar implicature depends on the prosodic realization of the scalar expression as well as on whether the scalar expression is part of the focus of the uttered sentence. In our experiment, in contrast, the target stimuli did not vary with respect to whether the scalar expression was realized with a pitch accent or with respect to whether the scalar expression was part of the focus of the indirect answer utterance: the weaker scalar adjectives in our target stimuli were always realized with a pitch accent and were always part of the focus. Rather, what varied in our target stimuli was the prosodic contour of the indirect answer. Our experiment thus established that it is not just the presence of a pitch accent or the realization as part of the focus that matters for whether a listener takes an utterance to give rise to a scalar implicature, but the prosodic contour of the utterances that contains the weaker scalar item. However, our experiment differed in one crucial aspect from the experiments reported on by Chevallier et al. (2008); Thorward (2009); Zondervan (2010) and Schwarz et al. (to appear): whereas their experiments involved truth value judgment paradigms, our experiment relied on an implication judgment paradigm (i.e., participants had to judge whether a particular implication arose; for discussion of implication judgment paradigms see Tonhauser et al. 2013 and Tonhauser & Matthewson 2015). To confirm that the finding that scalar implicature generation is sensitive to the prosodic contour of the utterance with the scalar expression, we conducted a follow-up experiment with a truth value judgment paradigm.

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4.2.1 Methods 4.2.1.1 Participants 35 individuals participated in the experiment. We discarded the data from one participant who did not consent and one who did not indicate that (s)he was a native American English speaker. This left us with data from 33 participants (12 female, 21 male; ages: 20–59, median age: 31). 4.2.1.2 Materials The target stimuli were Julie’s utterances from the 32 target stimuli in the experiment described in section 3. We also used six of the control stimuli from that experiment to assess whether participants were paying attention to the task. 4.2.1.3 Procedure Participants were told that Julie thinks that the stronger adjective is true (e.g., that her sister is beautiful). They then listened to Julie uttering the sentence with the weaker scalar adjective to Mike (e.g., Mike was told by Julie about her sister: She’s attractive). Participants were asked to judge whether what Julie said is true. A ‘no’ response meant that the participant took Julie to convey that the stronger adjective is false (e.g., ‘attractive but not beautiful’), i.e., the participant generated the scalar implicature. A ‘yes’ response, on the other hand, meant that the participant did not generate the implicature. 4.2.2 Results 11 of the 132 responses to target stimuli with the neutral contour were ‘no’, in contrast to 22 responses of the 132 responses to target stimuli with the risefall-rise contour.9 Thus, there was a numeric increase in implicature rate with the rise-fall-rise contour over the neutral contour. A logistic regression model predicting response from contour with by-participant and by-item random intercepts with random slope for contour for the by-item intercept revealed a significant difference between the contours: answers realized with the risefall-rise contour receive significantly more ‘no’ responses than answers realized with the neutral contour (β = 1.79, SE = 0.62, z = 2.87, p < .01), suggesting that answers with the rise-fall-rise contour are more likely to imply that the stronger alternative is not true than answers with the neutral contour. However, 9 The implicature rate in this experiment is 16% for utterances with the rise-fall-rise contour and 8% for utterances with the neutral contour. These implicature rates are lower than those observed in the experiment described in section 3. This finding suggests that scalar implicature rate is influenced by the experimental paradigm, as also noted in Geurts & Pouscoulous 2009 and Degen & Goodman 2014.

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it is important to note that this effect is not consistently found for all experiment participants: 16 of the 33 participants replied ‘yes’ to all stimuli, thus not generating any implicatures, and two participants categorically generated an implicature when the indirect answer was realized with the rise-fall-rise contour, but not when the indirect answer was realized with the neutral contour. In the regression model, we can take into consideration that participants differ in their sensitivity to the two contours by including random slope for contour in the by-participant random intercept. And, indeed, a logistic regression model predicting response from contour with by-participant and by-item random intercepts and random slopes for contour did not show a significant effect of contour. 4.2.3 Discussion These results show that whether an utterance with a weaker scalar adjective is realized with the neutral contour or with the rise-fall-rise contour may influence whether a listener generates a scalar implicature. Thus, scalar implicature generation may not only be sensitive to whether the scalar item is realized with a pitch accent or in focus, but may also be sensitive to the contour of the utterance that realizes the weaker scalar expression.

5

Conclusions

Polar questions frequently receive indirect answers: Stenström (1984) and de Marneffe et al. (2009) find that 13% versus 14% of the polar questions in their data receive indirect answers, and Hockey et al. (1997) report an even higher percentage, namely 38%. The interpretation of an indirect answer to a polar question is influenced by a number of factors, including the literal meaning of the answer, what the listener knows about the speaker and utterances following the indirect answer. In this paper, we provided empirical evidence that the prosodic realization of the indirect answer may provide a cue to the intended meaning of the indirect answer. Theoretical models of the interpretation of indirect answers thus need to incorporate information about the prosodic realization of the indirect answer. We also discussed the implications of our experimental finding for the meaning of the rise-fall-rise contour and for scalar implicature generation. Our finding also has implications for natural language processing: dialogue generation systems, for instance, may benefit from taking into consideration the prosodic realization of the indirect answer to a polar question.

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Appendix: Materials of the Norming Studies

The 30 pairs of adjectives tested in the norming studies are given in Table 1 with sample carrier sentences. An asterisk (∗) identifies those pairs of adjectives that did not pass a diagnostic. table 1

Pairs of adjectives tested in the norming studies

Adjective pairs ⟨obsessive, dedicated⟩ ⟨hostile, contentious⟩ ⟨faithful, devout⟩ ⟨terrifying, intimidating⟩ ⟨beautiful, attractive⟩ ⟨prominent, famous⟩ ⟨fatal, malignant⟩ ⟨dangerous, risky⟩ ⟨obnoxious, annoying⟩ ⟨life-threatening, serious⟩ ⟨hysterical, anxious⟩ ⟨decrepit, shabby⟩ ⟨exhausting, strenuous⟩ ⟨starving, hungry⟩ ⟨brilliant, intelligent⟩ ⟨unforgettable, memorable⟩ ⟨ridiculous, silly⟩ ⟨horrific, unsettling⟩ ⟨hot, good-looking⟩ ⟨petrified, scared⟩ ⟨hideous, ugly⟩ ⟨toxic, inedible⟩ ⟨corrupt, shady⟩ ⟨deadly, harmful⟩ ⟨disgusting, unpleasant⟩ ⟨articulate, understandable⟩ ⟨impeccable, polished⟩ ⟨delicious, tasty⟩ ⟨hilarious, funny⟩ ⟨filthy, dirty⟩

Even But not Sample carrier sentences

* *

* * *

* * *

* * *

*

*

*

Ann’s sister is dedicated, even/but not obsessive Bart’s debate was contentious, even/but not hostile Carl’s wife is devout, even/but not faithful Chris’ opponent was intimidating, even/but not terrifying Don’s sister is attractive, even/but not beautiful Finn’s boss is famous, even/but not prominent Gwen’s cancer is malignant, even/but not fatal Hugh’s mission was risky, even/but not dangerous Jack’s uncle is annoying, even/but not obnoxious Kaye’s illness was serious, even/but not life-threatening Kim’s patient was anxious, even/but not hysterical Lee’s house is shabby, even/but not decrepit Lynn’s hike was strenuous, even/but not exhausting Mark’s dog was hungry, even/but not starving Nick’s professor is intelligent, even/but not brilliant Pam’s honeymoon was memorable, even/but not unforgettable Pat’s costume was silly, even/but not ridiculous Rick’s nightmare was unsettling, even/but not horrific Sam’s date was good-looking, even/but not hot Stu’s daughter was scared, even/but not petrified Sue’s bridesmaid dress was ugly, even/but not hideous This mushroom is inedible, even/but not toxic This politician is shady, even/but not corrupt This toxin is harmful, even/but not deadly Tim’s bathroom was unpleasant, even/but not disgusting Tom’s interview was understandable, even/but not articulate Tom’s speech was polished, even/but not impeccable Val’s cake was tasty, even/but not delicious Will’s blog post was funny, even/but not hilarious Zack’s carpet was dirty, even/but not filthy

The controls used in the two norming studies are given in Table 2.

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Control stimuli used in the two norming studies

‘even’ study

Sentences used to create “not odd” control stimuli Blair’s room is comfortable. It’s even cozy. Troy’s mother is pleasant. She’s even charming. Jeff’s pants are snug. They’re even tight. Eve’s relationship is special. It’s even unique. Paige’s soup is warm. It’s even hot. Sentences used to create “odd” control stimuli Elle’s exam scores were perfect. They were even below average. Jane’s dog is well-behaved. He is even aggressive. Grant’s proposal was well-received. It was even dismissed. Pierce’s car was cheap. It was even pricy. John’s uncle is rich. He’s even poor.

‘but not’ study “non-contradictory” control stimuli Jeff’s mother is happy and creative. Eve’s husband is shy and handsome. Blair’s sofa is comfortable and old. Paige’s cat is long-haired and lazy. Troy’s beer is warm and flat. “contradictory” control stimuli Jane’s blouse is new and used. Elle’s door is open and closed. Grant’s towel is wet and dry. Pierce’s car was expensive and cheap. This nail is bent and straight.

7

Appendix: Materials of the Experiment

The 16 question-answer pairs that were recorded as target stimuli are given in Table 3, with the stressed syllable of the adjective in the answer capitalized.

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The filler stimuli differ from the target stimuli in that the weaker adjective of the pair is realized in the question and the stronger adjective is realized in the answer. table 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Question-answer pairs for target stimuli in the experiment

Question (Mike)

Answer (Julie)

Was your date hot? Was your hike exhausting? Was your patient hysterical? Was your opponent terrifying? Was your interview articulate? Is your sister beautiful? Was your speech impeccable? Was your carpet filthy? Is your house decrepit? Was your bathroom disgusting? Was your blog post hilarious? Was your dog starving? Is your professor brilliant? Was your bridesmaid dress hideous? Is your boss famous? Was your sister’s illness life-threatening?

He was good-LOOKing. It was STREnuous. She was ANxious. He was inTImidating. It was underSTANdable. She’s atTRACtive. It was POlished. It was DIRty. It’s SHABby. It was unPLEAsant. It was FUNny. It was HUNgry. She’s inTELligent It was UGly. She’s PROminent. It was SErious.

The question-answer pairs used for the control stimuli are given in Table 4, with the stressed syllable of the adjective in the answer capitalized. table 4

Question-answer pairs for control stimuli in the experiment

Question (Mike)

Answer (Julie)

Is your cell phone plan cheap? Was your suitcase light? Is your boss energetic? Was your brother rude? Was your sister innocent? Was your umbrella big?

It’s exPENsive. It was HEAvy. He’s leTHARgic. He was reSPECTful. She was GUILty. It was TIny.

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child English speakers’ interpretations of existential quantifiers. BA-Thesis The Ohio State University Columbus, OH. van Tiel, B., van Miltenburg, E., Zevakhina, N., & Geurts, B. (2016). Scalar diversity. Journal of semantics, 33, 137–175. Tonhauser, J., Beaver, D., Roberts, C., & Simons, M. (2013). Toward a taxonomy of projective content. Language, 89, 66–109. Tonhauser, J., & Matthewson, L. (2015). Empirical evidence in research on meaning. Unpublished Ms. The Ohio State University and the University of British Columbia. Wagner, M. (2012). Contrastive topics decomposed. Semantics & pragmatics, 5, 1–54. Wagner, M., McClay, E., & Mak, L. (2013). Incomplete answers and the rise-fall-rise contour. In Proceedings of the 17th Workshop on the Semantics and Pragmatics of Dialogue. Ward, G., & Hirschberg, J. (1985). Implicating uncertainty: The pragmatics of fall-rise intonation. Language, 61, 747–776. Wolter, L. (2003). Fall-rise, topic, and speaker noncommitment. In Proceedings of WECOL 14 (pp. 322–333). Zondervan, A.J. (2010). Scalar implicatures or focus: An experimental approach. Dissertation University of Utrecht. Utrecht.

chapter 6

Constructing QUD Trees* Arndt Riester

1

Introduction

In this article, we discuss the role of Questions under Discussion (QUD s) in analyses of both discourse structure and information structure, as well as possible ways to integrate them into discourse trees. The QUD notion is primarily associated with the work of Carlson (1983); Grosz & Sidner (1986); Ginzburg (1994, 1996); Roberts (1998, 2012) as well as Beaver & Clark (2008). It is assumed that (both conversational and single-speaker/-writer) discourse contains implicit questions for each of the assertions made, which are thereby turned into answers. Theories of discourse structure, from Hobbs (1985) to contemporary theories like Rhetorical Structure Theory (Mann & Thompson, 1988; Taboada & Mann, 2006) or Segmented Discourse Representation Theory (Asher & Lascarides, 2003), predict a structural analysis of discourse which is based on the identification of rhetorical relations, not of questions. However, recently, a number of new suggestions have been made how QUD s could be integrated into discourse structures; see for instance Onea (2016); Velleman & Beaver (2016); Hunter & Abrusán (2017) or Onea & Zimmermann (2019) but, in fact, the idea to relate the structuring of discourse to questions (or topics, which many scholars essentially see as the mirror images of questions) goes way back to proposals by Klein & von Stutterheim (1987); von Stutterheim & Klein (1989); Polanyi (1988) or van Kuppevelt (1995). In the introduction to his article, van Kuppevelt (1995, 110) sketches his plan and the state of the art at the time:

* The author would like to thank a number of people who, by way of discussion, have considerably contributed to this work; in particular, Lisa Brunetti, Kordula De Kuthy, Cristel Portes, Uwe Reyle and Yvonne Viesel. I am grateful to Nils Reiter for implementing the prototype of a QUD-annotation tool (TreeAnno), and to Kerstin Eckart, Markus Gärtner and Katrin Schweitzer for their work on the corpus infrastructure. Many thanks to the participants of the 2016 SemDial/JerSem Workshop at Rutgers University for comments and discussion, in particular Nicholas Asher, Kata Balogh, Julie Hunter, Hans Kamp, Sophia Malamud, Craige Roberts, Mandy Simons and Judith Tonhauser. Thank you to two anonymous reviewers for their comments, and to the editors of this volume, Malte Zimmermann, Klaus von Heusinger and Edgar Onea, for their support. This work was funded by Deutsche Forschungsgemeinschaft (DFG), Sonderforschungsbereich 732, Project A6, University of Stuttgart.

© koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004378322_007

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[A]n explication is given of our main subject of investigation, namely the way in which discourse structure results from the process of questioning. This is illustrated mainly by examples involving a succession of explicit question-answer pairs as they appear in question-answer dialogues. All principles which hold for explicit questioning are claimed also to apply to implicit questioning. However, an explanation of how implicit questions are reconstructed lies beyond the scope of the present paper. We would like to point out that explicit questions are, in fact, different entities from implicit questions in important respects because explicit questions can change the information status of the content they consist of (they can introduce new material into the discourse), while it is crucial for the reconstruction of implicit questions to not change the discourse. In our paper, we specify the principles according to which implicit questions are identified, making use of a new QUD-based methodology for the joint analysis of naturalistic text in terms of discourse structure and information structure, described in Reyle & Riester (2016) as well as Riester et al. (2018). Furthermore, our interest is aimed at different ways of how to represent QUD trees, i.e. discourse trees supplemented with implicit questions. A theoretical analysis of a given discourse can be visualized in different ways, and we show that representation formats are not necessarily self-explanatory and need to be interpreted. The paper is structured as follows: in Section 2, we introduce some relevant terminology and the discourse representation formats from QUD theory and SDRT, as well as existing ideas how to combine them. We also touch upon the issue of whether there is a direct correspondence between discourse relations and QUD s. Section 3 provides a solution to the general problem of how to identify implicit QUD s in a non-circular way, without relying on prosodic or morphosyntactic cues. We demonstrate the major traits of the procedure on examples taken from a spoken German radio interview (SWR2 public radio, Interview der Woche).1 For the sake of enhanced intelligibility, we will mostly work with (our own) English translations, but we assume that the underlying German version gives rise to exactly the same structures.2 This follows from the fact that our analysis procedure is based on interpretation rather than form, and we claim 1 All data cited in this work are used with the kind permission of Südwestrundfunk (SWR). 2 Of course, this requires that translations must closely follow the source text; potentially, at the expense of the elegance of formulation. At this point, we do not intend to enter a debate about the possibility of perfect translation but we assume that the pragmatic concepts that play a role in our work are indeed universal and fully translatable.

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that it is cross-linguistically applicable (provided, of course, that the analyst is able to understand the text); cf. Riester et al. (2018). After the conclusions and outlook, the paper contains an appendix with the complete analyses of QUD s, information structure and discourse structure in German and English as well as a representation of the QUD tree.

2

Prerequisites for a QUD Analysis of Natural Data

There is widespread consensus among linguists that the structure of natural discourse cannot be adequately represented by a mere linear sequence of assertions (or other speech acts), but that discourse (no matter if text or dialogue) is hierarchically organised in the form of discourse trees (or even more complex structures), which group the elementary units of the discourse into sections, subsections etc. and, thereby, highlight their hierarchical relations. Various theories of discourse structure, such as Mann & Thompson (1988); Polanyi (1988); van Kuppevelt (1995) or Asher & Lascarides (2003), have explicitly dealt with the question how to construe such trees and how to identify and interpret the so-called discourse relations between the nodes of these trees. Over the years, a substantial amount of corpus data have been annotated using RST, SDRT and other frameworks. 2.1 QUD Theory and D-trees Discourse structures, albeit of a different kind, also play a role in Roberts’s (2012) account of information structure. According to Roberts, natural discourse in general serves to answer hierarchically ordered Questions under Discussion (QUD s). Speakers devise strategies to answer general questions by breaking them down into more specific subquestions and answering them one by one. The processing of discourse is represented in terms of a dynamic stack of discourse moves. An important incentive of Roberts’s framework is that QUD s can be used to account for the information structure (Rooth, 1992; Lambrecht, 1994; Hajičová et al., 1998; Schwarzschild, 1999; Krifka, 2008; Beaver & Clark, 2008; Büring, 2016, 2019) of the discourse units in their context: that part of an assertion which is already contained in the denotation of the current question is called the background (or sometimes topic3) while the part which provides the actual answer is the focus. Moreover, Büring (2003) has

3 There is still, to date, an unfortunate terminological confusion about these notions. In our annotations, topics are referential expressions contained in a background, see Section 3.4.

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figure 1

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D-tree with subquestions and corresponding CT-F structures

used Roberts’s framework to explain the phenomenon of contrastive topics. A question with two wh-elements (e.g. Who ate what?) is often successively settled by providing answers to subquestions about each of the individuals in the relevant domain of one of the wh-words. (What did X eat? What did Y eat? …) These individuals – at the same time topics and contrastive / focused entities – are called contrastive topics, and the sequence of superquestion and subquestion-answer pairs is, again, arranged in the form of a “d-tree” (Büring, 2003), which can be interpreted as a static representation of Roberts’s dynamic QUD stacks. In the following, we would like to combine the main advantages of two frameworks: the coverage of natural discourse enabled by SDRT, and the insights about QUD s and their relation to the information structure of answers, as provided by Roberts (2012) and Büring (2003). We start by introducing Büring’s d-trees consisting of a superquestion and several subquestions that are required to account for the contrastive topics in their answers. A key example from Büring (2003, 520) is given in Figure 1. The tree is Büring’s original depiction with just a few cosmetic changes. We have added Qs and As to mark the questions and answers. Crucially, the subquestions in the tree are indicated by Q0.1 , Q0.2 , in order to express the fact that they are entailed by Q0.4 The contrastive topics are those elements which occur in (are topical with respect to) the subquestions but are new ( focal) with respect to the superquestion. 2.2 From SDRT Graphs to QUD Trees The second type of discourse structure we consider is an SDRT graph. We use the often-cited mini-discourse example in (1), from Asher & Lascarides (2003, 8 ff.) or Lascarides & Asher (2008), and its corresponding structural representation, given in Figure 2. 4 There are two ways of defining entailment between questions: a question Q0 entails its subquestion Q0.1 iff every proposition that completely answers Q0 also completely answers Q0.1 ; alternatively, Q0 entails Q0.1 iff every assertion that partially answers Q0.1 also partially answers Q0, cf. Groenendijk & Stokhof (1984); Roberts (2012).

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SDRT style discourse graph for (1)

(1) π1: Max had a lovely evening. π2: He had a great meal. π3: He ate salmon. π4: He devoured cheese. π5: He won a dancing competition. The structure in Figure 2 contains nodes for the assertions (or discourse units) in Example (1). It also contains the additional nodes π6 and π7, representing (implicit) complex propositions (Lascarides & Asher, 2008) or discourse topics. Roughly, π6 corresponds to Max’s activities on that lovely evening, and π7 to the courses that Max ate during his meal. The nodes of the graph are connected by vertical edges, representing subordinating discourse relations (e.g. Elaboration) or links between a complex unit and its parts, and horizontal edges representing coordinating relations (e.g. Narration). From the representation in Figure 2, it is only a small step to the QUD tree in Figure 3, which contains a QUD for each of the assertions. To indicate question-answer congruence, we have changed the names of the nodes into A and Q. The discourse topics have been translated into their question equivalents, Q0.1 : {What did Max do on that lovely evening?} and Q0.1.1 : {What did Max eat during his meal?}. Moreover, the tree now contains a root question Q0 for the intitial assertion, {What is the way things are?}, as suggested in Roberts (2012).5 Answers share the index of their question parent. Parallel,

5 Our questions and the structural analysis are by and large comparable to the assumptions

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figure 3

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QUD tree for (1)

partial answers are indicated as, for instance, A0.1′ , A0.1′′ etc. We have put the QUD s in curly brackets to indicate that they are implicit entities, while explicitly asked questions could occur – in a then different discourse – in the very same position without brackets. Note that, other than in Roberts (2012) and in Büring’s d-tree (Figure 1) we allow for the situation that question nodes may occur as children of answer nodes, thereby siding with van Kuppevelt (1995); Onea (2016) or Velleman & Beaver (2016). Van Kuppevelt (1995, 119) refers to answer nodes that dominate a question as feeders. In turn, we would like to refer to questions that are dominated by answers as anaphorically dependent questions, since they necessarily build on given material from the feeder. It is often the case that anaphorically dependent questions are entailed by the question of their feeder (e.g. in Figure 3, Q0.1.1 is entailed by Q0.1 , and Q0.1 is entailed by Q0, hence the indices), but this is neither necessary to preserve coherence nor is it, to our mind, a realistic assumption for naturally occurring discourse. For instance, it would sound perfectly acceptable – and normal – to replace the branch below A0.1′ with the one in Figure 4, headed by the, nonentailed, question Q1. This, in turn, amounts to yet another deviation from Roberts (2012), according to whom incoming discourse moves have to be relevant and contribute to

made by Hunter & Abrusán (2017, Sect. 2.2). The slightly different formulation of our questions is justified by the constraints formulated in Section 3.2 below.

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A non-entailed, anaphorically dependent question (Q1)

answering the questions which are already on the current QUD stack, but, as a matter of fact, people often insert strictly-speaking irrelevant things into the ongoing discourse, which nevertheless exhibit a topical connection to what has just been said. This insight, again, is already pointed out in van Kuppevelt (1995); Onea (2016) as well as Velleman & Beaver (2016). Another issue that we haven’t addressed so far is the fact that the horizontal Narration edges got lost during the transition from Figure 2 to Figure 3, thereby turning the initial graph structure into a proper tree. This touches upon the debate whether discourse relations can be replaced by QUD s or not. Hunter & Abrusán (2017, Sect. 2.1, 2.2) investigate two versions of this hypothesis. They reject a direct one-to-one correspondence between discourse relations and QUD s, partly for the limitations of Roberts’s strict QUD framework discussed above, and partly for the fact that SDRT enables discourse units to have two incoming edges, see e.g. π4 and π5 in Figure 2, while an answer can only have one immediate QUD as its parent. Instead, Hunter and Abrusán suggest that QUD s should, above all, occur when they address issues that can be represented by a complex discourse unit, “having a topic that glues its members together”. While we follow Hunter and Abrusán in most of their arguments, the conclusions that we draw are slightly different. We claim that, for a purely structural purpose, subordinating discourse relations can be replaced by questions (for instance, an Explanation can be formulated using a why question, an Elaboration by means of a what-about question). This does not mean that the two are always equally informative. As Hunter and Abrusán point out, different discourse relations can sometimes translate into the same QUD. On the other hand, the QUD defines the information structure of an answer while the discourse relation does not necessarily do so.

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QUD tree with temporally located questions

It is sometimes suggested that also structurally coordinating relations like Narration can be treated as simple and-then-what (or what-happened-next) questions, cf. Velleman & Beaver (2016). In this case, however, it is unclear how the resulting “QUD graph” should be interpreted; certainly not by use of a stack. By contrast, we think that there is actually a gain in going from discourse graphs to actual discourse trees, which express the hierarchy of discourse moves in a unanimous way. This, however, means that a simple and-then-what question will not suffice. Instead, in order to maintain the coordinating nature of a narrative sequence, we draw on a proposal made already in von Stutterheim & Klein (1989, 43), according to which temporal progression can be represented by a series of parallel questions about different times, see Figure 5. Note that, while Figure 5 reflects the order of the overt discourse moves according to their time of utterance, the representation says nothing about the temporal order of the reference times (t2, t3 etc.) and is therefore compatible with both the default situation of temporal progression from left to right and with other temporal configurations. This information must be encoded separately. Moreover, since we are primarily interested in the information structure of the assertions, the additional, temporally located questions of Figure 5 can

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be considered as optional because there are no overtly contrastive temporal expressions in the assertions about the eating or dancing events which could participate in a marked information-structural contrast like the one shown in Example (2). (2) FirstCT he ate salmonF. ThenCT he devoured cheeseF. This ends our short section on the relation between SDRT graphs and QUD s. For a much more formally elaborate approach on the same topic (and, in particular, the Result relation) see the article by Onea (2019) in the same volume. A legitimate question, of course, is: based on what rules have the QUD s in the above figures been formulated, in the first place? This is precisely what we are going to deal with in the next section.

3

Information-Structural Constraints on QUD s

In the previous section, we have mentioned a few essential aspects of discourse trees and the role of questions in the structuring of discourse. We now shift our attention away from discourse theory and towards the practical task of reconstructing QUD s in natural discourse. In doing so, we follow the spirit of van Kuppevelt (1995, 109), who proposed that topicality (or questions) should be seen as “the general organizing principle of discourse”. However, we go a step further in that our method not only accounts for the structure of discourse but, at the same time, for the information structure of the individual assertions the discourse consists of. In this article, we confine ourselves to the basic traits of the procedure. For a comprehensive annotation manual, see Riester et al. (2018), and Reyle & Riester (2016) for a formal account in terms of UDRT. To illustrate the constraints, we choose examples from a section of a spoken German radio interview.6 The entire section with annotations, English translation and a QUD tree can be found in Appendix 5. 3.1 Segmentation The first step of the analysis procedure is the segmentation of the text into separate discourse moves, which are mostly assertions. Each assertion is marked by 6 SWR2 Interview der Woche, 2015/02/28 (6:30p.m.), with Andrea Nahles (SPD), Federal Minister for Labour and Social Affairs. The interview is part of the GRAIN corpus (Eckart & Gärtner, 2016; Schweitzer et al., 2018).

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a letter A. Segmentation will, to a certain extent, ignore punctuation or a syntactic notion of clause. It will come as no surprise that assertions are split at clause-level coordinations. However, a split is sometimes also required below the clause level, as in the case of VP or DP conjunctions or disjunctions, see 3.7 In cases like these, it may be handy to reconstruct the elided (crossed out) material, in order to make each single assertion transparent. (3) A:

A:

Da sollen Fenster in Teeküchen vorgeschrieben werden, There shall windows in staff.kitchens prescribed be ‘It [the bill] will prescribe having windows in staff kitchens’ oder auch die Helligkeit am Heimarbeitsplatz soll or also the brightness at.the home.workplace shall vorgeschrieben werden. prescribed be ‘and even the brightness of home workplaces.’

On the other hand, we will not separate sentential arguments from their embedding matrix verbs, as shown in 4. The embedding part of such constructions will, later on, typically be analyzed as non-at-issue material, cf. Section 3.6 and Riester et al. (2018) for further details. (4) A:

Jetzt heißt es, das Kanzleramt hat diese Verordnung gestoppt. Now means it the Chancellery has this bill stopped ‘ Now they are saying that the Chancellery has stopped the bill.’

3.2 QUD s Consist of Given Material Suppose that the segmentation of a discourse has yielded a list of assertions. It is now the task of the analyst to provide, for each assertion, a QUD which is in fact answered by that particular assertion, and to arrange the questions and assertions in order to form a discourse tree. The identification of implicit QUD s has often been dismissed as a hopeless, or at least highly speculative, task. This is understandable if assertions are considered in isolation. Without knowing the information structure of a sentence (i.e. its focus span), there are (at least) as many possible QUD s as there are syntactic constituents in the sentence. Hence, in Reyle & Riester (2016) and Riester et al. (2018), we identify a number of discourse-contextual constraints that make the QUD identifica-

7 For a DP coordination, see the answers to Q4.1.2 in the appendix.

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tion task tractable and deterministic. In the following, we give a short sketch of the account. The constraints are derived from the focus literature of the past decades, in particular, Rooth (1992); Schwarzschild (1999) and Büring (2008). The first constraint on the formulation of QUD s is given below: Q-A-Congruence QUD s must be answerable by the assertion(s) that they immediately dominate. Q-A-Congruence is, of course, rather trivial. It means, for instance, that a sentence like (7) is an answer to any of the questions in (5) but not to (6). (5) a. {What happened?} b. {What about him?} c. {Who literally suffocated?} (6) {Who owns a bicycle?} (7) A:

He literally suffocated.

Note that our formulation of Q-A-Congruence is deliberately kept weak and does not make any reference to alternative sets (Rooth, 1992) or question sets (Hamblin, 1973; Groenendijk & Stokhof, 1984), precisely because we do not want to presuppose the focus-background structure of the answer. All we want is a question that can be answered by the assertion once its information structure has been determined. A second constraint, which takes the discourse context into account, is the following one: Q-Givenness Implicit QUD s can only consist of given (or, at least, highly salient) material. Q-Givenness restricts implicit QUD s in a way that renders them less flexible than explicit ones: they are not allowed to introduce new material into the discourse themselves. The only semantic material they can consist of – ignoring function words; in particular, wh-pronouns – is material that is already given8

8 We assume a strict definition of givenness in terms of referential or lexical availability of a word/phrase or discourse referent in the previous discourse context, which goes hand in hand

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in the discourse. We should point out, that Q-Givenness is, of course, the flipside of Schwarzschild’s (1999) Givenness constraint, which does not mention QUD s but requires that discourse-new material be F(ocus)-marked. Since the focus-marked material of an answer corresponds to the wh-expression of its QUD, it follows that new material is banned from occurring inside the QUD.9 Let us have a look at a simple example. (8) a. A: And all I can say is that his condition was extremely bad during his last years. b. A: He literally suffocated. As we said, when considering sentence (8b) in isolation, it can function as the answer to any of the questions in (5). However, in the context of sentence (8a), it is obvious that (5c) is ruled out as QUD, since it would introduce the sequence literally suffocated as new information and fail to provide a link to the previous discourse. Neither does (5a) contain any discourse-given material, but it is not ruled out by the above constraint. In order to capture the intuition that question (5b), which does in fact connect to the previous discourse via the pronoun him, should be preferred over (5a), we need a third constraint: Maximize-Q-Anaphoricity Implicit QUD s should contain as much given (or salient) material as possible. Maximize-Q-Anaphoricity corresponds to what has been discussed in the literature under the names AvoidF (Schwarzschild, 1999) or Maximize Anaphoricity (Büring, 2008). Their purpose is to ensure discourse coherence. In other words, two consecutive assertions are expected to be related to each other to a substantial extent, and this is mediated via the QUD. Note that the constraints, taken together, prefer question (5b) above either (5a) or (5c). However, they do not actually dictate that (5b) is the optimal QUD in general. In princi-

with cognitive activation, cf. Baumann & Riester (2012); Riester & Baumann (2017). Note that activation or salience can occasionally arise without explicit mention, see Q5 and Q7 in the appendix. 9 Occasionally, in particular at the beginning of a discourse, Q-Givenness is overruled by the effect of presupposition triggers (e.g. clefts). Presupposition accommodation (Beaver, 1999; Beaver & Zeevat, 2007) can lead to a narrower – though never wider – focus than predicted by our principles. In order to capture accommodation phenomena, our approach must be enhanced by language-specific rules.

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ple, it is possible to increase the degree of discourse coherence, by formulating other questions that contain even more given material, e.g. the ones in (9). (9) a. How bad was the situation10 for him? b. How bad was his condition? c. What was his bad condition like? The fact that there are still so many possible ways of formulating the actual QUD may have added to the impression that the identification of QUD s is a highly speculative matter. However, if we abstract away a bit and look for a common pattern, we note that questions (9a)–(9c), as well as (5b), all ask for an answer of property type; in other words, they give rise to the same information structure of their answer. The lesson we learn from the current discussion is that there normally isn’t a single way of formulating implicit QUD s – which are semantic objects, after all – since language allows for synonymous formulations. What is essential however, is that it is possible to identify a QUD as an object of meaning that does account for the discourse structure of a sequence of assertions, and for the information structure of the assertion that answers it. What is meant in the definition of Maximize-Q-Anaphoricity by “as much given (or salient) material as possible” is mainly that all the given material in the answer must show up in the question. (Certainly not all material available in the previous discourse context!) The interplay of the constraints also gives an answer to the question about the nature of QUD s. It is sometimes suggested that QUD s “arise” or “follow” from the previous context and then “guide” the way how the subsequent discourse is going to evolve. Nothing could be more wrong than that. In fact, the only rule that speakers or writers must observe when formulating their next move is to think about some topical connection to whatever was said before,11 but in all other respects they are free to formulate their own continuation of the plot. So, if ever QUD s can be said to “arise” then they do so only out of the interplay between the current discourse and the next assertion made by the speaker. 10

11

We assume that very general expressions like situation are always salient, i.e. quasi-given, although they might not be given in the strict sense of having been previously mentioned. Corpus examples of quasi-given (but strictly speaking discourse-new) nouns are discussed in Riester & Piontek (2015, pp. 243ff.). But even when this rule is not observed, a speaker can strictly-speaking never entirely “drop out of discourse”. The worst thing that can happen is that a speaker utters an all-new statement without any connection to the previous context, by which she simply jumps back to answering the root question What is the way things are? and, thereby, loses access to all previously given information.

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figure 6

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QUD trees (deep / compact) of the sequence in (8)

3.3 Compact Discourse Trees The discourse constellation that is associated with Example (8) is shown in Figure 6, in two variants. A practical problem when analysing larger sections of text in terms of QUD trees is that the trees quickly grow very deep. In order to minimize the problem, we introduce a new representation format for discourse trees, which is also used (in textual form) in the analyses given in the appendix. The left “deep” tree in Figure 6 is the SDRT-based format used already in Section 2.2 (as, for instance, in Figures 3 or 4). The tree on the right is meant to express the same analysis in the compact QUD-tree format, in which anaphorically dependent questions (here, Q7.1 ) occur to the right of their feeder (A7). Note that, in this format, it does not matter, whether the anaphorically dependent questions are entailed, like in the current example, or not (as any of the questions Q1-Q8 in the appendix).12 A compact QUD-tree representation of the SDRT example is shown in Figure 7. Apart from the space-saving aspect of the compact representations, a second big advantage is that there is now a clear spearation between questions, which form the non-terminal nodes, and assertions, which constitute the terminal nodes of the tree, and which can be read off from left to right.13 The three QUD constraints defined so far describe how Questions under Discussion should be formulated: they should allow for Q-A-Congruence, they should not contain any non-salient information (Q-Givenness) and 12

13

In Figure 12 in the appendix, we attach non-entailed questions via dashed lines and entailed questions via solid lines but this is actually redundant, since entailment is already indicated by means of the different indices. The only questions which are also terminal nodes are overt questions that remain unanswered and are therefore “left dangling”. See Q2.1 and Q3 in the appendix.

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figure 7

Compact QUD tree for (1)

they should consist of a maximal amount of given information (MaximizeQ-Anaphoricity). Taken together, this also has a crucial influence on the attachment site of an incoming QUD and its answer: a QUD must be subordinate to its feeder A, i.e. the assertion which provides its respective antecedental material, where subordinate to A means below A in the deep format and to the right of A in the compact format. Following common assumptions in discourse semantics, the only material that is accessible to anaphoric retrieval is material at the right frontier (Polanyi, 1988; Webber, 1991; Asher, 2008; Afantenos & Asher, 2010) of the current discourse tree. Any new piece of information should therefore attach as low as necessary in order to enable anaphoric retrieval, but as high as possible in order to allow the speakers to conclude a discourse section, to return to the starting point of a conversation or the main question of a text, and to raise new issues. This is captured by the constraint Back-to-theRoots. Back-to-the-Roots In the compact QUD-tree format, an incoming QUD (and its answers) must attach to the right of the lowest antecedent of its given content, but otherwise as high as possible.

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3.4 Information Structure In the previous sections, we have been talking about information structure in a loose way. We would now like to define it more precisely. Assuming the question-answer sequence from Figure 6, the information structure of assertion A7 will be the one shown in (10). (10) [HeBG [literally suffocated]F ]~ Following standard assumptions in the literature, we define the focus (F) of an assertion as that part of an assertion which actually answers the QUD. Moreover, the remaining part, i.e. the material which already occurs in the QUD, is called the background (BG). Note that our framework differs terminologically from the one by van Kuppevelt (1995) or Hajičová et al. (1998), in which backgrounded material is generally called topic.14 Together, the background (which may be empty) and the focus (which cannot be empty) form a focus domain (Rooth, 1992; Büring, 2008), which is marked using the ~ operator. Focus domains do double duty. On the one hand, a focus domain matches the structure of the QUD, since the backgrounded part of an assertion must recur inside the corresponding QUD. In other words, a QUD must have the same focus domain as its answer, except for the wh-/focus part. On the other hand, focus domains also play a role in the highlighting of parallel structures, as discussed in the next section. 3.5 Parallelism Besides the givenness-related constraints already defined, there is another important cue for the reconstruction of QUD s, viz. the identification of recurring patterns in the discourse, i.e. the search for semantically parallel structures. This is formulated in the following constraint.15 Parallelism The background of a QUD with two or more parallel answers consists of the (semantically) common material of the answers.

14

15

In the appendix, we have optionally marked referring expressions in the background as aboutness topics (T) (Reinhart, 1981; Krifka, 2008). Note that we assume that not every background has to contain an aboutness topic, but that every (non-contrastive) aboutness topic is necessarily backgrounded. See Reyle & Riester (2016, 18) for an example showing that Parallelism can override Q-Givenness.

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Discourse tree for the question (12) and the parallel answers in (11)

Two types of parallelisms play a role: simple ones, which semantically differ in only one position per assertion, and complex ones, which differ in two positions. An example of a simple parallelism is given in Example 3, reproduced below as (11). (11) a. A1′ : It will prescribe having windows in staff kitchens b. A1′′ : and it will also prescribe the brightness of home workplaces. Identifying semantically identical material or, as in Example (11), reconstructing elliptical material, in turn, helps us formulate the shared QUD: the constant material (i.e. the background) must re-occur inside the QUD, while the alternating parts (the foci) correspond to a wh-word in the QUD, which we formulate, for the current example, as in (12), and the corresponding discourse and information structure is the one in Figure 8. (12) Q1: {What will the bill prescribe?} A second, more complex form of parallelism, which we already encountered in Section 2.1, is the one in which two assertions differ in two positions. Unless we have reasons to believe that we are merely dealing with the special case of a complex (Krifka, 1992, 21) or discontinuous focus (e.g. Gussenhoven, 1999, 50), i.e. a single focus that merely consists of two disjoint parts, we follow the approach by Büring (2003) in assuming that such structures give rise to pairs of contrastive topic and focus. Beyond Büring’s simple examples (Figure 1), contrastive topics may, for instance, take the form of antecedent clauses of hypothetical conditionals (Iatridou, 1991). In those cases, the information structure is of the form: [If ACT then BF]~; [if CCT then DF]~. A corpus example of this kind is shown in Figure 9. 3.6 Non-at-Issue Content Not all information contained in a sentence takes part in the actual focusbackground divide signalled by the QUD. Potts (2005) has drawn the attention to the phenomenon of conventional implicatures, i.e. meaning components that are projective in the sense that their contribution survives after being embed-

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Conditionals that take the form of contrastive-topic/focus pairs

ded under negation and other operators, but which are nevertheless distinct from presuppositions in that conventional implicatures do not impose any identifiability constraints on the common ground or discourse context. On the contrary, they seem to represent genuinely new information. Among triggers of conventional implicatures, Potts (2005) originally lists supplements (appositions, non-restrictive relative clauses, speaker-oriented adverbs) as well as expressives (honorifics and expressions describing the speaker’s positive or negative attitude towards the asserted content). He makes it clear that a crucial trait of conventional implicatures is that they are independent from the atissue, or regularly asserted, content. Another very frequent phenomenon that can presumably be subsumed under conventional implicatures are evidentials (Faller, 2002; Murray, 2010; Tonhauser, 2012), which are grammaticalized in many languages or expressed by means of I think that, John said that etc. Examples (13) and (14) show corpus examples of non-at-issue expressions (in grey). (13) A2: Now they are saying that, the Chancellery has stopped the bill. (evidential) (14) A4.1.2.1 : […] and it is due to numerous measures in the past 40 years called occupational safety measures and workplace regulations – that’s indeed how they are called – that, Thank God, the numbers of casualties, injuries and accidents has decreased massively. (parenthesis, expressive) The distinction between at-issue and non-at-issue content has received considerable attention within the semantics-pragmatics community in recent years. For instance, the work by Simons et al. (2010) and Tonhauser et al. (2013) discusses projective content, subsuming conventional implicatures, presuppositions as well as anaphora and backgrounded material. In the light of this, it seems worthwhile to point out that using the term non-at-issue content inter-

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changeably with conventional implicatures, as it has become quite popular and as we will also do in the current paper, carries a mild terminological conflict since backgrounded content is, of course, also not “at issue” in the strict sense of not providing the answer to the QUD, but it is, of course, to be kept distinct from triggers of conventional implicatures. However, we argue that another phenomenon should be treated as (at least part-time) non-at-issue content, viz. adjunct phrases, i.e. certain locative, temporal and other adverbials, which are traditionally distinguished from argument phrases with respect to their syntactic optionality. Adjunct phrases (unless in focus) are optional in the sense that they can be left out without affecting the interpretability and the truth value of the main proposition denoted by the utterance. In fact, we propose that optionality could figure as the defining criterion for the type of non-at-issue content that we have in mind: to be nonat-issue with respect to the current Question under Discussion means nothing else than to be optional in the current assertion. In semantic terms, we therefore define non-at-issue content as follows: Non-at-issue (relative to Q) An expression X in an utterance U is non-at-issue with respect to the current Question under Discussion Q iff the deletion of X has no effect on the truth-conditions of the main proposition denoted by U. There is a point that we need to clarify, though: to be non-at-issue (with respect to the current QUD) does not – in the least – mean to represent unimportant information.16 If a speaker formulates an utterance that contains non-at-issue material, she is simply choosing a compact way of conveying two (or more) assertions in one go, and the most important piece of information may very well be formulated in the form of a supplement. To understand this point, consider example 15, overheard from German radio news.17 (15) In Deutschland sterben viele Patienten gegen ihren Willen im In Germany die many patients against their will in.the Krankenhaus. hospital. ‘In Germany, many patients die at the hospital(,) against their will.’

16 17

We are obliged to Maribel Romero (p.c.) for raising this issue. Deutschlandfunk Nachrichten, Nov. 02, 2015

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Example 15 has two drastically different interpretations that can be disambiguated in terms of information structure, i.e. in terms of assumptions about their implicit QUD. The rather worrisome interpretation is the one in (16a), which suggests that German hospitals are horrifying places in which constantly people are left to die, although they explicitly didn’t want to. The more harmless – hopefully intended – reading is the one in (16b), which merely expresses the sad fact that in Germany a lot of people end up dying in hospitals despite their explicit wish to die at home. (16) a. Q: {How do many patients die in German hospitals?} A: [In D. sterben viele Patienten [gegen ihren Willen]F im Krankenhaus.]~ b. Q: {Where do many patients die in Germany?} A: [In D. sterben viele Patienten gegen ihren Willen [im Krankenhaus]F.]~ The information-structural difference between the two readings consists in the choice of QUD and corresponding focus constituent. While the prepositional phrase against their will is the, non-optional, focus in (16a), it is merely an optional adjunct, and therefore non-at-issue, in (16b). We should, finally, point out that under the current interpretation of ‘non-at-issue content = optional content’ only adjuncts as well as certain evidentials and evaluatives, can change their (non-)at-issue status depending on the context, while e.g. appositions are presumably always non-at-issue. 3.7 The Discourse Status of Non-at-Issue Content Being non-at-issue with respect to the current QUD does not mean not being an answer at all. This may seem paradoxical at first, and yet it is obvious if non-at-issue content is defined as denoting a separate assertion. Like any other assertion, non-at-issue content must contain a focus of its own, which serves as the answer to a subordinate question, cf. Riester & Baumann (2013, Sect. 2). This focus may be called a non-at-issue focus. In other words, (any) piece of nonat-issue content is only non-at-issue with respect to the current QUD but it is, in fact, at-issue with respect to a subordinate question. Putting these insights into practice, we analyze the discourse structure of the reading in (16b) as shown in Figure 10. As we said in Section 3.3, an advantage of representing discourse trees in the compact format is that the textual order is preserved when the assertions are read off from left to right. The treatment of sentence-internal non-at-issue material as a separate, subordinate assertion, as shown in Figure 10, is the only

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figure 10

Treatment of sentence-internal non-at-issue content

figure 11

Treatment of sentence-final non-at-issue content

case that is disrupting the linear textual order, since the non-at-issue assertion is extracted from its original location. However, if non-at-issue material occurs in sentence-final position, no restructuring is necessary and the material can simply be treated as if it is a separate assertion right away, compare Example (17)18 and its corresponding discourse tree. (17) a. A5: He was working in a slate mine after the war, b. A6: in Mayen. Note that the discourse constellation in Figure 11 allows the speaker to continue the discourse in (at least) two ways: she may either continue talking about grandfather and his work, which would amount to a continuation at the level of the at-issue content (A5), or about the town of Mayen, at level A6. The question whether sentence-final non-at-issue content, e.g. appositive relative clauses, can behave like ordinary at-issue material is also addressed, for instance, in AnderBois et al. (2010) and Syrett & Koev (2014).

18

Here we assume that the temporal adverbial after the war / nach dem Krieg is quasi-given, i.e. salient, after the mention of grandpa. This is supported by the fact that it is deaccented in the German original.

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185

Conclusions and Outlook

We have presented a comprehensive framework for the analysis of dialogue and text data in terms of discourse structure and information structure. We have, furthermore, discussed representation formats of discourse trees from QUD theory and SDRT, and presented ways of how to combine them in so-called QUD trees, thereby integrating QUD s into SDRT-based structures, which allow for a more flexible analysis of discourse, mainly for the reason that subordinated discourse units can answer questions which are not (entailed) subquestions to other questions higher up in the tree. We have argued that it is necessary to loosen Roberts’s constraints on entailment and relevance. Furthermore, we adopt van Kuppevelt’s concept of questions that are triggered by (and therefore subordinate to) answer nodes (so-called feeders). However, in order to arrive at more compact tree representations (in which all answers are terminal nodes) we give up the graphical representation of answers dominating questions, while keeping the idea of questions being anaphorically dependent of previous answers. We argue that QUD s can replace subordinating discourse relations, and that ways can be found to represent coordinated assertions (e.g. those standing in a relation of Narration, Parallel or Contrast) as parallel siblings below a common QUD and possibly parallel subquestions. Finally, we argue that the identification of QUD s is not arbitrary but contrained by a number of contextual constraints derived from information-structure theory: QUD s must be congruent, non-novel, maximally given and attach as high as possible while maintaining givenness. The identification of parallelisms is a second way of determining QUD s in corpus data. The benefit of creating a pool of discourse- and information-structurally labelled data is to obtain a means for the study of prosodic and morphosyntactic variation within one language, or across several ones. Furthermore, such analyses would allow for a quantitative assessment of the coherence of texts or argumentation patterns. A further application, in the long run, is the establishment of training data for machine learning tasks like discourse parsing, co-reference resolution, text-to-speech synthesis and the like. And finally, since the method is pragmatic in nature and does not presuppose any specific morphosyntactic knowledge, it can also, in principle, be used to describe information-structural effects in lesser-studied languages.

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5

Appendix: Corpus Data

GRAIN corpus, cf. Eckart & Gärtner (2016), Schweitzer et al. (2018) Südwestrundfunk, SWR2 Interview der Woche Interview partner: Andrea Nahles (SPD), German Federal Minister for Labour and Social Affairs Date, time: 2015/02/28, 6:30–6:40 p.m. Parts of the corpus (13 interviews, 1,356 sentences, 24,114 tokens) have been annotated for QUD s, information structure and discourse structure according to the guidelines in Riester et al. (2018). Note that, in the following, we represent tree edges (in the compact tree format) by use of indentation marks (>), i.e. the following two representations in (18) are equivalent: (18) a.

b.

Notes to the interview: (a) We assume here that the pronoun da ‘there’ refers anaphorically to Arbeitsstättenverordnung ‘workplace regulation bill’ and is, therefore, topical. (b) We assume that, in the respective contexts, the phrases nach dem Krieg ‘after the war’ and in den letzten Jahren ‘in the last years’ are salient and, therefore, backgrounded althought they are not literally given in the previous discourse. (c) The sentence is ungrammatical in the German original. Context: The previous discussion between the journalist and the politician is about a conflict between the Social-Democratic Minister and the more business-friendly Christian Democratic Party (CDU), specifically, about the Minister’s newly introduced statutory minimum wages. The CDU is complaining that the new law means a lot of bureaucracy for employers. Nahles is defending herself against the accusations. End of the minium-wage topic.

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Analysis of Original German Data

Journalist: (Notes) Q0: {Bei welchem anderen Projekt wird Nahles von den Arbeitgebern Bürokratisierung vorgeworfen?} > A0: [Ein anderesCT Projekt, bei dem die Arbeitgeber Sie mit dem Bürokratievorwurf überziehen, ist [die Arbeitsstättenverordnung]F.]~ > Q1: {Was soll verordnet/vorgeschrieben werden?} (a) > > A1′ : [DaT sollen [Fenster in Teeküchen]F vorgeschrieben werden,]~ > > A1′′ : oder auch [[die Helligkeit am Heimarbeitsplatz]F ]~. > Q2: {Wie ist der Status der Verordnung?} > > A2: Jetzt heißt es, [[das Kanzleramt]F hat [diese Verordnung]T [gestoppt]F ]~. > > Q2.1 : Können Sie das bestätigen? > Q3: Sind Sie da gescheitert? Andrea Nahles: > Q4: Also zunächst muss man vielleicht mal sagen, worum es da eigentlich geht. {= Worum geht es bei der Verordnung eigentlich?} > > Q4.1 : {Wie war der Arbeitsschutz früher und wie ist er heutzutage?} > > > Q4.1.1 : {Wie war der Arbeitsschutz früher?} > > > > Q4.1.1.1 : {Welche persönlichen Beispiele hat Nahles?} > > > > > A4.1.1.1 : [MeinT [Opa hat eine Staublunge gehabt]F,]~ (b) > > > > > Q5: {Was war mit Nahles’ Opa nach dem Krieg?} > > > > > > A5: [derT war [im Schieferbergwerk]F nach dem Krieg]~ > > > > > > Q6: {Wo war das Schieferbergwerk?} > > > > > > > A6: [[in Mayen]F ]~ (b) > > > > > Q7: {Wie ging es dem Opa in den letzten Jahren?} > > > > > > A7: und ich kann nur sagen, [das war [schlimm]F in den letzten Jahren, wie es demT ging]~. > > > > > > Q7.1 : {Wie schlimm ging es ihm?} > > > > > > > A7.1 : [DerT ist [richtig erstickt]F.]~ > > > Q4.1.2 : {Wie ist der Arbeitsschutz heutzutage?} > > > > Q4.1.2.1 : {Die Anzahl wovon ist durch die Arbeitsschutzmaßnahmen massiv zurückgegangen?} (c) > > > > > A4.1.2.1′ : Und [es ist [durch viele Maßnahmen in den letzten 40 Jahren, die man unter dem Stichwort “Arbeitsschutz und Arbeitsstättenverordnung”, so heißt das Ding nun mal, firmiert,]T sind Gott sei Dank die Anzahl [der Toten]F,]~ > > > > > A4.1.2.1′′ : [[der Kranken]F,]~ > > > > > A4.1.2.1′′′ : [[der Unfälle]F massiv zurückgegangen]~. > A4: Und deswegen [ist dasT schon [etwas sehr Wertvolles,]F [diese Arbeitsschutzpolitik und auch diese Arbeitsstättenverordnung]T ]~. > Q8: {Was ist Nahles’ Reaktion zu Vorbehalten gegenüber der Verordnung?} > > Q8.1 : {Was tut sie, wenn sich jemand über Kleinigkeiten aufregt?} > > > A8.1 : [Wenn man daT jetzt [sich aufregt wegen einem abschließbaren Spind,]CT na Gott dann wäre ich [der Letzte der sagt, da kann man nicht über einzelne Punkte reden]F.]~ > > Q8.2 : {Was tut sie, wenn jemand die ganze Verordnung in Frage stellt?} > > > A8.2 : Aber [wenn man dasT [grundsätzlich in Frage stellt,]CT dann werde ich [allerdings doch ernst]F ]~.

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English Translation

Journalist: (Notes) Q0: {For which other projects is Nahles accused of bureaucratisation by the employers?} > A0: [AnotherCT project for which employers are accusing you of bureaucratisation is [the workplace regulation bill]F.]~ > Q1: {What will be prescribed?} > > A1′ : [[The bill]T will prescribe [having windows in staff kitchens]F ]~ > > A1′′ : and even [[the brightness of home workplaces]F ]~. > Q2: {What is the current status of the bill?} > > A2: Now they are saying that [[the Chancellery has stopped]F [the bill]T ]~. > > Q2.1 : Can you confirm this? > Q3: Have you failed there? Andrea Nahles: > Q4: All right, first I need to say what this is all about. {= What about this bill?} > > Q4.1 : {What about occupational safety in earlier times and nowadays?} > > > Q4.1.1 : {What about occupational safety in earlier times?} > > > > Q4.1.1.1 : {What personal examples does Nahles have?} > > > > > A4.1.1.1 : [MyT [grandpa suffered from silicosis]F.]~ (b) > > > > > Q5: {What about Nahles’s grandpa after the war?} > > > > > > A5: [HeT [was working in a slate mine]F after the war,]~ > > > > > > Q6: {Where was the slate mine?} > > > > > > > A6: [[in Mayen]F ]~ (b) > > > > > Q7: {How was grandpa’s health during his last years?} > > > > > > A7: and all I can say is that [hisT condition was [extremely bad]F during his last years]~. > > > > > > Q7.1 : {How bad was his condition?} > > > > > > > A7.1 : [HeT [literally suffocated]F.]~ > > > Q4.1.2 : {What about occupational safety nowadays?} > > > > Q4.1.2.1 : The number of what has massively decreased due to occupational safety measures? > > > > > A4.1.2.1′ : and [it is [due to the numerous measures in the past 40 years called occupational safety measures and workplace regulations]T – that’s indeed how they are called – that, Thank God, the numbers of casualtiesF ]~ > > > > > A4.1.2.1′′ : [injuriesF ]~ > > > > > A4.1.2.1′′′ : and [accidentsF has decreased massively]~. > A4: And, therefore, [[these safety measures and the workplace regulation bill]T are [something very valuable]F ]~. > Q8: {What is Nahles’s reaction to different attitudes regarding the bill?} > > Q8.1 : {What does she do if someone is upset about minor issues?} > > > A8.1 : [If someone is [upset because of some lockers]CT, oh well, then IT would be [the last person unwilling to discuss a compromise]F.]~ > > Q8.2 : {What does she do if someone is fundamentally opposed to the bill?} > > > A8.2 : But [if someone is [fundamentally opposed]CT to itT, then IT [won’t be joking anymore]F ]~.

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figure 12

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Q-tree for the interview section

5.3 QUD Tree The tree in Figure 12 makes the structure of the textual analyses (of both German and English) transparent. Questions nodes are rectangular, answer nodes are oval. Entailment between question nodes is represented by solid edges, while non-entailment is represented by dashed edges. Questions attached via non-entailed edges must be anaphorically dependent on a previous answer to the superquestion (the feeder).

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Bibliography Afantenos, S., & Asher, N. (2010). Testing SDRT’s right frontier. In Proceedings of the 23rd International Conference on computational linguistics (pp. 1–9). AnderBois, S., Brasoveanu, A., & Henderson, R. (2010). Crossing the appositive/at-issue meaning boundary. In Proceedings of SALT 20 (pp. 328–346). Asher, N. (2008). Troubles on the right frontier. In A. Benz, & P. Kühnlein (Eds.), Constraints in Discourse (pp. 29–52). Amsterdam: John Benjamins. Asher, N., & Lascarides, A. (2003). Logics of Conversation. Cambridge: Cambridge University Press. Baumann, S., & Riester, A. (2012). Referential and Lexical Givenness: Semantic, prosodic and cognitive aspects. In G. Elordieta, & P. Prieto (Eds.), Prosody and Meaning number 25 in Interface Explorations (pp. 119–161). Berlin: De Gruyter Mouton. Beaver, D. (1999). Presupposition accommodation: A plea for common sense. In L. Moss, J. Ginzburg, & M.D. Rijke (Eds.), Logic, Language and Computation. Volume 2 (pp. 21–44). Stanford, CA: CSLI Publications. Beaver, D., & Clark, B. (2008). Sense and Sensitivity. How Focus Determines Meaning. Oxford: Wiley-Blackwell. Beaver, D., & Zeevat, H. (2007). Accommodation. In G. Ramchand, & C. Reiss (Eds.), The Oxford Handbook of Linguistic Interfaces (pp. 503–539). Oxford: Oxford University Press. Büring, D. (2003). On D-trees, beans, and b-accents. Linguistics and philosophy, 26, 511– 545. Büring, D. (2008). What’s new (and what’s given) in the theory of focus? In Proceedings of the 34th Annual Meeting of the Berkeley Linguistics Society 34(1) (pp. 403–424). Büring, D. (2016). Intonation and Meaning. Oxford: Oxford University Press. Büring, D. (2019). Focus, questions and givenness. In M. Zimmermann, K. von Heusinger, & E. Onea (Eds.), Questions in Discourse. Volume 2: Pragmatics (pp. 6–44). Leiden: Brill. Carlson, L. (1983). Dialogue Games: An Approach to Discourse Analysis. Dordrecht: Reidel. Eckart, K., & Gärtner, M. (2016). Creating silver standard annotations for a corpus of non-standard data. In Proceedings of the 13th Conference on Natural Language Processing (pp. 90–96). Faller, M. (2002). Semantics and Pragmatics of Evidentials in Cuzco Quechua. Dissertation Stanford University. Stanford, CA. Ginzburg, J. (1994). An update semantics for dialogue. In Proceedings of the 1st international workshop on computational semantics (pp. 1–10). Ginzburg, J. (1996). Dynamics and the semantics of dialogue. In J. Seligman, & D. Westerståhl (Eds.), Logic, Language, and Computation (pp. 221–237). Stanford, CA: CSLI.

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Syrett, K., & Koev, T. (2014). Experimental evidence for the truth conditional contribution and shifting information status of appositives. Journal of Semantics, 32, 525– 577. Taboada, M., & Mann, W. (2006). Rhetorical structure theory: Looking back and moving ahead. Discourse Studies, 8, 423–459. Tonhauser, J. (2012). Diagnosing (not)-at-issue content. In Proceedings of semantics of underrepresented languages in the Americas (pp. 239–254). Tonhauser, J., Beaver, D., Roberts, C., & Simons, M. (2013). Toward a taxonomy of projective content. Language, 89, 66–109. Velleman, L., & Beaver, D. (2016). Question-based models of information structure. In C. Féry, & S. Ishihara (Eds.), The Oxford Handbook of Information Structure (pp. 86– 107). Oxford: Oxford University Press. Webber, B. (1991). Structure and ostension in the interpretation of discourse deixis. Natural Language and Cognitive Processes, 6, 107–135.

chapter 7

Underneath Rhetorical Relations: the Case of Result* Edgar Onea

1

Introduction

There are at least two reasonable goals a theory of discourse representation may have. The first one is to derive one or all correct interpretation(s) of a discourse given its surface and potentially additional cues. The second one is to make transparent a given interpretation of some discourse. Let us phrase these aims a bit more precisely. Let d be some arbitrary coherent discourse, and ℐ(d) the set such that iff Ii ∈ ℐ(d) then Ii is a correct interpretation of d. A theory of discourse pursuing the first goal, then, is a map from d to a subset of ℐ(d). What are the elements of ℐ(d), however? Arguably an interpretation is some complex propositional entity or some more or less complex web of thoughts. It is not trivial to identify, to characterize or even distinguish such interpretations. Hence, there is an issue to (scientifically) communicate about such interpretations as distinguished entities. A representation of an interpretation of a discourse, hence, is a useful theoretic construction. If Rd (Ii ) is the representation of some interpretation Ii of d, then for any two interpretations Ii and Ij of any discourse d, Rd (Ii ) = Rd (Ij ) ↔ Ii = Ij . Moreover, Rd (Ii ) should be spelled out in some well-defined formal language. Let us define ℛd as the set of all representations of all interpretations in ℐ(d). A theory of discourse may then be (mainly) preoccupied to provide a subset of ℛd , hence being a map from either a d or from d and some subset of ℐ(d) to a subset of ℛd . Various theories with varying degree of success and formal rigor have been put forth to address these problems. To my knowledge, the most formally precise and complete one is Segmented Discourse Representation Theory (SDRT, Asher & Lascarides 2003). The way in * I wish to thank Julie Hunter, Márta Abrusán and Nicholas Asher for invaluable comments on previous versions of this paper. This paper also greatly profited from discussions with Katja Jasinskaja, Anton Benz, Hans Kamp, Uwe Reyle and Arndt Riester which I gratefully acknowledge. Finally, I wish to thank Madeleine Butschety and Swantje Tönnis for comments on the final version of the paper.

© koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004378322_008

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which SDRT generally represents interpretations of discourse involves a complex hierarchic web of rhetorical relations between the units constituting discourse. Let us call the arising representation of a discourse d under an interpretation Ii the rhetorical structure of d (under Ii). The rhetorical structure is semantically transparent, i.e., given a representation, we have an algorithm to derive logical entailments of that discourse under the relevant interpretation. Moreover, rules of introduction of rhetorical relations are provided which combine world knowledge, specific definitions of rhetorical relations, formal cues and further elements of a complex glue logic. These are reasonably successful in deriving a subset of all correct rhetorical structures of an arbitrary coherent discourse. Consider the toy example in (1), which consists of two discourse units, π1 and π2, delimited by square brackets. Under one natural interpretation, I1, π1 reports an event that happened temporally before the event reported by π2. Under another (potentially less natural but still fairly plausible) interpretation, I2, the reason why the event reported in π1 happened is the event reported in π2. In this case, the temporal order of the events is reversed. (1) [π1 John kissed Mary.] [π2 She smiled.] If we assume that the rhetorical relation between π1 and π2 is narration, we get the temporal order in I1. If we assume the rhetorical relation explanation instead, we can infer the reverse temporal order and the desired causality in I2. Moreover, we are entitled to infer narration for I1 because there is a scriptal information in our domain knowledge that allows us to infer that a kiss is a good occasion for smiling; analogous procedures apply for I2. Taking for granted that SDRT comes with a well-defined formal language that can express these rhetorical relations, representing (1) using rhetorical relations and discourse units appears to be in line with the goals outlined at the very beginning of this paper. Put differently, the rhetorical structure of discourse appears to be a good way to represent discourse thereby making its interpretation transparent (at least to some degree). However, what if any ontological status are we willing to assign to the rhetorical structure of discourse? In analogy to the syntax-semantics interface, one can think of the rhetorical structure of discourse as the LF of discourse. Making the interpretation explicit from an LF is the job of a compositional semantic theory of LFs and inferring LFs is the job of a generative syntax/parser. With this background, the aim of this paper is to provide a better understanding of what the rhetorical structure of discourse, the LF of discourse, actually stands for.

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But why even ask such a question? Returning to the syntax-semantics analogy, it has been occasionally argued that grammar (and LF as a component thereof) is some basic function of our brain. Under that analogy, rhetorical relations might be primitive notions expressing the way in which our brains glues together discourse units and nothing is left to say. However, it is not obvious whether one would really want to push the analogy that far. Alternatively, one could view rhetorical relations as a theoretical construct. By contrast, the speech acts constituting discourse seem to be intentional, goal-oriented human action (Roberts, 2012) and should, therefore, be captured at a ‘lower’ level of analysis. Say, Michael utters both sentences in (1). Would we want to say that he intended to establish the relation narration between them? Probably, we would rather want to understand what Michael is doing at a more natural, teleological level. It is far from obvious that a theory of discourse from such a perspective can be given eventually. Yet, it is certainly more likely that such a teleological theory can be given for discourse structure as compared to a basic teleological theory of syntactic structure. Indeed, there are at least some reasonable starting points. One possibility is that discourse is about answering questions, whereby questions stand either for discourse goals simpliciter (Onea, 2016) or they are a particularly ubiquitous species of discourse goals (Roberts, 1996, 2012). Hence, when a speaker conveys information to the hearer, the speaker should (at least for the sake of general cooperativity) assume that the speaker is actually answering some question the hearer was reasonably assumed to entertain. Discourse coherence, then, comes about by virtue of the inquisitive attention of individuals not jumping around erratically during an interaction. Instead, there may be rules that govern or at least constrain the way in which questions pop up in the minds of interlocutors. These rules then lead to reconstructing some kind of hierarchic web of questions as an intelligible “structure” of discourse. Then, a coherent discourse is a discourse which addresses questions that are connected to each other in some systematic (as opposed to random) way. One way in which questions may connect is that each part of a discourse addresses a question that is relevant for answering one main question the entire discourse is, in some sense, about, cf. Klein & von Stutterheim (1987) and Roberts (1996). Let us call the arising structure the erotetic structure of discourse, following terminology from Wisniewski (1995). Under such a view, something different can be said about examples such as (1). In particular, one can suggest that under I1, π2 answers the question What happened next? and under I2, π2 answers the question Why π1? Saying that Michael answers a particular question by uttering π2 seems more of an explanation of his action than mentioning the kind of rhetorical relation that ends

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up being established. Moreover, if we assume any standard theory of questions and answers (e.g. Hamblin 1973, Groenendijk & Stokhof 1984, Krifka 2001), we may also be able to infer the temporal order and causality of the respective events from the question-answer paradigm. Hence, we can think of such questions as an alternative to rhetorical relations. In conclusion, we can consider the erotetic structure of discourse as an alternative to the rhetorical structure of discourse. Unfortunately, a well-founded theory of erotetic structure with a significant level of empirical coverage has never been provided. In fact, the questions used in theories of erotetic structure or in more local theories of the semanticspragmatics interface (e.g. Mayol & Castroviejo 2011, Simons et al. 2010, 2016 and many others) have more often than not been acting as quaestiones ex machina when needed, without any systematic discourse justification as correctly observed in Asher (2004). Alternatively, such questions end up actually inferred from rhetorical relations as (partially) in Benz & Salfner (2014). Moreover, the few systematic proposals in the literature (Klein & von Stutterheim 1987, Ginzburg 1992, 2012, van Kuppevelt 1995a, b, Roberts 1996, Onea 2013, Riester 2019) seem to all focus on different aspects of discourse structure and are – in general – far away from what one might want to call a theory of discourse structure or discourse coherence. While I suggest a fragment-version of the theory in this paper, which is precise enough to allow comparison to SDRT, the empirical range remains minimal. Moreover, apart from some relatively minor structural constraints, I do not provide any generative algorithm that derives valid interpretations of discourse.1 For this very reason, the aim of this paper is not to compare SDRT with a competing theory, but rather to learn something about how the erotetic structure of discourse might relate to SDRT.2 In particular, I suggest that the

1 Interestingly, Benz & Salfner (2011) actually use the question under discussion as an extension of the glue logic in SDRT, hence they seem to suggest that the generative algorithm of SDRT can be extended in a theory of the erotetic structure. I acknowledge that this really makes the question urgent what kind of generative algorithm there might be in a theory of erotetic structure if reaching a more mature state in future. I have absolutely nothing to say regarding this question in this paper, except that this is a natural possible continuation of the research proposed here. 2 I am certainly not the only one to address this question. Some previous attempts to discuss this question include Jasinskaja (2011, 2012), Jasinskaja & Zeevat (2008), Asher (2004), Benz & Salfner (2014) and some others, but all these attempts have been much more limited in scope and generality. Having said this, much of what I say here has been present more or less

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erotetic structure of discourse and the rhetorical structure of discourse are nothing but the two sides of the same coin; put differently, two distinct levels of analysis of the very same phenomenon. One can think of the erotetic structure of discourse as some deeper level of discourse representation and the rhetorical structure of discourse is a particularly useful level of abstraction at which reasonable things can be said about discourse, including, mainly, the possibility to infer rhetorical relations. In other words, the erotetic structure of discourse is like a microscopic view of what lies behind rhetorical relations. Such a microscopic zoom can help understand not only subtleties of lexical meaning and grammar but also hitherto little-understood complexities about SDRT itself. For instance, it has been argued extensively (Klein & von Stutterheim 1987, Roberts 1996, Riester & Baumann 2013 and others) that a theory of the questions addressed by the utterances forming a discourse can be used to a better understanding of the information structure and of the prosodic realization of discourse. In addition, I suggest that by looking at the erotetic structure of discourse we can also gain a better understanding of subordination and coordination in SDRT. In SDRT, rhetorical relations can either be subordinative (such as background or explanation) or coordinative (such as narration or alternation), but question-based models have not been successful in making this distinction in an elaborate fashion. The problem is fairly obvious: in questionbased approaches, the glue between discourse units are questions. There is a sense in which the answer to a question is subordinated as compared to the question. Moreover, there might be some sense in which a question is somehow licensed by some other discourse unit, e.g. in the sense of the feeders van Kuppevelt (1995a) has in mind, or sub-questions in the sense of Roberts (1996). Then, questions might be subordinated as compared to their licensing discourse units. But this is true in every single case when a question somehow connects two discourse units. So, if we just think of questions as a replacement for rhetorical relations, coordination seems to disappear.3 Of course, there might be other, more elaborate ways to define some notion of coordination. Hence, coordination and subordination fail to be primitive notions. This fundamentally distinguishes question-based approaches from SDRT. So,

explicitly in these papers, but put in so different terms that a detailed comparison would be way too tedious for the purposes of this paper. 3 This is an insight that has motivated much of the research of Katja Jasinskaja in the past years. In fact, I gratefully acknowledge that it was she who drew my attention to this problem for the first time.

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the distinction between subordination and coordination must be at the very heart of the comparison between question based approaches and SDRT. In this paper, I show in a case study that this comparison is well worth the effort. In particular, I discuss the rhetorical relation result which has been argued to be either subordinative or coordinative depending on some further constraints in Asher & Vieu (2005). I show that by looking at the erotetic structure behind the rhetorical structure we can disentangle this Janus-headed character of result. The paper is structured as follows. In the next section (Section 2), I discuss an abstract and general way to represent discourse as graphs, very closely related to SDRT, but spelled out in a slightly different way. That section aims to facilitate comparison of theories by presenting the theories of discourse representation we have in mind in a compact and transparent way. Following this, I first introduce the relevant aspects of SDRT (Section 3), and then the relevant aspects of the theory of the erotetic structure of discourse I have in mind (Section 4). In Section 5, I show how one can think of subordination and coordination in the erotetic structure of discourse, i.e., how one can actually map fragments of question trees into SDRT graphs. In Section 6, I present, as mentioned above, a case study on the rhetorical relation result, followed by a case study of the lexical semantics of the German discourse marker schließlich (‘finally’) (Section 7), which further supports the kind of analysis of subordination and coordination put forth in the previous sections. The paper ends with a summary and outlook.

2

A General Framework for Discourse Representation

This section introduces a general format of representing discourse in terms of directed graphs together with a bunch of useful definitions. On the one hand, this abstract discussion requires a certain formal effort, but this effort pays off inasmuch as it allows to discuss and compare theories much more easily in the following sections. As a starting point, we define discourse representations based on the wellknown definition of directed (but not necessarily acyclic) graphs with labeled arrows as follows: Definition 1. (Discourse State) Let a discourse state D be represented as a tuple ⟨𝒩, 𝒮, 𝒞, L⟩ where: – 𝒩 is a set of nodes usually written as π1 …πn . π1 …πn are unique labels for discourse entities.

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– L ∈ 𝒩 is the distinguished node (usually the last node).4 – 𝒮 is a set of non commutative and non-reflexive subordinating arrows. We write subordinating arrows as l(s, t) and we represent them graphically as:

– 𝒞 is a set of non commutative and non-reflexive coordinating arrows. We write coordinating arrows as l(s, t) and we represent them graphically as:

Notational Convention 1. We write the LD in a box in the graphical representation.

Notational Convention 2. We may write 𝒜, which stands for 𝒮 ∪ 𝒞. We call 𝒜 simply the set of arrows. Notational Convention 3. We write l(s, t) if we do not want to signal whether the arrow is subordinating or coordinating.

Notational Convention 4. We call s the source, t the target and l is the label of the arrow. We may also refer to l(s, t) as an arrow from s to t.

As an example, consider the graph in (2), which we note as D. Then, 𝒩D = {π1 , π2 , π3 , π4 }, 𝒞D = {l1 (π1 , π2 )}, 𝒮D = {l2 (π1 , π3 ), l3 (π2 , π4 ), l4 (π2 , π3 )} and LD = π4

4 Attentive readers may observe that this essentially implies that there is no empty discourse. A discourse must contain at least one discourse move. In practice, there are cases in which we want to be able to have an empty discourse. A simple strategy to allow empty discourse states is to define L as a singleton (but potentially empty) set of nodes. Such moves always complicate notation, however. I generally opt for simpler notation whenever the problems arising are a) orthogonal to the aims of the paper and b) easy to fix but c) the fix would complicate notation.

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We stipulate that for any discourse state D, the set 𝒩D consists of semantic objects, i.e. meanings. Some theory of discourse 𝔗 may impose constraints on what kind of semantic objects it can represent, e.g. 𝔗 may stipulate that meanings are to be equated with strings of some formal or natural language or model theoretic objects. Moreover, let us stipulate that a theory 𝔗 ought to have definitions for all possible labels of arrows concerning the conditions under which l(s, t) can be added to D and (potentially) concerning the effects l(s, t) has on the overall interpretation of D. Moreover, a theory of discourse 𝔗 typically specifies rules for attachments of new nodes and new arrows to an existing discourse representation, i.e. update rules written as Dn + α yielding a new discourse state Dn+1 . Let us furthermore assume that any reasonable 𝔗 somehow makes use of LD in explicating Dn + α. It seems a natural stipulation that the sets 𝒞 and 𝒮 are disjoint. Furthermore, we assume that 𝒜 and 𝒩 may be partially or fully ordered by a number of ordering relations stipulated by 𝔗. One natural ordering relation is the linear order in discourse, which is naturally reflected in the left to right orientation of the graphical representation. We can now give some useful definitions. The definitions only make selfunderstood notions transparent given our specific definition of discourse states, hence I refrain from giving informal explanations for them: Definition 2. (Discourse navigation) Give a discourse D and a ∈ 𝒩D : – The parents of a, is the maximal set Par(a) ⊂ 𝒩D , such that for all b ∈ Par(a), there is an l such that l(b, a) ∈ 𝒜D . – The ancestors of a, Anc(a), is computed by the transitive closure of Par. – The children of a is the maximal set Child(a) ⊂ 𝒩D , such that for all b ∈ Child(a), there is an l such that l(a, b) ∈ 𝒜D – The descendants of a, Desc(a), is computed by the transitive closure of Child. – The direct relatives of a, DirRel(a) is the set Child(a) ∪ Par(a). – The relatives of a, Rel(a) is is computed by the transitive closure of DirRel(a).

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– The nodes directly dominating a, is the maximal set DirDom(a), such that for any y ∈ DirDom(a) there is an l such that l(y, x) ∈ 𝒮D . – The nodes dominating x, Dom(x), is computed by the transitive closure of DirDom. Definition 3. (Connectedness) A discourse representation D is connected iff for any a, b ∈ 𝒩D , a ∈ Rel(b) and b ∈ Rel(a). Definition 4. (Main Node) Iff a discourse representation D is connected, and there is exactly one a ∈ 𝒩D such that Par(a) = ∅, a is the main node of D.

Definition 5. (Discourse Tree) A discourse representation D is a discourse tree iff 𝒞D = ∅, D is connected, there is a main node m of D and for any a ≠ m, a ∈ 𝒩D , |Par(a)| = 1.

We can apply the definition of a tree for the example (2) above. There are two independent reasons why the example is not a tree. Firstly |Par(π3 )| = 2 and, secondly, l1 (π1 , π2 ) ∈ 𝒞. By removing one single arrow, and additionally moving l1 (π1 , π2 ) from the set of coordinating arrows 𝒞 to the set of subordinating arrows 𝒮, we can create two different trees from (2), as shown in (3). (3) a.

b.

With these tools we can give a minimal constraint of discourse coherence that any theory of discourse is assumed to share, namely that a coherent dis-

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course must be connected. Apart from this, we can spell out various frameworks of discourse representation by spelling out what the nodes are, what the arrows are and how arrows and nodes are defined by the respective theory. In addition we can spell out update rules and the constraints on the graph geometry that comes about in this way.

3

The Rhetorical Structure of Discourse

Given the formal framework developed in the previous section, we can spell out SDRT (Asher & Lascarides, 2003), as a theory of rhetorical discourse representation by specifying the nodes, arrows and rules of generation and interpretation.5 In a discourse representation D the nodes can be labeled Discourse Representation Structures in the sense of Kamp (1981); Kamp & Reyle (1993), i.e. representations of the meanings of discourse units. An example is given in (4). Of course, this has the immediate advantage that potential anaphoric antecedents, i.e., the discourse referents j and m for the individuals as well as e for the relevant event are already represented and easy to exploit. (4) John loves Mary.

Apart from the fact that SDRT inherits from DRT the capacity to account for anaphora this way, the fact that meanings are DRSs is not further relevant and I ignore this aspect in this paper. Hence, I only use labels like π1 …πn as nodes for simplicity. Hence, we represent (4) merely as π1. The arrows in SDRT stand for rhetorical relations, such as narration, explanation, contrast, elaboration etc. We write the name of a rhetorical relation as a label in the arrow representation. Some are subordinative,

5 Of course, a full specification of SDRT would go way beyond the possibilities of this paper. Hence, we only attempt to capture the main structural characteristics of SDRT in the characteristic format developed above. For additional discussion concerning the representation format of SDRT, consider also Asher & Lascarides (2003) and Danlos (2006).

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some coordinative. In SDRT, all rhetorical relations have a semantic interpretation, i.e. they license a set of inferences. For instance, if two discourse units π1 and π2 are connected by an arrow labelled narration, i.e. narration(π1 , π2 ), we can infer that the event reported in π1 happened before the event reported by π2. Elementary discourse units are simple sentences, as e.g. (4), non restrictive relative clauses, some adverbial clauses and the like. Complex discourse units are postulated abstract entities, entire discourses represented as discourse states in their own right. Therefore, complex discourse units may have some internal structure. Assume, for instance, that π2 and π3 in (5) form a complex discourse unit π′ , which is part of a discourse. This can be represented as in (6). (5) [π1 Peter had a beautiful evening.] [π′ [π2 He had a great meal] and [π3 he won a dancing competition].] (6)

Since representations as in (6) are tedious, we write them, as usual in SDRT, in a unified representation format in which sub-graphs are directly represented as part of the respective graph as in (7), in which the non-arrow edges graphically represent that we are dealing with an embedded discourse representation. Complex discourse units can only arise by coordination in SDRT. This reminiscent of the idea that coordinative arrows are symmetric, i.e. multinuclear in the sense of RST (Mann & Thompson, 1988b), while subordinating arrows are asymmetric, nucleus-satellite relations, i.e. they are fully represented by their superordinate nucleus. (7)

Notice that this is not actually extending the graph-representation postulated in the previous chapter, it is just a statement about what can be a node in SDRT.

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In particular, discourse representations can be a node in SDRT. Then, nonarrow edges are not really elements of a graph, but rather a graphical sign suggesting that we are transitioning from a super-graph to a sub-graph. This also means that for a graph such as (7), the main discourse representation only has two nodes: π1, π′ . The nodes π2 and π3 are only elements of the graph π′ . For the very same reason, whenever a discourse representation has a discourse representation as its node, each discourse representation needs to have, per definition, a distinguished node, whence the two boxed nodes in (7). Update in SDRT happens by means of attachment of new nodes. New nodes are always attached as targets of arrows from existing nodes. In SDRT, all rhetorical relations have rules of introduction, i.e. some facts must hold before one can attach a new arrow. In these rules, a major role is played by discourse markers such as and, and then, nevertheless, because, etc. which are often associated with particular rhetorical relations. We have nothing to say about the generative algorithm here and take for granted (with some charity, indeed) that for any given discourse the respective representation can be derived in a formally respectable way. One constraint, however, remains important for our purposes, the so called Right Frontier Constraint (Polanyi, 1988; Asher, 1993b; Asher & Lascarides, 2003). This constraint governs the possible attachment sites for discourse updates and, thereby, also the possible anaphoric antecedents. We can state the right frontier constraint in our framework. It leads to some slight complications, however, due to the format which we use to present SDRT:6 Definition 6. Right Frontier The right frontier of some discourse D, RF(D), is defined as: RF(D) = DomD (DL ) ∪ B, where – B = {DL } iff DL is not a discourse representation, – B = RF(DL ) iff DL is a discourse representation.

6 Notice that in standard SDRT practice, complex discourse units are treated as standard nodes and are actually available attachment sites for nodes. However, attaching to a complex discourse unit directly does not actually happen. Instead, most generally, some topical node is computed for the complex discourse node and this then serves as an attachment site. In our framework we can make this more transparent by not allowing complex discourse units to be attachment sites at all. We do this, by not making them part of the right frontier to start with.

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Definition 7. The Right Frontier Constraint Given a discourse D and a new discourse unit π, only arrows l(π1 , π) can arise such that π1 ∈ RF(D), i.e. all possible attachments must be along the right frontier of D. Only anaphoric antecedents along the right frontier are visible to π.

The right frontier of a discourse D is not necessarily a subset of 𝒩D . Having said this, the following statement is contigent: π ∈ 𝒩D+π . If it is true, some arrow from π′ ∈ RF(D) ∩ 𝒩D to π will be introduced and LD+π will be π. If not, the update applies to some sub-discourse D′′ in D + π (or in some sub-discourse of D + π etc.) and only within D′′ arrows will be established. Consider the two possibilities in (8a) and (8b): (8) [π1 Peter had a beautiful evening.] [π′ [π2 He had a great meal] and [π3 he won a dancing competition].] a. alternative update: [π4 He spent it with Mary.] b. alternative update: [π′4 He danced with Mary.] First, consider the update (8a). In this case we can safely assume that π4 gives background or elaborates on π1, which is, of course part of the right frontier of the discourse. Hence, the update will be the one in (9), in which the main discourse is extended by an additional node. (9)

As opposed to this, the update in (8b) actually updates the embedded representation π′ by elaborating on the event of winning the dancing competition.7

7 Alternatively, one could assume that the update provides explanation for the winning of the dancing competition. This would only lead to a change of the label of the new arrow.

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Update does not necessarily mean just adding a node. It can also mean that a node is removed from a discourse and it is replaced by a complex discourse unit formed by the removed node and the new discourse move. Moreover, update can also involve the accommodation of nodes either in the main discourse or in some sub-discourse.8 Especially when accommodation is involved, we can have cases in which existing arrows are ‘disrupted’, i.e. replaced by a chain of arrows. In other words, holistic update may involve full scale reinterpretation. We do not consider the dynamics of update here in more detail and simply note that, whatever update rules there may be, they can be expressed in the current framework. The only complication we consider is the possibility that there may be several arrows with the same target. This is, in a sense, trivial, for many rhetorical relations are compatible with each other. For instance, if we have result between two nodes, more often than not narration obtains between them as well. But in some cases, it can happen that the sources of the arrows differ even if the target is the same. Crucially, the source could be in the main discourse D and the target in some sub-discourse D′ . Suppose, for instance (ignoring plausibility), that in some larger context we manage to infer that in (10) π′4 also explains π1, say: the very fact that John danced with Mary is the reason why he considered the evening great. Given an SDRT internal principle (Maximize Discourse Coherence, Asher & Lascarides 2003, pp. 234) that entitles us to establish as many valid rhetorical relations as possible, we would want to get a representation such as (11).

8 Accommodation is, however, quite heavily constrained in SDRT by a small set of structure building rules and presupposition projection rules.

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But how can an arrow be postulated between two entities which are not in the same discourse state? One way to achieve this is that when we intend to add a new arrow which bridges across two discourse states such that one is part of the other, we spuriously introduce the target node into the discourse state the source is a node of. This would make π′4 both an element of the main discourse representation and of the sub-discourse labelled π′ . While this seems to be a somewhat dubious solution, it seems to naturally fit with the observation that, indeed, the kind of connection we are after is not very common. Such ‘long distance’ connections are mostly limited to certain specific dialogue situations, cf. Asher & Lascarides (2003, pp. 14) and Prévot & Vieu (2008).

4

The Erotetic Structure of Discourse

As mentioned in the introduction, the situation concerning theories of the erotetic structure of discourse is more delicate than the one concerning the rhetorical structure of discourse. The most prominent theory at the semanticspragmatics interface and – arguably – the most formally explicit one is the question under discussion approach of Roberts (1996, 2012). However, this theory was never meant to have the full empirical coverage of monologue/text structure as SDRT has. Moreover, it has never been used for such purposes in a systematic way. As opposed to this, the only theory of erotetic structure that has been tested in the empirical practice of corpus annotation is Ginzburg (2012). However, Ginzburg provides a totally different, computational, approach and mainly focuses on dialogs. On the other hand, theories that have been designed to have a wider empirical coverage, such as Klein & von Stutterheim (1987) and van Kuppevelt (1995a,b, 1996), have been quite informal and they also have hardly been tested in annotation practice comparable to SDRT annotated corpora. While Onea (2016) develops a more explicit but also in many ways dif-

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ferent version of van Kuppevelt (1995a), that proposal is mainly focusing on the semantics-pragmatics interface rather than discourse modeling. With this in mind, I present one explicit but very fragmentary version of a theory of erotetic structure which is defined at a reasonable level of formal precision. Thereby, I first discuss what the nodes and arrows are and then I discuss constraints on update and accommodation. The presentation is more detailed than the presentation of SDRT because we are now building up a theory instead of just presenting one. Hence, some additional discussion, motivation and explanations are required. 4.1 Nodes and arrows We assume that nodes can be questions or assertions.9 We use π1, π2, etc. for assertions and q1, q2, etc. for questions. Since questions and assertions are meanings and not natural language expressions, we may use English interrogatives and declaratives to circumscribe them. Thereby we may use odd formulations to eliminate as many ambiguities as possible. Moreover, both types of nodes may be implicit as well as explicit. This assumption is commonly made for questions (e.g. Roberts 1996) i.e. in many cases, questions will need to be accommodated, but here we allow the accommodation of assertion nodes as well. We discuss accommodation in the next section. Notational Convention 5. We write implicit nodes in angles, e.g. ⟨q1 ⟩ or ⟨π1 ⟩.

There is one important common characteristic of theories of erotetic structure that we also adhere to here, namely that they give rise to discourse representation in terms of question trees defined as follows: Definition 8. Full Erotetic Structure A discourse D exhibits full erotetic structure iff, for any l(a, b) ∈ 𝒜D , at least a or b is a question.

9 By questions and assertions we mean semantic objects in the sense of some standard semantic theory of questions and answers, e.g. the classical Rooth-Hamblin semantics for questions and answers (Hamblin 1973, Rooth 1992), partition semantics (Groenendijk & Stokhof, 1984) or structured meanings as in Krifka (2001). Moreover, since in a theory of discourse we also need to somehow handle anaphora, we must assume some dynamic version of such theories. We remain neutral here regarding these theoretical choices as they involve theoretical issues orthogonal to our aims and refer to questions and assertions simply using labels.

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Definition 9. Question Tree A discourse D is a question tree, if it is a discourse tree and it has full erotetic structure. So, questions are not only usual nodes in a discourse representation, but rather the glue between assertions. Assertions cannot be connected with each other by arrows. Since the arising structure is a discourse tree, only subordinating arrows exist. We consider four types of arrows in this paper: answerhood, licensing of potential questions, sub-questions and dependent questions. 4.1.1 Answers The only arrows from questions to assertions we look at represent that the assertion answers the respective question. We write ans(q, π) to mean that the assertion π answers the question q.10 Generally, it is assumed that an answer π must exhibit the right information structural properties to be a congruent answer to q. If we assume that information structure is fully transparent in meanings, this may also apply to implicit nodes. Congruence is a complicated issue, cf. e.g. Roberts (1996), Rooth (1992), Krifka (2008), but we leave it at two fairly simple examples here: (12) shows congruent question-answer-pairs, whereas (13) does not. (12) a. A: B: b. A: B:

Who danced? PETER. Who danced? PETER danced.

(13) a. A: B: b. A: B:

Who danced? #Peter DANCED. Who danced? #PETER talked.

short answer ong answer

not congruent does not settle the question.

Generally, a theory of answerhood predicts the right inferences from the question-answer pattern. For example (12a) should license the inference that Peter danced.

10

Alternative arrows of this kind are also conceivable, e.g. commenting on a question, contradicting the relevance of a question etc. But for the limited range of this paper, such arrows are not relevant.

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4.1.2 Potential Questions According to van Kuppevelt (1995a) and Onea (2016) an additional type of arrow must be assumed which has an assertion as its source and a question as its target. Van Kuppevelt calls this feeders whereas Onea calls this licensing of potential questions. Question feeders and licensing of potential questions should be similar or exactly the same, but potential questions are defined in stricter terms, so we use this notion here. For the purposes of this paper, we take the following informal definition: Definition 10. Potential Questions If a question q has a supposition p and some assertion π in discourse makes p significantly more probable, then π licenses q as a potential question. Thereby, a supposition is the kind of possibility the person who asks a question is usually assumed to have in mind in order to ask that question, some kind of a general, weak pragmatic presupposition. To get the intuition of what this means, consider the example in (14). B’s question in (14), does not have any clear semantic presupposition. However, there is a sense in which there should be a vivid possibility that there is an Apple Shop around. Otherwise, why would B ask A about that. This we call the supposition. Certainly, the way in which B phrased his question would be quite inappropriate if the person addressed would carry a Samsung bag instead. B would probably rather ask: Do you know by any chance whether there is an Apple Shop around here?. Then, the supposition would be that the addressee could conceivably know whether there is an Apple Shop around, which is, again, supported by evidence, since someone who carries a Samsung bag might be interested in electronic equipment. (14) Context: B is desperately searching for a new Apple MacBook charger. A: Look, the guy over there carries an Apple bag. B: (addressing the guy) Excuse me, is there an Apple Shop around here? To avoid the intricacies of a recursive definition of suppositions, we simply postulate that the supposition of wh-question is the respective existential closure, as in (15a), the supposition of polar question is the mentioned alternative as in (15b) (though for negative polar questions the situation is arguably much more complicated, cf. e.g. Romero & Han 2004, Romero 2005) and disjunctive questions have the disjunction itself as their supposition, as in (15c).11 11

A formal definition of potential questions can be given following Onea (2016) as fol-

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(15) a. Question: Who danced? Supposition: Someone danced. b. Question: Did John dance? Supposition: John danced.12 c. Question: Did John dance, or Mary? Supposition: John or Mary danced. One example of licensing a potential question is then in (16). The supposition that someone might be in the house is made more probable by the observation that the lights are on. Hence, the question is licensed as a potential question. (16) Context: A and B are in front of a house. A: Look, the lights are on. B: I wonder who might be in the house? Some additional examples are the ones in (17). The question (17a) has the supposition that John was wasted in the end, and the information that he drank a lot of vodka makes this supposition much more probable, hence licensing (17a) as a potential question. Similarly, the question (17b) has the supposition (arguably even the presupposition) that John suffered some injuries. Given the information that he had a bad fall, this supposition is much more probable, hence A’s assertion licenses B’s question as a potential question. (17) a. B: John drank a lot of vodka. A: Was he wasted in the end? b. A: John had a bad fall yesterday. B: What injuries did he suffer?

12

lows: A potential question q licensed by some utterance u in some context c is such that: c + u ⊧def p and c ⊭def p, where p is the union of all highlighted alternatives of q, and there is no p′ , a highlighted alternative of q, such that c + u ⊧ p′ Thereby, ⊧def means defeasible entailment, whereas ⊧ means classical entailment. Defeasible entailment is to be understood as in Asher & Lascarides (2003). Moreover, highlighted alternatives of wh-questions are all positive alternatives, and for polar questions, the explicitly mentioned alternative is highlighted, following Roelofsen & van Gool (2010) and subsequent research in inquisitive semantics. Crucially, we do not commit to any formal semantic theory of questions in this paper, hence, we stick to an informal definition only. The idea that for polar questions the explicitly mentioned alternative constitutes a supposition appears to be not very intuitive. In Onea (2016), this leads to a number of issues that are ultimately solved in ways that go beyond the scope of this paper. We keep in line with Onea (2016) here, acknowledging a potential problem.

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In the case of polar questions, the assertion should not entail the supposition of the question. This is because in that case the question is answered already and there is no point in asking it. For wh-questions, the supposition may well be entailed by the assertion that licenses the potential question, the only requirement is that none of the actual alternatives under consideration are entailed. Consider, as an example, (18). (18) a. A: A friend of mine told me that I am an idiot. b. B: Why did he say that? alternatives: {He said that because he believes A is an idiot, He said that because he wanted to upset A … } A why-question requires the interlocutor to pick a possible causal explanation: some possibilities are listed in (18b). The supposition of the why-question is then simply that there is a reason why the proposition under question happened. This supposition is the disjunction of all the alternatives under question in (18b). I assume that the latter inference is entailed by (18a). Crucially, none of the alternatives themselves are entailed by (18a) in the context. Therefore, we say that (18a) licenses (18b) as a potential questions in the given context. This is such a general phenomenon, that why-questions are called likely potential questions in Onea (2016). In (19), two examples of questions are given which are not licensed as potential questions. (19) Mary kissed John. a. Who kissed John? b. Does Anna know that Mary kissed John? While (19) entails the supposition of (19a), i.e. that someone kissed John, it also answers the question, hence there is no longer a question to raise. Moreover, even the question Who else kissed John? would not be a licit potential question, since the probability that someone else kissed John is not increased by the information that Mary kissed John. (Of course, there might be situations in which Mary would only kiss particularly kissable individuals, and, hence, others would also be likely to kiss John. Then, we would indeed have Who else kissed John? as a potential question.) For (19b), on the other hand, the definition of potential questions does not seem to apply at all. Only in special contexts one could even defeasibly infer from the fact that Mary kissed John that Anna knows that, or that she would even care. In such contexts, arguably, (19b) would be a natural discourse continuation indeed.

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Potential questions are a fairly weak notion. One should want to assume that there is some salience or likelihood ranking over them. For instance in (20), (20b) is a much more likely continuation question, even though both questions qualify as potential questions. The likelyhood of potential questions is, in my view, not only a linguistic notion but rather a derivate of general domain knowledge and psychological facts about humans. It will play a role in our analysis of the rhetorical relation result. (20) Peter fell out of the window of his 2nd floor flat. a. What was the top speed he reached while falling? b. Did he break anything? Finally, there are some examples which lead to a natural worry about the very essence of the definition of potential questions. (21) seems a very plausible discourse, very similar to (17a), but not covered by the definition even though the example is just a reformulation of (17a). The question (21) has the supposition that John was sober at the end, but actually this is made less instead of more probable by B’s utterance. Hence, (21) is not a potential question. (21) B: A:

John drank a lot of vodka. Was he still sober at the end?

Following Onea (2016), I assume that questions which are derived from licit potential questions by a set of falsifiable principles are an additional kind of potential questions called derived potential questions. Such principles include, for instance, politeness, superstition or wishful thinking. (21) can be understood as a reformulation of the licit potential questions based on the principle that the speaker chooses to explicitly mention the alternative he hopes to be true. A case of politeness or superstition could be the one in (22), in which the licit potential question is Did John die?, however there seems to be a social convention based on politeness or superstition that in such a case one should rather mention the more positive alternative. This would make (22) an example of a derived potential question. (22) a. John had a terrible car accident. b. Did he survive? When π licenses q as a potential question, we write PQ(π, q). In the definition of potential questions, only assertions have been considered to license potential questions. This is because, under a classical perspec-

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tive, only assertions provide new information, and only new information can change the probability of some proposition. But, of course, this is a strong simplification. A speech act does not only update a discourse by the propositional content it has but also by information about the particular wording used, the information that the particular speech act occurred, when it occurred, who the speaker was etc. (cf. Stalnaker 1996 for a similar view concerning anaphora). Hence, there is no reason why questions, for instance, could not license potential questions as e.g. in (23). However, we disregard such cases for simplicity. (23) A: B:

Who invited John to the party? Why are you asking?

Finally, one should keep in mind that just as feeders in van Kuppevelt (1995a), potential questions are just possible discourse continuations given some utterance, and do not incorporate a claim about the urgency or probability of such a continuation. Similarly, potential questions are not a filter for valid/coherent discourse moves. There may be licit potential questions which are still not possible in a coherent discourse for independent reasons and there are many valid discourse continuations which are not instances of potential questions. For instance, in the paragraph immediately following example (19), I have suggested that the question Who else kissed John? is not a licit potential question in the respective context, still, it is a perfectly acceptable discourse continuation. 4.1.3 Sub-questions and Dependent Questions For Roberts (1996) (and arguably also for Klein & von Stutterheim 1987, at least for the main structure of a narrative discourse) sub-questionhood applies iff the information requested by the sub-question is a strict subset of the information requested by the super-question. Hence, in general (though this partially depends on assumptions about the interpretation of the respective interrogatives) one can assume that the question pairs in (24), are examples of superand sub-questions. We can then write sub(q1 , q2 ) as a corresponding arrow. (24) a. super-question: Who loves whom? sub-question: Whom does Max love? b. super-question: Who loves John? sub-question: Does Anna love John? c. super-question: What happened last year? sub-question: What happened in the first half of last year?

For van Kuppevelt (1995a,b), the notion of sub-questionhood (also known as sub-topic) applies when some answer to a question is not satisfactory in

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thereby feeds another question attempting to solve the same issue. One way to capture this would not involve a direct arrow between sub-question and superquestion, but instead this relation could be determined in a more indirect way by looking at a chain of arrows, as in (25): (25) A: B: A: B:

[π1 Mary is worried.] [q1 Why?] [π2 John, her husband, wants to buy a DAT-recorder.] [q2 Why is she worried about that?]

Onea (2016) shares the notion of sub-question put forth by Roberts (1996), but suggests that it might be a special case of so called dependent questions, cf. Ciardelli (2014), Groenendijk (2015) and partly also Wisniewski (1995). Consider for example (24b). Certainly, there is a sense in which one can address the superquestion in a systematic way by going through a series of individuals and asking of each of them, whether they love John, as suggested in (26). But this seems to be the special case in which the speaker actually knows the answer and goes through a series of sub-questions just to make sure she does not miss any alternative. However, there are many cases in which there is lack of information, and one can only address some question by first requesting information that allow to derive an answer, as in (27). Dependent questions are noted as dep(q1 , q2 ) (26) q1: Who loves John? q2: Does Anna love John? q3: Does Peter love John? q4: Does Michael love John?

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[q1 Who loves John?] [q2 Did Mary get divorced last year?] [π1 Yes] [π2 Then, it is Mary who loves John.]

I have outlined above all major types of nodes and arrows that have been considered in the literature. It seems reasonable to assume that for a general theory of erotetic structure not only both types of nodes and all four types of arrows are necessary but also more arrows and potentially more types of nodes need to be introduced. Just think of exclamatives, imperatives etc. which are entirely missing for now. However, for the particular purposes of this paper, I only consider two types of arrows: PQ and ans, and the nodes for questions and assertions. I readily admit that sub-questions and dependent questions seem to be important notions. For instance, it seems that the overall architecture of a news-flash is very naturally captured by an inquiry strategy such as the one in (28). (28) q1: What happened today? q11: What happened today in politics? q111: What happened today in local politics? q112: What happened today in federal politics? q12: What happened today in the economy? q13: What happened today in sports?

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But many problems arise once sub-questions enter the picture. One problem is that making sub-questions overt often does not lead to an acceptable discourse. For instance, in (28), one can neither felicitously reply by q11 to someone uttering q1, nor can one continue a text/monologue with a sequence of sub-questions such as q1, q11, q111 etc. Moreover, even for a simple case such as (28), it seems to be entirely ad hoc that we decided to write q111 as a subquestion of q11 and not directly as a sub-question of q1, even though, techically, q111 does qualify as a sub-question of q1 as well. Moreover, we could have just as well assumed an entire chain of intermediate sub-questions between q11 and q111. Last but not least, just any assertion with default intonation would count as an answer to q1, as observed already by Tichy (1978). Hence, it seems ad hoc to assume any sub-questions in the first place. For sure, there is a deep intuition in the idea that sub-questions do contribute to structuring discourse in some strategic sense, cf. Roberts (1996); Klein & von Stutterheim (1987); but making this intuition a constitutive part of a theory of discourse turns out to be difficult, cf. also Asher (2004). For this reason, it seems reasonable to ignore sub-questions for now leaving their integration into the theory for a later time. The same applies mutatis mutandis for dependent questions as well.13 4.2 Update and Accommodation In this section, we focus on the discourse update mechanism. This incorporates some structural constraints on what can be represented in the present framework. Similarly, we consider some constraints on accommodation. These constraints implicitly impose a certain limitation to the range of discourse interpretations that can be made transparent in this framework. Given a non-empty discourse representation D and a new node α, the direct update (+) is specified as follows.

13

A clarification is in order here. Since PQ is the only question licensing arrow in our theory, any discourse move that cannot be accounted for with PQs is predicted to be incoherent by our theory. This seems to imply that potential questions are a filter of coherence of discourse. This, however, should not be taken too seriously. The reason is that the empirical range of the theory we are building up is very limited, and, therefore, we cannot make any serious claims about discourse coherence in general. The aim should be to extend the theory in future research to capture all coherent interpretations – but our aim in this paper is not to gain insights into discourse coherence but to compare theories and thereby learn something interesting about the nature of subordination and coordination. Using the two arrows only, suffices for this – and only for this – purpose.

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Definition 11. Discourse Update

iff α is licensed by LD ⎧ ⟨𝒩D ∪ {α}, 𝒮D ∪ {PQ(LD , α)}, 𝒞D , α⟩ { { as a potential question in D { { { ⟨𝒩D ∪ {α}, 𝒮D ∪ {ans(LD , α)}, 𝒞D , α⟩ iff α is a congruent answer to LD { D+α=⎨ and there is no x ∈ 𝒩D { { such that ans(LD , x) ∈ 𝒮D { { ⟨𝒩 , 𝒮 , 𝒞 , ιx. x ∈ DirDom(L )⟩ + α iff DirDom(L ) ≠ ∅ { D D D D D { ⎩ undefined otherwise

Notice that + has not only the possibility to update the last node but recursively navigates up until the main node of a discourse if needed and attempts to update any node on the way until success or ultimate failure. Hence, given some arbitrary discourse state in (29), we get the marked geometrically possible attachment sites for the new utterance α. Whether or not a real attachment can happen depends on the nodes themselves of course. (29)

However, we need a mechanism of accommodation as well. Otherwise we cannot have any implicit nodes in the discourse representation. Accommodation in a purely mechanical sense amounts to the following rule: Definition 12. Accommodation Iff D + α is undefined, one is allowed to compute D′ + α where D′ is the representation of the same discourse underlying D, however enriched with one question or one assertion complying with the constraints on accommodation. The way the definition of accommodation should be understood is that accommodation is not actually a geometric operation on discourse structure. It rather

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literally means: do as if the text contained some more material, calculate the representation of the text under this assumption and re-try the update. Since this is a recursive procedure, this means that unlimited steps of accommodation are possible (in a purely technical sense). Consider an example like (30). (30) [π1 Mary is worried.] [π2 John, her husband, wants to buy a DAT-recorder.] Clearly, the discourse cannot be updated by π2 if it only contains the node π1 as a starting situation because there is no arrow that connects two assertions. Then, one solution is to parse the text in (31) instead, which would lead to a simple update. But nothing in what has been said before blocks one from ending up with absurd accommodation series leading to something like (32): (31) [π1 Mary is worried.] [q1 Why?] [π2 John, her husband, wants to buy a DATrecorder.] (32) [q0 How was Michael doing today?] [π0 Not so fine.] [q1 Why?] [π1 Mary is worried.] [q2 Why?] [π2 John, her husband, wants to buy a DAT-recorder.] On the one hand that means that accommodation is powerful enough to find any interpretation that is valid according to the theory. One the other hand, that also means that accommodation needs to be heavily constrained if it is supposed to help building erotetic structure of coherent discourse and not deliver absurd interpretations.14 We assume that any utterance in discourse has some kind of pragmatic relevance presupposition of whatever is being said. Hence, accommodation of discourse nodes essentially means that the hearer is trying to find a way to make sense of what her interlocutor said under the presumption that there must be a valid interpretation. Then, accommodation is generally constrained by the principles of retrievability and economy. The hearer always assumes that there must be some non-random, non-erratic way to reconstruct validity (as a minimal ingredient of coherence) and that simpler solutions amounting, e.g.,

14

Some ideas about accommodation in question trees have been already proposed in the literature. For instance, in accommodating questions, one can arguably make use of the mechanism of presupposition accommodation in the sense that questions are focuspresuppositions of their answers, cf. Rooth (1992).

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to more likely potential questions or shorter accommodation chains are preferable. This will suffice to predict the superiority of (31) over (32), but certainly not deliver the kind of generative algorithm SDRT can provide. Whenever there is some explicit expression (including intonation) that conventionally signals a particular tree architecture or the presence of a particular source node, we just use standard presupposition accommodation to handle such cases. In other words: whatever is marked explicitly cannot be ignored in the discourse representation, unless it is already part of the previous discourse. We consider an example later in this section. For now, I focus on some basic constraints on accommodation for non-conventional cases: Definition 13. Constraints on assertion accommodation – The entailment constraint No proposition can be accommodated if it is not entailed by the discourse it dominates. – The structure constraint Propositions lumping together chains of eventualities/propositions can only be accommodated if they have temporal, causal or logical structure. Both constraints are in need of some explanation, partly because they seem to contradict each other. Consider, for example, that we have two propositions π1 and π2 which are explicitly expressed. They denote the events e1 and e2 respectively. Suppose that we want to accommodate the questions q1: What happened first? and q2: What happened second? to which the two utterances would be congruent answers. Hence, there would be no difficulty in accommodating these questions. But in order to connect these two questions we would need to accommodate some additional node like π0: e1 and e2 happened in a temporal order. Now, according to the structure constraint we would be allowed to do this, but the overt material namely the propositions actually expressing the events do not entail π0. And vice versa, if we wanted to accommodate a node which is actually entailed by the two propositions, we would need to find something at least as weak as π1 ∧ π2 , but that will never have any kind of structure the structure constraint would possibly have in mind. At this point it is useful to be reminded that we are only looking at ways to make a particular interpretation transparent and not ways to arrive at a valid interpretation in a predictive way. Hence, it is not necessary that the overt material entails the propositions which gets accommodated. It is the entire discourse tree the respective proposition dominates which will need to entail it, because a discourse tree cannot represent anything other than a particular

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interpretation. Of course, if π1 answers the question q1 and π2 the question q2 as suggested above, from this it follows that e1 happened before e2 and this will entail π0. In other words, the entailment constraint is purely geometric.15 The structure requirement is, essentially, a measure against triviality. Consider the arguably incoherent discourse in (33). In a theory such as Roberts (1996) there is a valid analysis of this discourse and it is quite easy to find. In fact, if we allow accommodation of questions and we have the sub-question arrow, any text can get a trivial analysis similar to the one in (33), i.e. we accommodate the corresponding congruent question for each assertion and then we accommodate a trivial super-question which connects the tree. (33) [π1 John loves JANE.] [π2 A CAR is burning.] [π3 It is raining.] (34) q0: What is the way things are? q1: Whom does John love? q2: What is burning? q3: How is the weather?

Of course, in principle we can do something very similar in our version of the theory as well. In particular, we could just merge the existential versions of the three propositions together, hence allowing the very same congruent questions as potential questions, which would lead to the analysis in (35). (35) π0: John loves someone, and something is burning, and a there are specific weather conditions.

15

Little surprisingly, this means that by accommodating questions with presuppositions we can circumvent the entailment constraint, which would be a terrible problem if we were considering an algorithm to derive valid interpretations.

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Crucially, accommodating π0 is now blocked by the structure constraint, since there is no information about the temporal, causal or logical structure involving the propositions which were merged together. Hence, even though we do not want to claim that in this fragmentary theory only coherent discourse segments have a valid representation, we can at least say that we impose non-trivial constraints on interpretation and that at least some incoherent discourse is judged non-valid. Of course, spelling out in model theoretic terms what we mean by temporal, causal and logical structure is not a trivial issue, and I leave this implicit in this paper; but some examples are provided in sections 6 and 7. Returning to the peculiarities of the update operation +, attentive readers might have observed that it complies to the Single Answer Constraint defined below. Definition 14. The Single Answer Constraint A discourse D complies with the single answer constraint iff, for any x ∈ 𝒩D , if x is a question, there is at most one y ∈ 𝒩D , such that there is some ans(x, y) ∈ 𝒜D

The Single Answer Constraint is mainly motivated by parsimony and simplicity. Roberts (1996) explicitly allows multiple (partial) answers to a question. In her view, a question like q in (36) can be addressed in at least two ways. The first one is a direct way to address the question. In this case, several direct and congruent answers are given to the very same question. As opposed to this, the second way to address the question involves addressing sub-questions. Usually, one expects a contrastive topic intonation for the second strategy (Büring, 2003). Hence, it is information structure that decides which strategy should be chosen in the discourse representation. (36) A: [q Who loves whom?] B: [π1 JOHN loves JANE] and [π2 MAX loves IDA.] q1: Whom does John love? q2: Whom does Max love?

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a. Direct strategy:

b. Contrastive topic strategy:

The Single Answer Constraint means that the direct strategy in (36a) is not available. One reason to disallow multiple answers to a question is that the notion of answerhood itself tends to get ambiguous otherwise. In particular, when one single answer is given and interlocutors assume that this answer settles the question, the question is – obviously – no longer open for attachment and discussion. Put differently, if a question is already answered, there is neither a point in delivering one more answer nor in raising a sub-question. Hence, we can think of that question as a node that is invisible i.e. not accessible for any further development of discourse. When multiple answers are allowed, we do not know whether a question that has received an answer is still available or not for discourse attachment. Hence, we need some extrageometric constraint that will decide whether the question is still open, hence further sub-questions and answers can be added, or not. While there are several quite obvious ideas one may try to implement, e.g. a distinction between complete and partial answers, the single answer constraint appears to be particularly simple. It ensures that – on purely geometric terms – when an answer is given to a question, we know that that question is settled.16 Hence, answerhood imposes visible constraints on further discourse developments.

16

This does not entail in any way that answers need to be exhaustive. It fully suffices if they settle the question to the degree which is necessary given the goals of the interaction or the knowledge horizon of the interlocutors.

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Applying update bluntly would – of course – mean that in (36) the information that John loves Jane settles the question who loves whom and the second assertion connected by conjunction would then remain an unattached node or would require some other licensor. We solve this problem by assuming a more complex tree gained by accommodation of some intermediate nodes. In particular, one way to account for the direct strategy is the one in (37). (37) π3: There are two pairs of lovers. q1: Who loves whom as part of the first pair? q2: Who loves whom as part of the second pair?

Accommodating the three nodes in (37) seems ad hoc. However, in general, one cannot give two answers to the same question unless explicitly marked by intonation and some discourse markes such as and and but. If we now claim that it is part of the lexical meaning of such discourse markers to allow accommodation of the respective kind, we do not say anything very surprising given the analysis of contrast and conjunction in Jasinskaja & Zeevat (2008) and Toosarvandani (2014). The second strategy in (36) is also not available in the current theory, since we do not use sub-questions. Still, we can reproduce the result as follows.17 (38) π3: Max and John love each someone. q1: Whom does John love? q2: Whom does Max love?

17

One could argue that (9)b) is a geometric alternative to the trees compositionally derived by Büring (2003).

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One immediate advantage of the current approach is that now the two answers only differing in intonation give rise to structurally identical trees, the only difference being the particular nodes. While the answers target different questions, it is still transparent that the two sentences relate to the main question q in the same way.

5

Rhetorical Relations as Families of Questions

5.1 The General Idea As discussed in the introduction, one fundamental question about rhetorical relations concerns their ontological status. In particular, if we think of discourse moves as goal oriented human actions, it is not obvious how rhetorical relations can explain them. I have suggested above that there are reasons to believe that the erotetic structure of discourse might be a deeper, cognitively more realistic way to represent the very same kind of structure the rhetorical structure of discourse attempts to capture. If this way of putting the problem is correct, then it is natural to think of rhetorical relations in SDRT as families of question tree fragments. In other words, when we establish a particular rhetorical relation between two nodes, we find a particular pattern of nodes and arrows in the erotetic structure of discourse which makes transparent the very same interpretation. Then, a non-injective but surjective mapping ⇒ from question trees to SDRT graphs can be defined (at least for the range of rhetorical relations that can be captured using the very limited theory sketched here). I first pseudo-formally illustrate the claim by considering a few rhetorical relations. For subordinating rhetorical relations I choose explanation and elaboration, and for coordinating ones narration. Then, we discuss the issue at a somewhat more technical level. Explanation can be understood as the rhetorical relation between two assertions that occurs whenever they are connected by a why-question in a discourse

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tree, as in (39). Elaboration is the rhetorical relation corresponding to the family of questions which is gained from some eventuality description by replacing any of the explicit18 or non-articulated constituents with a wh-word or by asking about sub-events of some eventuality, an example is given in (40). (39) π1: Max fell. π2: John pushed him. q1: Why did Max fall?

(40) π1: John met a girl. π2: It was Mary. q1: Which girl did John meet?

For coordinative rhetorical relations, the situation is a bit more complicated. The idea thereby is that a rhetorical relation does not correspond to one single question type, but rather to a type of structure involving certain types of questions. Coordination arises when two assertions are both answering potential questions licensed by the same node. As a particular case, narration arises when the superordinate discourse node contains a temporally ordered chain of events and the two questions are about temporally ordered sub-events of that chain.

18

This is only going to license a potential questions if the explicit constituent is indefinite or vague.

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(41) π1: Max fell. π2: He got up. π0: A temporally ordered chain of events occurred q1: What happened first? q2: What happened second?

The idea that narration involves an accommodated assertion node is not very surprising, since it is generally assumed that even in SDRT narration requires a discourse topic constituent. This topic node contains a more abstract summary of what is actually being narrated as discussed e.g. in Asher (2004). Since in the erotetic structure we always need a superordinate node licensing the two sister potential questions for all coordinative rhetorical relations, we can generalize that any coordinative relation requires a topic (little surprisingly this is the very definition of coordination according to some scholars e.g. van Kuppevelt 1995a, 1996). So, in essence, coordination amounts to symmetric subordination under the same node. But one should keep in mind that not every single time that two nodes appear under the same dominating node we expect some coordinating rhetorical relation between them. All that can be said is that whenever such a tree geometry arises, coordinating relations in the rhetorical structure could exist. Let us consider the mapping function in more detail. The correspondence between question tree fragments and SDRT arrows can be spelled out as formal rules. The degree of formal precision in the formal rules below is fairly low. It would increase if we had a precise semantic theory of what questions are. Similarly, we might need more elaborate representations of assertion and question nodes. For example, we would need to make formally explicit what it means to ask about the temporal order of two events. However, for the aims of this paper, our level of explicitness appears to suffice: Definition 15. The explanation rule A question tree: ⟨{a, b, c}, {ans(b, c), PQ(a, b)}, ∅, c⟩ translates to an SDRT representation ⟨{a, c},

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{explanation(a, c)}, ∅, c⟩ iff b is a question about the reasons of the events depicted by a. Definition 16. The narration rule A question tree: ⟨{a, b, c, d, e}, {ans(b, c), ans(d, e), PQ(a, b), PQ(a, d)}, ∅, e⟩ translates to an SDRT graph ⟨{a, D′ }, {l(a, D′ )},∅,D′ ⟩ where D′ = ⟨{c, e},∅, {narration(a, d)},c⟩ iff a is an assertion about an event with temporal structure, and b and d are questions about the temporal order of the sub-events of the event denoted by a. Thereby l is a topic relation.

With this in mind, we can spell out a partial function f from question tree fragments X1 involving at least three nodes and two arrows to SDRT graphs X2 involving one arrow and two nodes. Then, translating a question tree into an SDRT graph requires a recursive mapping ⇒ that makes sure that each fragment of the question tree which has an f-mapping into SDRT is represented by the f-arrow of the respective fragment. Crucially, assuming that a full mapping can be given, the relation between the erotetic structure and the rhetorical structure appears to be twofold. On the one hand, one can immediately derive an SDRT graph from a discourse tree. On the other hand, SDRT graphs naturally constrain discourse trees in the sense that if a valid SDRT graph has been found, the rough structure of the discourse tree is determined. It is only the details, i.e. the particular questions, which remain to be worked out. Finally, let us briefly consider the correspondent of the Right Frontier Constraint in the erotetic structure of discourse. In particular, the update rule + for question trees only allows attachment to nodes that dominate the distinguished last node as shown in (29). That means that as long as we only have subordinative relations, the SDRT Right Frontier Constraint is fully mirrored in the question tree theory. But once we have coordination the situation is a bit more complicated. Consider the graphs in (41). Technically, the update by π2 directly extends the node π1 in SDRT, but in the question tree approach the update by π2 stands in absolutely no direct relation to neither π1 nor to q1, the question addressed by π1. Since the Right Frontier Constraint arguably has effects on anaphoric accessibility, one would also want to capture the Right Frontier Constraint in the erotetic structure of discourse. We can replicate this by defining the domain of anaphoric accessibility for each update in question trees such that those nodes that were accessible before the accommodation of the question nodes are going to be good referential anchors even if they do not end up

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dominating the new node. Then, π1 will be an anaphorically accessible node for π2. Put differently, accommodation cannot influence anaphoric accessibility. 5.2 Problems and Limitations I have suggested above that the mapping ⇒ can be – in principle – spelled out at least within the limited empirical range of the theory sketched here. However, at a closer look, even this turns out to be problematic. One of the main problems is that one discourse unit may be involved in several distinct rhetorical relations with various other units in SDRT, as already mentioned above. In fact, the higher the number of rhetorical relations that can be inferred at the same time, the higher the coherence of discourse is judged. As opposed to this, in the erotetic structure, such an option fails to exist. Each node can have maximally one parent. That means that our mapping from question trees to SDRT graphs is incomplete in many cases, as SDRT graphs would make explicit information the question trees would potentially overlook. Consider, for instance the example (8) repeated here as (42). As mentioned above, in certain contexts, one could come up with the interpretation that the fact that Peter danced with Mary not only elaborates on the dancing competition (in fact it may also explain π3) but actually also explains why Peter had a beautiful evening, i.e. why π1. After all, Peter could be in love with Mary and only evenings which he spends with her would ever count as potentially beautiful. (42) [π1 Peter had a beautiful evening.] [π′ [π2 He had a great meal] and [π3 he won a dancing competition].] [π4 He danced with Mary.] One way to think about the problem is to assume that multiple rhetorical relations between nodes in SDRT are a range of ambiguities at the discourse trees level. If one can infer several rhetorical relations a node is involved in, one should understand these as the possibility to construct several distinct question trees, each reflecting a different choice of rhetorical relations. Support to this approach comes from the observation that in a question-answer paradigm the information structure of the answer matches the question, thereby signalling that it is one question that is addressed. If other questions are (contentwise) answered as well, this is to be considered an indirect effect, and it is certainly not marked grammatically. For example, in (43), one could argue that C’s utterance answers both A’s and B’s question at the same time. However, the grammatical marking clearly suggests that C is answering B’s question in

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a primary way and the relation to A’s question in this discourse needs to be pragmatically inferred. (43) A: B: C:

Why is Mary so happy? Who danced with Mary yesterday? ALFRED danced with Mary yesterday.

Moreover, answering a question is a sufficient teleological rationale of existence for a discourse move, answering several questions at once does not seem to conceptually add anything noteworthy. However, Nicholas Asher (p.c.) pointed out to me that in some cases there is overt marking of co-existing multiple rhetorical relations, as e.g. in (44) in which both contrast and narration are overtly marked and need to be inferred for semantic reasons. In particular, but marks contrast and and marks narration. (44) [π1 Peter kissed Mary] [π2 but then she slapped him in the face]. There seems to be a way to resolve this problem. In particular, it has been claimed at various occasions that but and similar expressions in other languages mark constraints on information structure, on the QUD and on inquiry strategies, cf. Umbach (2005), Jasinskaja & Zeevat (2008), Jasinskaja (2012) and Toosarvandani (2014), as also noted in section 4.2 above. Translating these approaches of the semantic contribution of but into the current framework is not trivial. Part of the reason is that Jasinskaja & Zeevat (2008) and Toosarvandani (2014) heavily make use of sub-questions and strategic inquiries. However, at least for the sake of the argument (and limited to some counterexpectational cases) we could assume that contrast can be captured by a question tree that is compatible with narration, hence licensing both arrows in SDRT, as roughly suggested in (45). Then, the hypothesis ought to be that several rhetorical relations can co-occur in general precisely iff the question trees underlying them are compatible, i.e. they can satisfy the translation rule for both of them. (45) π1: Peter kissed Mary. π2: She slapped him in the face. π0: A temporally ordered chain of events occurred in which the second is event was unexpected given the first one q1: What happened first? q2: What happened second?

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Other cases, such as cases in which multiple discourse relations involve ‘long distance’ arrows, are not easily (in fact probably not at all) captured in this erotetic framework. But then again, such cases are generally quite marked and should be considered in a separate research project.

6

Subordination or Coordination: the Case of Result

In this section, I turn to a case study which is intended to show the additional flexibility gained from considering rhetorical relations in SDRT as more abstract level representations of underlying question patterns. The topic of the case study is the distinction between coordinating and subordinating rhetorical relations. Above, we have treated subordination and coordination as primitive notions, partly because we have built these notions into the very definition of the representation of discourse states. Hence, we could just state that narration is a coordinative relation in SDRT, simply because narration arrows appear in 𝒞D where D is some discourse state. But of course, one may also think about the deeper nature of these notions. One way to conceptually distinguish these kinds of rhetorical relations is based on the notion of topicality, cf. van Kuppevelt (1995a). Coordinating rhetorical relations share a topic while subordinating ones are such that the subordinated sentence is about the superordinated one. Other scholars have been mainly considering the symmetrical nature of coordinating relations in terms of nucleus and satellite cf. Mann & Thompson (1988b) and further research in the RST tradition. Also, Polanyi (1988), Scha & Polanyi (1988) propose further formal distinctions mainly in terms of accessibility of attachment and anaphoric antecedents. Here, we consider two linguistic tests which help distinguishing these types of relations at an empirical, linguistic level. Thereby we follow Asher & Vieu (2005), but their ideas are very closely related to the ideas of Polanyi (1988), Scha & Polanyi (1988). Firstly, if R(π1 , π2 ) and R is coordinating, attachment of new discourse material to π1 is disallowed, which naturally follows from the Right Frontier Constraint discussed above. We illustrate with (46).

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(46) [π1 One plaintiff was passed over for promotion three times.] [π2 Another didn’t get a raise for five years.] [π3 A third plaintiff was given a lower wage compared to males who were doing the same work. [π4 But the jury didn’t believe this.] (Asher & Lascarides, 2003)

In (46), π4 either can either be attached to the topic node π0, or to the last coordinated segment π3. Accordingly, the anaphoric this in π4 can either refer to some summary of π′ or π3. Crucially, π1 and π2 alone are no available discourse antecedents, since they are involved in coordinating relations with each other and π3. Secondly, adding the conjunction and is generally possible only to coordinating rhetorical relations (Txurruka, 2000), as witnessed in (47) (from Asher & Vieu 2005): (47) a. John went home, and then he called Sam. (narration) b. # John has a good time, and for instance he had a great meal. (elaboration) In SDRT, in most cases the question whether a relation is coordinating or subordinating is decided by the semantics of the rhetorical relation itself. Since it is excluded that both a coordinating and a subordinating relation holds between the very same two segments, and since rhetorical relations are defined on semantic grounds alone, one indeed expects a natural clustering of relations which are compatible with each other. Asher & Vieu (2005), however, observe that there seems to be variation in the coordinating or subordinating nature of rhetorical relations in SDRT. As a case in point they discuss the rhetorical relation result. result is a kind of reversed explanation, such that if result(π1 , π2 ), π1 causes π2. Result is often overtly marked by so or as a result. As a default, result has been considered coordinating, but in some cases, it seems to exhibit subordinating properties. The examples in (48) and (49) are the ones discussed in Asher & Vieu (2005).

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(48) [π1 A woman screamed,] [π2so the burglar ran away.] [π3 Max woke up] # [π4 She also got a sore throat.] (49) [π1 Lea bought a new car.] [π2 As a result, she’ll be able to go to Mexico this Christmas,] [π3 and she will get to work more quickly.] [π4 It’s a Subaru.] In (48), it seems that the result relation between π1 and π2 blocks the anaphoric reference in π4, whereas in (49), the very same does not happen. Asher & Vieu (2005) conclude that there seems to be a default coordinative function of result, but in some contexts this can be altered such that sometimes subordination is achieved. They argue that in some cases the coordinative vs. subordinative nature of rhetorical relations therefore depends on the information packaging/the way the relations are presented, rather than just their semantic content. Unfortunately, they do not go much beyond observing this. In what follows, I argue that by considering the erotetic structure of discourse a comprehensive explanation can be given. The explanation to be provided naturally complements the idea of Asher & Vieu (2005). If one takes seriously that result involves causality and that this is a solid truth conditional inference in discourse, this must be reflected in the question trees as well. Moreover, since in the erotetic structure of discourse, as argued above, it is the questions that carry the truth conditional burden for any discourse inference, causality must somehow be reflected in the question itself. The only way this seems possible is when the question answered by the assertion of the result is about the cause. One natural approach then is that if π2 is the result of π1, the question π2 answers is roughly q: What is the result of π1? or a somewhat more specific q′ : Did π2 happen as a result of π1?, depending on the information structure of the answer. This way, one can make sure that interpreting π2 as an answer to q (or q′ ), the causal connection between π1 and π2 is entailed at least at the level of the tree fragment. Under such a view, result is subordinating. However, the notion of potential questions naturally constrains the domain in which this analysis may apply to cases in which q is a potential question raised by π1. This can only happen if π1 is contextually likely to have a result. Otherwise, the probability that the event encoded by π1 has a result is not sufficiently increased to serve as the supposition of a licit a potential question about the resulting event.19 One example, in which the probability of a resulting-event is sufficiently increased is given in (50). 19

Of course, one may argue that in an infinite chain of causality every event will – by necessity – end up having results (in the sense that every event causes something). So, it is clear

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(50) [π1 Black unleashed an unstoppable king side attack.] [π2 So white resigned.] q: What was the result of the attack?

Any chess player would agree that π1 licenses the question about the result of the attack in terms of whether the king side attack has eventually lead to a victory. After all, an unstoppable king side attack is one of the best pathes to victory. Still, it does not invariably lead to victory, since one could always blunder or loose on time. While this analysis seems attractive, it is limited to cases in which the potential question about the result of some event is actually raised, as suggested above. What about cases, in which some event does not raise the question about its potential outcome or result? This leads to an alternative structure, which we call the coordinative analysis. In fact, the coordinative analysis is the more general case, rather than a special one. The coordinative analysis of result involves a similar structure as the analysis of narration. The accommodated assertive node lumping together the eventualities denoted by the propositions connected by the coordinative arrow in SDRT, needs to form a causally connected chain. For the example in (50), this leads to the analysis in (51). (51) [π1 Black unleashed an unstoppable king side attack.] [π2 So white resigned.] π0: A causally ordered chain of events occurred. q1: What was the cause? q2: What was the effect?

that the contextual likelihood of having a result is a not a physical or metaphysical notion. Instead we are really talking about some psychological shift of attention to resulting states associated with the type of event reported by π1. A theory of such psychological effects is not provided in this paper, but – hopefully – readers will find it intuitively clear what I have in mind given the examples to follow.

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The arising structure is coordinating. It mainly differs from the subordinating one in that it is not constrained to cases in which the first sentence could license the question addressed by the second sentence as a potential question. In this sense, coordination is the default for result. In fact, there is no simple two-sentence discourse that could be analysed in SDRT as establishing the rhetorical relation result and for which the coordinative analysis in discourse trees could be ruled out. I suggest to think of the rhetorical relation result as bundling both possible structures. The structures are distinct but truth conditionally equivalent, hence, under the logic of SDRT, they should not give rise to distinct rhetorical relations. However, the fact that at a lower level, in discourse trees, differences come up is not insignificant. There are predictions associated with these strategies. The main prediction is that result can only be a subordinating rhetorical relation in cases in which the first sentence licenses a potential question about its result. Whenever this does not happen, result can only be a coordinative relation. There is no case in which one can generally rule out the possibility that result is coordinating, but there are cases in which one can rule out that result is subordinating. In addition, the likelihood of the potential question licensed by the first assertion also plays a role in the likelihood of a subordinative analysis. Let us assume that the likelihood of potential questions is in some sense related to typical human curiosity. Then, some possible results of events are much more likely to be subject of inquiry than others. Consider, for instance the sentences in (52) and the respective questions following them. (52) a. John had some mushrooms for dinner. What happened to him as a result? b. John had poisonous mushrooms for dinner. What happened to him as a result? Considering (52a), it is not per se unlikely that having mushrooms for dinner has a result. For instance, John might be satisfied afterwards or he might

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wake up hungry at night because the energetic value of mushrooms may be too low for his needs. Or, if John is attempting to lose weight, he might as a result of eating mushrooms feel very happy about his dietary success. However, humans do not tend to get excited about the likely outcomes of eating mushrooms for dinner. Therefore it is not very likely that the respective question about the result will be raised. As opposed to this, the question in (52b) is much more dramatic and much more salient. Hence, we predict that subordination is much more likely in (52b). Then, we can check how this complies to the right frontier constraint in analogy to the examples above. It seems that the (53b) example is indeed better because the first sentence is still an accessible attachment point. (53) a. John had tasty mushrooms for dinner. As a result, he woke up hungry in the night. # Jane cooked them. b. John had poisoned mushrooms for dinner. As a result, he woke up sick in the night. Jane cooked them. As another example, in (54a),20 it is very hard to understand π3 as explaining why Lea screamed, even though, content-wise, this is a very good explanation. In fact, the most likely interpretation of (54a) is that the burglar was female and panicked when Lea screamed. As opposed to this, it is very easy to understand π′3 as explaining why/under what circumstances Lea had a bad fall in (54b). The main difference is that in (54b), π′1 very saliently raises a question about the outcome/result of the falling event, which allows a subordinative analysis, by accommodating the respective potential question. (54) a. [π1Lea screamed], [π2 so the burglar ran away.] [π3 She was in terrible panic.] b. [π′1 Lea had a terrible fall], [π′2 so she was taken to hospital] [π′3 She was trying to clean the windows.] Uwe Reyle (p.c) brought to my attention that such examples involve quite a lot of differences in terms of lexical material and therefore might be subject to independent explanations for the observed contrasts. For instance, for (53), even though I have tried to control as much as possible for minimal differences between the a. and b. examples, still, it happens to be true that poi-

20

Julie Hunter (p.c.) helped me significantly in discovering the right kind of examples, which I gratefully acknowledge.

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soned mushrooms are much more important discourse referents than just tasty mushrooms. Hence, even just on grounds of working memory, one would predict that they are much better anaphoric antecedents. Similar arguments could be given about the example in (54) as well (and in fact about (48) and (49) as well). Notice that the existence of alternative explanations does in no way contradict the explanations given in the spirit of SDRT. Potentially more clear-cut examples are then suggested in (55). In this case, we can keep the last two sentences identical. In (55a), the anaphoric he seems to more naturally target the black player in one of the readings, resulting in the interpretation that black had a good intuition when to start the attack, whereas in (55b) this seems very difficult. In fact, in (55b), the interpretation that white had a good intuition when to resign is much more prominent. This is of course, predicted by the right frontier constraint under the assumption that (55a) involves a subordinating result. Again, there is no difference between the examples in terms of rhetorical relations. At the level of erotetic structure, however, it is correctly predicted that only (55a) has a natural subordinative analysis, because the first sentence in (55b) does not license a result-targeting potential question, or at least not so clearly (after all, any move in a chess game will have some result, but just taking some piece per se is anything but dramatic in terms of the result of a game). (55) a. Black unleashed an unstoppable king side attack on move 25. As a result, white resigned just a few moves later. He really had a good intuition. b. Black took on g6 with the bishop on move 25. As a result, white resigned just a few moves later. He really had a good intuition. Another way to test the predictions involves using and as a test for coordination. Suppose we add and to one of the examples which we claim to have a subordinating result reading and which would violate the Right Frontier Constraint if result were coordinating. The addition of and would then force a coordinating reading and then the examples should deteriorate because of the Right Frontier Constraint. It seems to me that this prediction is borne out as suggested in (56) and (57).21 (56) a. John had tasty mushrooms for dinner. As a result, he woke up hungry in the night. # Jane cooked them.

21

Judgements are somewhat subtle, as one should acknowledge. In particular, it seems that

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b. John had tasty mushrooms for dinner and, as a result, he woke up hungry in the night. #Jane cooked them. c. John had poisoned mushrooms for dinner. As a result, he woke up sick in the night. Jane cooked them. d. John had poisoned mushrooms for dinner and, as a result, he woke up sick in the night. # Jane cooked them. (57) a. Black unleashed an unstoppable king side attack on move 25. As a result, white resigned two moves later. Heblack really had a good intuition. b. Black unleashed an unstoppable king side attack on move 25 and, as a result, white resigned two moves later. # Heblack really had a good intuition. Summing up, the kind of analysis suggested here comes with a prediction that SDRT as such lacks: it is more likely that result ends up as a subordinating relation when the first sentence is likely to have some result interlocutors are generally keen on asking about. This suggest that it is possible to provide the kind of correspondence rules between the erotetic structure of discourse and its rhetorical structure. Moreover, it is well worth the effort to provide a deeper look into the erotetic structure, thereby discovering new regularities which go unnoticed in SDRT.

7

Some Evidence from German

The analysis of coordination suggested above seems to be somewhat ad hoc in the sense that there is a lot of material that is accommodated. In a sense, this is similar in SDRT as well. Still, if we could show that the lexical meaning of some discourse marker is sensitive to the kind of mechanism we use to model coordination, this would be reassuring that we are heading in the right direction. In this last section, I provide such an empirical argument. The argument comes from the lexical semantics of the German adverbial particle schließlich, in some respects comparable with English after all. Schließlich has three main readings: a list enumeration ending reading (58a), a result-reading (58b) and a temporal reading (58c). Interestingly, a fourth read-

(56d) is somewhat better than (56b), but still significantly worse then (56c) which suffices to confirm the prediction.

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ing also exists, which seems to be a metatalk explanative (explanation* in SDRT terms) or plain explanative reading (58d).22 (58) a. Es gibt drei Kategorien: Exzellenz-Cluster, Graduiertenschulen und schließlich “Zukunftskonzepte” (Elite-Unis). (BRZ05/NOV.21709 Braunschweiger Zeitung, 07.11.2005) There are three categories: Excellence Clusters, Graduate Colleges and finally future strategies (elite universities). b. Sascha Schlamilch (22), der Vater des Kindes, hatte sich den Namen Tamara gewünscht. Und sie selbst wünschte sich eben Charlene. Und so erhielt das Mädchen schließlich beide Namen. (BRZ13/JAN.00086 Braunschweiger Zeitung, 02.01.2013) Sascha Schlamilch (22), the father of the child, wanted to give her the name Tamara. She wanted the name Charlene. And so the child eventually got both names. c. Die Feuerwehr konnte das Tier einfangen und schließlich im Wald wieder aussetzen, sagte ein Sprecher. (BRZ13/MAI.04259 Braunschweiger Zeitung, 13.05.2013) The firefighters could catch the animal and eventually release it in a forest, a spokeman said. d. Die Tendenz geht aber dahin, dass wir Klimo halten wollen. Er hat schließlich mit Ausnahme einer Phase in der vergangenen Saison immer seine Tore gemacht. (BRZ05/NOV.20322 Braunschweiger Zeitung, 26.11.2005) We tend to keep Klimo. After all, except for a phase in the last season, he always scored his goals. The explanation* or explanation reading of schließlich is very similar to a reading English after all has been reported to have in Traugott (1997) under the label justification of some aspect of a proposition. This is witnessed in (59). (59) The president … may be able to show strong leadership and strengthen himself for 1992. Democrats, meanwhile, cannot at this point seriously attack the president simply for saying taxes are needed. After all, they have spent more than a year pushing him to take that very stand. (Traugott, 1997, pp. 3)

22

The examples in (58) are all from the corpus COSMAS II of the Institute für Deutsche Sprache.

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Notice that Traugott additionally distinguishes a reading of English after all which she calls an epistemic reading as shown in (60), a reading that German schließlich shares. (60) Grodin [an actor] also captures the movie star’s obsessive concern with his image, which is, after all, what he has to sell. In a diminishing market, he will do whatever can to protect it. (Traugott, 1997, pp. 2) It seems to me that this reading can be understood as a sub-class of the explanative reading under the assumption that in this case the explanandum is not overtly expressed. To my understanding this is compatible with the way Traugott (1997) characterizes this reading, even if there seems to be a historic complication here to the extent that for English the epistemic readings seem to be earlier on the grammaticalization path. I return to this complication below. German schließlich does not have a concessive reading reported for English after all as in (61). (61) The federal fund that finances presidential campaigns should have enough money to pay for the 1992 race after all, but by 1996 the could be depleted, a new report said Wednesday. (Traugott, 1997, pp. 2) The literature generally consideres schließlich as a discourse connective, c.f. Breindl et al. (2014). It is, however, hard to find a truth conditional meaning for schließlich which naturally captures all of the proposed readings in a direct way, though one can certainly find similarities at a functional level following Traugott (1997) who observes, for instance, that English after all generally has a temporal reading only in combination with an NP (e.g. after all this pain). This may have grammaticalized later into more abstract discourse oriented readings. Moreover, it seems that the four readings shown in (61) correspond to four distinct rhetorical relations in SDRT from which the list enumeration and the temporal reading seem to be coordinative and the explanative reading is clearly subordinative. The result reading is then potentially ambiguous as discussed above. Hence, we have a puzzle to deal with. One strategy would be to provide a non-discourse-functional semantics for schließlich and attempt to derive all rhetorical-relation-related readings indirectly. However, whatever approach one may take, it is certain that a) schließlich is in some sense anaphoric, that b) the anaphoric antecedent of schließlich can be complex and that c) schließlich has at least as clear a discourse structuring role as classical discourse markers such as and or because are generally assumed

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to have. Hence, it seems reasonable to attempt to spell out the semantics of schließlich in terms of its discourse function as directly as possible. We start with the following proposal within the theory of erotetic structure defined above. Schließlich encodes that there is an overt or accommodated topical chain of events, and that the clause marked with schließlich answers the last structural question about that chain of events. Since chains of events may be structured causally, temporally or simply based on some other logic (e.g. importance in the case of (58a)), all three readings come out as special cases of the coordination pattern. Notice that when we say that schließlich answers the last question, we are not actually assuming an ordering of arrows in the discourse representation. This simply follows from the claim that the schließlich sentence needs to be the distinguished node after the update and that the other questions need to be already present in the representation. I show how this captures the first three readings in what follows by creating the respective question trees from the English translations of the respective German sentences in (58). (62) List enumeration reading for (58a): π0: There are three categories. π′ : They are ordered by importance. π1: Excellence clusters. π2: Graduate colleges. π3: Elite universities. q0: How are they ordered? q1: What is the first category? q2: What is the second category? q3: What is the third category?

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(63) Result reading for (58b): π1: A causally ordered chain of events happened. π2: There was a discussion about the name of the girl. π3: Father wanted Tamara. π4: Mother wanted Charlene. π5: She got both names. q0: What was the cause? q1: What name did the father want? q2: What name did the mother want? q3: What was the effect?

(64) Temporal reading for (58c): π1: A temporally ordered chain of events happened. π2: They caught the animal. π3: They released the animal. q1: What happened first? q2: What happened last?

One can easily see that in all three cases schließlich establishes a coordinative frame and, depending on the kind of structure that is assumed in the node

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dominating the question directly answered by schließlich, we get three distinct relations: narration, result or continuation, which are signaled in the question trees with dotted lines and boldface characters. This clearly suggests that the mechanism of accommodating chains of eventualities with various structuring principles is useful to unify the lexical semantics of at least one discourse marker. The explanation* reading appears to be puzzling under such a view. This is because explanation is a subordinating relation and it would seem highly surprising if we could spell out subordination in discourse exactly in the same way in which we spelled out coordination. Hence, the situation seems hopeless. However, the kind of explanation introduced by schließlich seems to be restricted. Roughly following Breindl (2014) and Traugott (1997), the generalisation seems to be that the proposition being explained by schließlich-clauses must be held true despite potential worries or contrary evidence. We can spell out the intuition that there are other arguments against the proposition for which the host of schließlich provides some justification as follows: There is a discourse presupposition associated with schließlich that there is an ordered set of arguments in discourse for or against the proposition to be justified. But then, the job of schließlich is just to introduce the last argument in the list, which is the strongest one (because of the ordering!) and which defends the proposition under discussion. This reading of schließlich seems to differ from the first three in terms of lexical semantics, but the difference merely amounts to the constraint that the argument provided by the host favors the proposition under discussion. This leads to the analysis of (58d) as follows: (65) Explanative reading for (58d): π1: Want to keep Klimo. π2: There is a series of reasons for and against keeping him, but the strongest one is in favor of keeping him. π3: He has always scored. q1: Why do you say this? q2: What is the first reason? q3: What is the last reason (to keep him)?

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Support for this generalisation comes from (66). Here, the assertion that the speaker has inherited the crown from his father can be supported with further evidence using both the causal denn and and the causal nämlich, which can establish the explanation relation. In the case of nämlich, this is by virtue of a conventional answer to a how come question according to Onea & Volodina (2009, 2011). In such a case, however, one cannot use schließlich, or at least, using schließlich leads to a very marked interpretation that appears odd in many contexts. (66) Ich habe die Krone von meinem Vater geerbt. I have inherited the crown from my father a. # Er war schließlich der König von Frankreich. After all, he was the king of France. b. Denn er war der König von Frankreich. Since he was the king of France. c. Er war nämlich der König von Frankreich. Since was the king of France. The reason why schließlich cannot be used in an explanative reading in (66) is that schließlich marks the last argument in an ordered list. However, it is not really conceivable that any argument against the claim that the speaker inherited the crown from his father was weaker than that his father was the king of France. After all, the latter is just a precondition of inheritance and therefore a very weak argument. A counter-argument could be, for instance, that the speaker has an older brother, who would have inherited the crown. This is, of course, a much stronger argument. Of course, one can imagine various strange scenarios in which schließlich would be conceivable. While I do not suggest that the proposal spelled out in this section is a full analysis of German schließlich, it should suffice for our purposes. The discus-

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sion provides empirical background to the assumption that structured chains of eventualities can be accommodated as nodes in the erotetic structure of discourse thereby serving as an important pillar in our understanding of coordination. But at the same time it also shows an interesting transition from a coordinating discourse marker to a subordinating reading which nevertheless keeps important aspects of the coordinative reading, albeit dispersed in the question tree.

8

Outlook and Conclusion

It is well known that theories of the erotetic structure of discourse, also known as question under discussion based theories, are very useful in modelling the grammar-pragmatics interface and there are a number of successful analysis in this research tradition. But such theories generally use very small fragments of a discourse and are mostly operating in a very local domain. Their larger implications concerning the overall architecture of discourse remains, for the most time, in the background and widely ignored. At the same time, theories of discourse structure have been mainly dominated by rhetorical structure theories such as SDRT. The connection between rhetorical relations and the erotetic structure of discourse has widely been unclear despite some attempts to capture some rhetorical relations in terms of question patterns. Such is, for instance, the analysis of contrastive markers in Umbach (2005); Jasinskaja & Zeevat (2008); Jasinskaja (2012); Toosarvandani (2014). In this paper, I have attempted to explore this connection in a specific version of a theory of the erotetic structure of discourse which assumes potential questions as the basic licensing mechanism of questions in discourse, following van Kuppevelt (1995a) and Onea (2016), instead of the better known notion of strategic question-sub-question chains in Roberts (1996). I have shown that, at least in a limited domain, it is not only possible to explicate rhetorical relations of SDRT (Asher & Lascarides, 2003) in terms of fragments of question trees, but actually question trees bear the potential to allow a more detailed, finer grained analysis of discourse phenomena. I have shown this focusing on the rhetorical relation result, thereby exploiting the idea of Asher & Vieu (2005) that the subordinative or coordinative interpretation of some rhetorical relations depends not only on their semantics but also on information packaging – which amounts to different erotetic structure in this framework. One possible research program naturally following from this suggestion is to attempt to translate all rhetorical relations in SDRT to question trees. Moreover,

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one may ask how to spell out rules of discourse parsing resulting in question trees. In other words, a possible research program concerns the analogy of glue logic for the erotetic structure of discourse. Another approach, however, has more modest aims. I am not sure that one should consider the erotetic structure as something essentially independent of the rhetorical structure of discourse. I rather suggest to think of the erotetic structure of discourse as supplementing the rhetorical structure as spelled out for instance in SDRT. Discourse structure is captured “correctly enough” by SDRT, for general purposes. But whenever interesting puzzles arise at the level of SDRT analysis of discourse, whenever SDRT analysis is not sufficiently fine grained to capture grammatical phenomena, etc. one can consider the view from the erotetic structure and locally extend SDRT representations by the underlying question tree representations. Precisely this happens in Benz & Salfner (2014) in a limited domain; but while for them the question under discussion is derived on the fly from information structure and discourse relations, this paper provides a background that allows the import of questions into a theory of discourse structure as something that naturally belongs there, but might have been invisible at the level of abstraction at which SDRT operates. In the end, this seems to allow not only a better handle of information structure but also may reveal slight structural differences lumped together in the notion of rhetorical relations. Put differently: it seems possible to represent a whole complex discourse as a question tree, but the theoretical gain as compared to an SDRT representation does not seem to be worth the effort. Discourse trees are rather to be compared to a microscope that allows us to look behind rhetorical relations when needed. And while microscopes are useful, they should not replace usual glasses.

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chapter 8

Two Alternatives for Disjunction: an Inquisitive Reconciliation* Floris Roelofsen

1

Introduction

There is a long tradition in formal semantics that analyzes disjunction words like English or as expressing an operator which, when applied to two elements A and B of a Boolean algebra, yields their join, that is, their least upper bound w.r.t. the partial order that the algebra is based on. In particular, if A and B are propositions, ordered by entailment, then disjunction delivers their union, A ∪ B. An important virtue of this analysis is that it provides a uniform account of disjunction words across different languages and across different syntactic categories (Gazdar, 1980; Partee & Rooth, 1983; Keenan & Faltz, 1985). Moreover, it provides an explanation of the very fact that such words exist in virtually all languages: since the join operator is one of the most basic algebraic operations that can be performed on the elements of any Boolean algebra, and since the meanings of expressions of the relevant syntactic categories constitute such Boolean algebras, it is to be expected that languages generally have words to express the join operation on such meanings; just like it is to be expected, for instance, that many languages have words to express basic operations on quantities, like addition and subtraction. However, there is also a substantial body of work, initiated by Aloni (2002), Simons (2005a), and Alonso-Ovalle (2006), which promotes a different semantic treatment of disjunction, namely as generating sets of alternatives. In partic* This paper was presented at the Third Questions in Discourse Workshop in Berlin, in 2013. I am grateful to the participants of the workshop for their useful feedback, and to the editors for including the paper in the Questions in Discourse volume. The main result presented here was obtained in the context of a more general investigation of the algebraic foundations of inquisitive semantics, reported in Roelofsen (2013). Here, the technicalities behind the result are largely suppressed and the emphasis is rather on its relevance for linguistic theories of disjunction. The paper has benefited enormously from extensive discussion and collaboration with Maria Aloni, Ivano Ciardelli, Donka Farkas, and Jeroen Groenendijk. Finally, financial support from the Netherlands Organisation for Scientific Research (NWO) is gratefully acknowledged.

© koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004378322_009

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ular, when applied to two propositions A and B, disjunction is taken to generate a set of two propositional alternatives, {A, B}. This treatment has been fruitfully applied to account for a number of phenomena, including disjunctive questions (e.g., Roelofsen & van Gool, 2010; AnderBois, 2011; Biezma & Rawlins, 2012), free choice effects arising from disjunction under modals and in imperatives (e.g., Aloni, 2002, 2007b; Simons, 2005a,b), counterfactuals with disjunctive antecedents (e.g., Alonso-Ovalle, 2006), unconditionals with disjunctive adjuncts (Rawlins, 2013), and sluicing (AnderBois, 2014). However, this alternative account of disjunction lacks the algebraic underpinning that made the traditional account so attractive. This makes it less explanatory: it is motivated by the empirical observations that it is designed to account for, but not by considerations that are independent of these observations. Given that both approaches have their own merits, one would like to know whether it is possible to reconcile the two, combining their respective strengths. The dominant opinion in the literature seems to be that this is impossible. The treatment of disjunction as generating sets of alternatives has been presented as a real alternative for the traditional treatment, not as a refinement or an extension thereof. For instance, Alonso-Ovalle (2006) writes in the conclusion section of his dissertation: This dissertation has investigated the interpretation of counterfactuals with disjunctive antecedents, unembedded disjunctions, and disjunctions under the scope of modals. We have seen that capturing the natural interpretation of these constructions proves to be challenging if the standard analysis of disjunction, under which or is the Boolean join, is assumed. Similarly, Simons (2005a) starts her paper as follows: In this paper, the meanings of sentences containing the word or and a modal verb are used to arrive at a novel account of the meaning of or coordinations. It has long been known that such sentences […] pose a problem for the standard treatment of or as a Boolean connective equivalent to set union. The aim of this paper is to show that the two approaches can be reconciled after all. What this requires, however, is that we move from the traditional notion of meaning, which only takes truth-conditional, informative content into consideration, to a more fine-grained notion that also takes inquisitive content into

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account, as proposed in recent work on inquisitive semantics (Ciardelli, Groenendijk & Roelofsen, 2017a). If we enrich our notion of meaning to encompass both informative and inquisitive content, entailment also becomes sensitive to these two aspects of meaning. What we will show is that, if disjunction is treated as a join operator with respect to this more fine-grained notion of entailment, it automatically generates the desired alternatives. Thus, we can have our cake and eat it: disjunction can be treated as a join operator and as introducing sets of alternatives at the same time – in inquisitive semantics the two go hand in hand. The paper is organized as follows. Section 2 reviews the traditional treatment of disjunction as a join operator, highlighting what makes this treatment particularly attractive from a linguistic perspective. Section 3 reviews the treatment of disjunction as generating sets of alternatives, and briefly reviews a number of phenomena to which this treatment has been successfully applied. Section 4 shows how the two approaches can be reconciled, and Section 5 concludes. The appendix briefly discusses some extensions of the basic result obtained here. Before getting started, two remarks about the intended scope of the paper are in order. First, we will largely restrict our attention to sentential disjunction. The resulting treatment of sentential disjunction can be generalized to a cross-categorial account, but there are no particular novelties in that part of the proposal: the generalization works exactly the same way as in the traditional account. The main contribution of the paper is a treatment of sentential disjunction that incorporates both the rigorous algebraic underpinning of the traditional approach and the alternative generating behavior assumed in the more recent analyses. Second, it should be emphasized that the main aim of the paper is a theoretical one, i.e., to show that two prominent semantic analyses of disjunction, which are generally thought of as competing analyses, can in fact be reconciled in a principled way. The aim is not to critically assess the empirical evidence that has been given in favor of these semantic analyses, let alone to provide any new empirical evidence for or against them. In this regard, it should be noted that some of the phenomena that have been dealt with by treating disjunction semantically as introducing sets of propositional alternatives – in particular free choice effects in modal constructions, as well as counterfactuals with disjunctive antecedents – have also received various other treatments. Some of these rely on a different non-standard semantic treatment of disjunction (e.g., Zimmermann, 2000; Geurts, 2005); others place the explanatory burden on pragmatics rather than invoking a non-standard semantics for disjunction (see, e.g. Schulz, 2005; Aloni, 2007a; Fox, 2007; Klinedinst, 2009; Chemla, 2009; Franke, 2009; van Rooij, 2010). A detailed comparison between the different

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accounts of these particular empirical phenomena is beyond the scope of the present paper. The contribution of the paper to this debate is just to show that one important objection against the propositional alternatives approach – namely that it forces us to give up the advantages of the traditional algebraic treatment of disjunction – can in fact be overcome. Finally, note that in some other empirical domains – in particular that of disjunctive questions – there is a rather broad consensus that a treatment of disjunction as generating sets of propositional alternatives is indispensable. So, even if this treatment of disjunction may not be strictly needed to account for modal free choice effects and counterfactuals with disjunctive antecedents, it is still well worth taking into serious consideration and trying to place on firmer theoretical ground.

2

The Traditional Treatment of Disjunction

The meaning of a sentence – the proposition that it expresses – is standardly construed as a set of possible worlds, namely, those worlds in which the sentence is true. Thus, the proposition expressed by a sentence standardly embodies its truth conditions. As such, a proposition can be thought of as carving out a region in the space of all possible worlds. In asserting a sentence, a speaker is taken to provide the information that the actual world is located within this region, i.e., that the actual world is one in which the uttered sentence is true. Thus, the proposition expressed by a sentence captures the informative content of that sentence, i.e., the information that is provided by a speaker in uttering the sentence. This means that we can compare two propositions in terms of their informative strength. One proposition is more informative than another if it carves out a smaller region, i.e., if it locates the actual world more precisely. Formally, we say that one proposition A entails another proposition B, notation A ⊧ B, just in case A ⊆ B. Entailment forms a partial order over the set of all propositions. Every partially ordered set has a certain algebraic structure and comes with certain basic algebraic operations. The set of propositions in standard truth-conditional semantics, ordered by entailment, forms a so-called Boolean algebra, which comes with three basic operations: join, meet, and complementation. As depicted in Figure 1, the join of two propositions A and B is the least upper bound of A and B with respect to entailment, i.e., the strongest proposition that is entailed by both A and B. This least upper bound amounts to the union of the two propositions: A ∪ B.

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figure 1

Join and meet

The meet of A and B on the other hand, is the greatest lower bound of A and B with respect to entailment, i.e., the weakest proposition that entails both A and B. This greatest lower bound amounts to the intersection of the two propositions: A ∩ B. The complement of a proposition A, which we denote as A∗ , is the weakest proposition C such that A ∩ C entails any other proposition. The only proposition that entails any other proposition is the empty proposition, ∅. Therefore, A∗ can be characterized as the weakest proposition C such that A ∩ C = ∅. It consists simply of all worlds that are not in A itself: A∗ = {w | w ∉ A}. Now, the standard treatment of disjunction, conjunction, and negation consists in associating each of these connectives with one of the basic algebraic operations: disjunction is taken to express the join operator, conjunction is taken to express the meet operator, and negation is taken to express complementation. ⟦ϕ ∨ ψ⟧ = ⟦ϕ⟧ ∪ ⟦ψ⟧ join ⟦ϕ ∧ ψ⟧ = ⟦ϕ⟧ ∩ ⟦ψ⟧ meet ⟦¬ϕ⟧ = ⟦ϕ⟧∗ complementation

Some simple propositions are depicted in Figure 2. In these examples, it is assumed that there are just two elementary sentences, p and q, which means that there are just four distinct possible worlds: one where both p and q are true, labeled 11, one where p is true but q is false, labeled 10, et cetera. Figure 2(i) depicts the proposition expressed by p, denoted ⟦p⟧, which is the set of all worlds where p is true, and Figure 2(ii) does the same for the proposition expressed by q, denoted ⟦q⟧. Figure 2(iii) depicts the proposition expressed by p ∨ q, which is the join of ⟦p⟧ and ⟦q⟧. Figure 2(iv) depicts the proposition

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Propositions expressed by some simple sentences in standard truth-conditional semantics

expressed by p ∧ q, which is the meet of ⟦p⟧ and ⟦q⟧. And finally, Figure 2(v) depicts the proposition expressed by ¬p, which is the complement of ⟦p⟧. As mentioned above, since these algebraic operations are so basic, it is to be expected that natural languages will generally have lexical items that can be used to express them. And indeed, in virtually all languages words or morphemes have been found that may be taken to fulfil exactly this purpose (see, e.g., Haspelmath, 2007). The algebraic perspective provides an explanation for this finding. Moreover, the account leads us to expect that disjunction, conjunction, and negation are not only applicable to full sentences, but also to expressions of other syntactic categories whose denotations form a suitable algebra, and that in this case they express exactly the same operations. This is again generally found to be the case across languages. Note that the algebraic account is an explanatory account in that it is motivated by considerations that are independent from empirical observations concerning the behavior of connectives in natural languages. This makes the account particularly attractive, and indeed, it has for a long time been the standard. However, in relatively recent work, the treatment of disjunction as a join operator has been challenged, and an alternative account has been proposed.1 To this we turn next.

3

Disjunction in Alternative Semantics

3.1 Alternative Semantics On the alternative account (Simons, 2005a; Alonso-Ovalle, 2006; Aloni, 2007b, among others), sentential disjunction does not yield the join of the two propo1 The algebraic treatment of conjunction has also been subject to critical debate. In particular, it has been debated whether the word and can be treated as a meet operator in sentences involving collective predication, like John and Sue got married (see Champollion, 2015, for a recent overview and defense of the algebraic approach).

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figure 3

⟦p ∨ q⟧ in standard truthconditional semantics and in alternative semantics

sitions to which it applies, but rather generates a set containing these two propositions. For instance, as depicted in Figure 3, ⟦p ∨ q⟧ is not taken to amount to ⟦p⟧ ∪ ⟦q⟧, but rather to {⟦p⟧, ⟦q⟧}. The treatment of disjunction as introducing sets of alternatives is part of a broader line of work, which analyzes various other kinds of constructions as introducing sets of alternatives as well, including wh-words (Hamblin, 1973), focus (Rooth, 1985), indeterminate pronouns (e.g., Kratzer & Shimoyama, 2002) and indefinites (e.g., Kratzer, 2005; Menéndez-Benito, 2005; Aloni, 2007b). The general framework that has emerged from this work is referred to as alternative semantics. As mentioned in the introduction, the treatment of disjunction proposed in alternative semantics has been fruitfully applied to a number of empirical phenomena, involving questions, imperatives, modals, conditionals, unconditionals, and sluicing. To illustrate the approach, let us briefly review two of these applications.2 3.2 Some Illustrations 3.2.1 Disjunctive Questions A disjunctive question like (1) can be pronounced in various ways, resulting in different interpretations (von Stechow, 1991; Bartels, 1999; Han & Romero, 2004; Roelofsen & van Gool, 2010; Biezma & Rawlins, 2012; Pruitt & Roelofsen, 2013; Roelofsen & Farkas, 2015, among others). (1) Does Igor speak English or French? 2 These brief illustrations are not intended to provide an overview of the literature on the phenomena at hand, let alone to argue for a specific account of them. They are just meant to give a sense for why the treatment of disjunction as generating multiple propositional alternatives has been found useful in these empirical domains.

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If pronounced with a prosodic phrase break after the first disjunct, pitch accents on both disjuncts, and falling intonation on the second disjunct, (1) is interpreted as an alternative question. In this case, it presupposes that Igor speaks exactly one of the two languages and elicits a response that establishes which of the two languages it is. If pronounced without a prosodic phrase break after the first disjunct, without a pitch accent on the first disjunct, and with rising intonation on the second disjunct, (1) is interpreted as a polar question. In this case, it does not presuppose that Igor speaks one of the two languages; rather, it elicits a response that establishes whether this holds or not. That is, the issue that the question expresses with this intonation pattern can be resolved either by establishing that Igor speaks one of the two languages (without necessarily specifying which of the two), or by establishing that he doesn’t speak either of them. Finally, if pronounced with a prosodic phrase break after the first disjunct, pitch accents on both disjuncts, and rising intonation on both disjuncts, (1) is interpreted as an open disjunctive question. In this case, it does not presuppose that Igor speaks one of the two languages, just like in the polar question interpretation; however, the issue that it expresses with this intonation pattern is different, namely one that can be resolved either by establishing that Igor speaks English, or by establishing that he speaks French, or by establishing that he doesn’t speak either of the two (establishing that he speaks one of the two languages without specifying which of the two is not sufficient).3,4 These different readings of disjunctive questions can be derived if we assume that disjunction generates a set of propositional alternatives; in our 3 This third reading is not as often considered in the literature as the first two; people often find it difficult to distinguish from the polar question reading if the context of utterance is left unspecified. A context in which the open disjunctive question reading of (1) is very prominent is the following: the speaker wants to write a letter to Igor, a distant relative from Russia who she has never met before; the addressee does know Igor pretty well; the speaker of course wants to write to Igor in a language that they both speak; the speaker doesn’t speak any Russian, so she is listing some languages that she does speak; since she doesn’t know much about Igor she cannot presuppose that he does indeed speak one of these languages, let alone that he speaks exactly one of them. Note that a plain Yes response to an open disjunctive question is not satisfactory, though Yes, English or Yes, French are fine, and No is also fine (see Roelofsen & van Gool, 2010; Pruitt & Roelofsen, 2011; Roelofsen & Farkas, 2015, for further discussion and an account). 4 The three intonation patterns are described here at a rather superficial level. For more elaborate discussion and some experimental results concerning the precise connection between the possible interpretations of disjunctive questions and their possible intonation patterns, see Bartels (1999) and Pruitt & Roelofsen (2013).

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figure 4

A bare disjunction p ∨ q and three types of disjunctive questions formed out of it. Translation key: p stands for ‘Igor speaks English’, q for ‘Igor speaks French, 11 is a world where both are true, 10 a world where only p is true, et cetera.

example, there are two such alternatives, as depicted in Figure 4(i). One alternative consists of all worlds where Igor speaks English, the other consists of all worlds where Igor speaks French. On a simplistic account, each intonation pattern may be taken to reflect the presence of a different question operator: Qalt , Qpolar , and Qopen , respectively. These operators may then be taken to apply to the two alternatives generated by the disjunction, each with a different output. As depicted in Figure 4(ii), we may assume that Qalt strengthens both alternatives in such a way that they become mutually exclusive (removing the overlap between them), and that it further adds a presupposition that one of these strengthened alternatives holds (this presupposition is depicted in Figure 4(ii) with dashed borders). On the other hand, as depicted in Figure 4(iii), we may assume that Qpolar ‘merges’ the two alternatives generated by the disjunction into one big alternative, consisting of all worlds where Igor speaks at least one of the two languages, and then adds the complement of this alternative, consisting of all worlds where Igor does not speak either of the two languages. Finally, as depicted in Figure 4(iv), we may assume that Qopen does not merge the two alternatives generated by the disjunction, and does not make them mutually exclusive either, but leaves them untouched and just adds the set of worlds where Igor does not speak either of the two languages as a third alternative. Of course, while this simplistic account derives the three different readings, the real challenge is to unravel how the various syntactic and intonational properties of each question type conspire to bring these readings about. This challenge has been addressed in the literature in much more depth than can be done justice to here (see, e.g., von Stechow, 1991; Aloni & van Rooij, 2002; Han & Romero, 2004; Beck & Kim, 2006; Aloni & Égré, 2010; Haida, 2010; Roelofsen & van Gool, 2010; Pruitt & Roelofsen, 2011; AnderBois, 2011; Biezma & Rawlins, 2012; Uegaki, 2014; Roelofsen & Farkas, 2015). Our purpose here is just to

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illustrate why the treatment of disjunction as generating sets of propositional alternatives has been particularly successful in this empirical domain: what is crucial is that this treatment makes it possible for operators that scope over a disjunction – here, the various Q operators – to access the alternatives contributed by each individual disjunct. This would not be possible on the traditional treatment of disjunction, where the semantic value of a disjunctive clause is a single proposition, without any trace of what was contributed by each individual disjunct (compare Figures 3(i) and 3(ii)). 3.2.2 Counterfactuals with Disjunctive Antecedents Consider the following scenario. Sally had a birthday party at her house, and some friends brought their instruments. One of Sally’s friends, Bart Balloon, who has a terrible musical taste, fortunately forgot to bring his trumpet. Now consider the following sentence: (2) If Bart Balloon had played the trumpet, people would have left.

ϕ>ψ

According to the classical treatment of counterfactuals due to Stalnaker (1968) and Lewis (1973), ϕ > ψ is true in a world w just in case, among all worlds that make ϕ true, those that differ minimally from w also make ψ true. This correctly predicts that (2) is true in the given scenario. But now consider a counterfactual with a disjunctive antecedent: (3) If Bart Balloon or Louis Armstrong had played the trumpet, people would have left. The Stalnaker/Lewis treatment of counterfactuals, together with the classical treatment of disjunction, wrongly predicts that (3) is true in the given scenario as well. This is because all worlds that make the antecedent true and differ minimally from the actual world are ones where Bart Balloon played the trumpet, and not Louis Armstrong. The second disjunct in the antecedent is thus effectively disregarded. Initially, this observation was presented as an argument against the Stalnaker/Lewis treatment of counterfactuals (Fine, 1975; Nute, 1975; Ellis et al., 1977; Warmbrōd, 1981). But another way to approach the problem is to pursue an alternative treatment of disjunction (Alonso-Ovalle, 2006, 2009; van Rooij, 2006; Fine, 2012; Ciardelli et al., 2017c). Indeed, if the disjunctive antecedent is taken to generate two propositional alternatives and if verifying the counterfactual involves separately supposing each of the alternatives generated by the antecedent, the problem is avoided.

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Thus, just like in the case of disjunctive questions, what makes the treatment of disjunction as generating multiple propositional alternatives attractive here is that it allows operators that scope over a disjunction – in this case the counterfactual – to access the alternatives contributed by each individual disjunct, something that would be impossible on the traditional account.5 3.3 Impasse We have just given two brief illustrations of phenomena which have been fruitfully analyzed in alternative semantics. As mentioned above, the full range of such phenomena is much broader. However, while the treatment of disjunction as generating multiple alternatives has been successful in terms of empirical coverage, it has limited explanatory power. After all, unlike the traditional algebraic account, it has not been motivated by considerations that are independent from the empirical observations that it is intended to capture. Thus, we seem to have reached an impasse. Both semantic treatments of disjunction have their own merits, but the two approaches rest on different, seemingly incompatible assumptions. Ideally we would be able to bring the two closer together and obtain an analysis that shares their respective virtues. But how could this be achieved?

4

Reconciliation

I will show that the two approaches can be reconciled after all. In order to make this possible, however, a rather fundamental step needs to be taken. Namely, we need to move from the traditional truth-conditional notion of meaning, which captures only informative content, to a more general notion of meaning that encompasses both informative and inquisitive content. Such a generalized notion of meaning has been developed in recent work on inquisitive semantics (Ciardelli et al., 2017a). This work is rooted in the seminal work of Hamblin (1973), Karttunen (1977), and Groenendijk & Stokhof (1984) on the semantics of

5 As already anticipated in the introduction, there are also approaches to the puzzle presented by counterfactuals with disjunctive antecedents that place the entire explanatory burden on pragmatics rather than invoking a non-standard semantic treatment of disjunction (e.g., Chemla, 2009; Franke, 2009; Klinedinst, 2009; van Rooij, 2010). A critical assessment of the different approaches to the puzzle would of course be interesting in its own right, but is beyond the scope of the present paper.

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questions. However, it involves some innovations that are essential for our purposes here. Most importantly, inquisitive semantics comes with a well-behaved notion of entailment, which is sensitive to both informative and inquisitive content. This is crucial to preserve the algebraic treatment of the connectives.6 Indeed, disjunction can be treated in this framework as a join operator, just like in standard truth-conditional semantics, but now with respect to a more fine-grained notion of entailment. And indeed, if we do this, disjunction automatically generates the desired alternatives. Let us see how this works in more detail. 4.1 Propositions in Inquisitive Semantics We start by recalling some standard notions. Let W be the set of all possible worlds. Each possible world encodes a possible way the world may be. A set of possible worlds s ⊆ W can be thought of as encoding a certain body of information, namely the information that the actual world corresponds to one of the elements of s. In particular, s can be taken to encode the information state of one of the conversational participants, or the body of information that is shared among the conversational participants at a given point. Following Stalnaker (1978), we will refer to the latter body of information as the common ground of the conversation. In standard truth-conditional semantics, the proposition expressed by a sentence is also construed as a set of possible worlds. As remarked above, in this framework a proposition intuitively carves out a region in the space of all possible worlds, and in asserting a sentence, a speaker is taken to provide the information that the actual world is located within this region. In this way, the proposition expressed by the sentence captures the informative content of the sentence. Now, if we want propositions to be able to capture both informative and inquisitive content, i.e., both the information that is provided and the issue

6 The lack of an appropriate notion of entailment was one of the main criticisms that Groenendijk & Stokhof (1984) brought up against Hamblin (1973), Karttunen (1977), and other early work on the semantics of questions. Groenendijk & Stokhof’s partition framework partly overcomes this problem; however, as noted by Groenendijk & Stokhof themselves, while the resulting notion of entailment yields a suitable treatment of conjunction as a meet operator, it does not yield an appropriate treatment of disjunction and the other connectives. Inquisitive semantics can be seen as a generalization of the partition framework, which fully regains the traditional algebraic treatment of the connectives (see Roelofsen, 2013; Ciardelli, 2017; Ciardelli & Roelofsen, 2017, for more detailed comparison of inquisitive semantics with earlier approaches to the semantics of questions).

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that is raised by a speaker in uttering a sentence, propositions cannot simply be construed as sets of possible worlds. However, there is a very natural generalization of the traditional notion of propositions that does suit this purpose. Namely, propositions can be construed as sets of information states. In uttering a sentence, a speaker can then be taken to steer the common ground of the conversation towards one of the states in the proposition expressed, while at the same time providing the information that the actual world must be contained in one of these states. The proposition expressed by a sentence thus encodes a proposal to enhance the common ground in one or more ways. If the common ground is enhanced in one of these ways, we say that the proposal is settled in the resulting information state. Furthermore, we assume that the proposal remains settled if the resulting state is further enhanced. That is, the set of information states in which a proposal is settled is downward closed: if a proposal is settled in a state s, then it remains settled in any state s′ ⊆ s. In particular, as a limit case, any proposal is taken to be settled in the inconsistent state ∅. A proposition is taken to consist of all information states that settle the proposal that it encodes. This means that not just any set of information states constitutes a proposition. In order for this to be the case, the set has to be downward closed, and it has to contain the inconsistent state. Equivalently, it has to be downward closed and non-empty. These considerations lead to the following notion of propositions in inquisitive semantics:7 Definition 17. (Propositions in inquisitive semantics) A proposition in inquisitive semantics is a non-empty, downward closed set of information states. Among the states that settle a proposition A, the ones that are easiest to reach are those that contain least information. The states in A that contain least information are those that contain most possible worlds, i.e., they are the maximal elements of A. These maximal elements are refered to in inquisitive semantics

7 It is sometimes found confusing at first sight that the term ‘proposition’ does not refer to sets of possible worlds in inquisitive semantics, as it does in truth-conditional semantics, but rather to sets of information states. To appreciate this terminological choice it helps to recognize that, even though propositions in inquisitive semantics are different kinds of objects than in truth-conditional semantics, they play exactly the same role as they do in the traditional framework. To use Frege’s familiar distinction, the term refers to different kinds of entities in the two frameworks, but its sense is kept constant.

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Some simple propositions in inquisitive semantics

as the alternatives in A. In depicting a proposition, we will generally only depict the alternatives that it contains. Finally, since in uttering a sentence that expresses a proposition A a speaker is taken to provide the information that the actual world is contained in one of the elements of A, i.e., in ⋃ A, we refer to ⋃ A as the informative content of A, and denote it as info(A). To illustrate these notions, consider the following two sentences: (4) Did Amy leave? (5) Amy left. These sentences may be taken to express the propositions depicted in Figure 5, where w1 and w2 are worlds where Amy left, w3 and w4 are worlds where Amy didn’t leave, and the shaded rectangles are the alternatives contained in the given propositions (by downward closure, all substates of these alternatives are also contained in the given propositions). The proposition in Figure 5(i) captures the fact that in uttering the polar question Did Amy leave?, a speaker (i) provides the trivial information that the actual world must be w1, w2, w3, or w4 (all options are open) and (ii) steers the common ground towards a state that is either within {w1 , w2 }, where it is known that Amy left, or within {w3 , w4 }, where it is known that Amy didn’t leave. Other conversational participants need provide information in order to establish such a common ground. On the other hand, the proposition in Figure 5(ii) captures the fact that in uttering the declarative Amy left, a speaker (i) provides the information that the actual world must be either w1 or w2, i.e., one where Amy left, and (ii) steers the common ground of the conversation towards a state in which it is commonly

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accepted that Amy left. In order to reach such a common ground, it is sufficient for other participants to accept the information that the speaker herself already provided in uttering the sentence; no further information is needed. Notice that in the case of the polar question Did Amy leave?, the information that is provided is trivial in the sense that it does not exclude any possible world as a candidate for the actual world. A proposition A is called informative in case it excludes at least one world, i.e., iff info(A) ≠ W. On the other hand, in the case of the declarative Amy left, the inquisitive component of the proposition expressed is trivial, in the sense that in order to reach a state where the proposition is settled, other conversational participants only need to accept the informative content of the proposition expressed, and no further information is required. A proposition A is called inquisitive just in case settling A requires more than just mutual acceptance of info(A), i.e., iff info(A) ∉ A. Given a picture of a proposition it is easy to see whether it is inquisitive or not. This is because, under the assumption that there are only finitely many possible worlds – and this is a safe assumption to make for all the examples to be considered in this paper – a proposition is inquisitive just in case it contains at least two alternatives. For instance, the proposition in Figure 5(i) contains two alternatives, which means that it is inquisitive, while the proposition in Figure 5(ii) contains only one alternative, which means that it is not inquisitive. 4.2 Entailment and Algebraic Operations In order for one proposition A to entail another proposition B in inquisitive semantics, two conditions need to be fulfilled: (i) A has to be at least as informative as B, and (ii) A has to be at least as inquisitive as B. Whether the first condition is satisfied can be checked by comparing info(A) to info(B). Just as in truthconditional semantics, A is at least as informative as B iff info(A) ⊆ info(B). But what does it mean for A to be at least as inquisitive as B? This can be made precise by comparing what it takes to settle A with what it takes to settle B. More specifically, A is at least as inquisitive as B just in case every state that settles A also settles B. But this just means that A ⊆ B. And moreover, if A ⊆ B, then it automatically holds that info(A) ⊆ info(B) as well. Thus, at a formal level entailment in inquisitive semantics just amounts to inclusion, exactly as in standard truth-conditional semantics. Definition 18. (Entailment in inquisitive semantics) A ⊧ B iff A ⊆ B

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At this point we are back on familiar ground: we have a generalized notion of propositions and a corresponding generalized notion of entailment which induces a partial order on the set of all propositions. The next thing to do is to consider the algebraic structure of this partially ordered set, and the basic algebraic operations that can be performed on propositions in this setting. What we find is that in inquisitive semantics, the set of propositions ordered by entailment forms a so-called Heyting algebra (Roelofsen, 2013). This is a slight generalization of the Boolean algebra that we have in truth-conditional semantics. That is, Boolean algebras are a specific kind of Heyting algebras, ones where complements have a special property. Namely, while in all Heyting algebras it holds for any element A that A ∩ A∗ = ⊥, where ⊥ is the strongest element of the algebra, in Boolean algebras it also holds for any element A that A ∪ A∗ = ⊤, where ⊤ is the weakest element of the algebra. While this difference in algebraic structure is of course interesting in its own right, and has particular consequences for the behavior of negation in inquisitive semantics, what is most relevant for our purposes here is that any proposition in inquisitive semantics still has a complement, and that any two propositions still have a join and a meet. Moreover, the join and the meet of two propositions can still be constructed simply by taking their union and intersection, respectively.8 So, just like in truth-conditional semantics, disjunction can be taken to express the join operator, and similarly conjunction and negation can be taken to express the meet operator and complementation, respectively. Thus, while the notion of meaning has been enriched, the essence of the standard treatment of the connectives has been preserved. ⟦ϕ ∨ ψ⟧ = ⟦ϕ⟧ ∪ ⟦ψ⟧ join ⟦ϕ ∧ ψ⟧ = ⟦ϕ⟧ ∩ ⟦ψ⟧ meet ⟦¬ϕ⟧ = ⟦ϕ⟧∗ complementation

Let us look at a number of concrete examples to see how the algebraic operators behave in the inquisitive setting. For easy comparison, let us consider the simple sentences that we also considered above when discussing standard truth-conditional semantics (see Figure 2). The propositions expressed by these sentences in inquisitive semantics are depicted in Figure 6.

8 For a proof of these claims and more elaborate formal discussion of the algebraic structure of the space of propositions in inquisitive semantics, see Roelofsen (2013).

two alternatives for disjunction: an inquisitive reconciliation 267

figure 6

Propositions expressed by some simple sentences in inquisitive semantics.

The proposition expressed by an atomic sentence p is the set of all states consisting of worlds where p is true: ⟦p⟧ = {s | ∀w ∈ s : w(p) = 1}. This proposition contains a unique alternative, i.e., a unique maximal element, which is the set of all worlds where p is true, {11, 10}. This is depicted in Figure 6(i). Similarly, the proposition expressed by q is the set of all states consisting of worlds where q is true. Again, this proposition contains a unique alternative, which is the set of all worlds where q is true, {11, 01}. This is depicted in Figure 6(ii). Now consider the proposition expressed by p ∨ q, depicted in Figure 6(iii). This proposition contains two alternatives, precisely those associated with p ∨ q in alternative semantics, cf. Figure 3(ii). Thus, while disjunction is treated as a join operator, just like in standard truth-conditional semantics, it also has the alternative-generating behavior that is assumed in alternative semantics. Finally, the propositions expressed by p ∧ q and by ¬p, depicted in Figures 6(iv) and 6(v), respectively, both contain a single alternative, corresponding to the propositions expressed by these sentence in truth-conditional semantics.

5

Conclusion

Our aim has been accomplished: the two competing analyses of disjunction have been reconciled. This means that the empirical phenomena involving disjunction that have been successfully dealt with in alternative semantics can be accounted for without giving up the idea that disjunction expresses one of the most basic algebraic operations on meanings. In short, the obtained account unites the empirical advantages of alternative semantics with the explanatory merits of the traditional algebraic account.

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Appendix: Some Extensions There are a number of ways in which the basic result obtained here can be further extended. This appendix provides some pointers to recent and ongoing work where such extensions are pursued. Disjunction across syntactic categories. First, while we have restricted our attention here to sentential disjunction, an important property of disjunction words in natural languages that was mentioned in the introduction is that they typically apply to expressions of many other syntactic categories as well. An important feature of the traditional treatment of the sentential connectives is that it can be generalized in a principled way to apply to expressions of all suitable categories (Gazdar, 1980; Partee & Rooth, 1983; Keenan & Faltz, 1985). This generalization can also be carried out in inquisitive semantics, in essentially the same way. This is done in detail in Ciardelli, Roelofsen & Theiler (2017b), as part of a more general enterprise to develop a full-fledged type-theoretic inquisitive semantics. Disjunction across clause types. Second, while we have focused in this paper on disjunction as such, the interpretation of sentences containing disjunction in natural languages of course depends on all kinds of factors that interact with the disjunction operator. Among such factors are clause type marking (e.g., declarative/interrogative word order) and intonation (e.g., pitch contour, prosodic phrase structure). This is illustrated in (6) below, where ↑ and ↓ indicate rising and falling pitch contours, respectively, and hyphenation and commas indicate the absence and presence of prosodic phrase breaks, respectively (examples (6b-d) are like our earlier example (1) but now each with a specific intonation pattern): (6) a. b. c. d.

Igor speaks English-or-French↓. Does Igor speak English-or-French↑? Does Igor speak English↑, or French↑? Does Igor speak English↑, or French↓?

While all these disjunctive sentences contain exactly the same lexical material, they each receive a different interpretation. A treatment of disjunction that takes both informative and inquisitive aspects of meaning into consideration is necessary to account for these different interpretations in a uniform way, i.e., without stipulating lexical ambiguity of the disjunction word. However, such a treatment of disjunction is not sufficient; it needs to be complemented by

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an account of the different clause type markers and intonational features. For an explicit account of disjunctive declaratives and interrogatives that treats disjunction uniformly as the inquisitive join operator see Roelofsen & Farkas (2015) and Ciardelli et al. (2017a). Disjunction across languages. No matter whether we construe propositions as sets of possible worlds, as in standard truth-conditional semantics, or as downward closed sets of information states, as in inquisitive semantics, the algebraic perspective on meaning leads us to expect that many natural languages contain words or morphemes that can be used to express the basic algebraic operations on propositions, like the join operator. The inquisitive algebraic perspective on meaning gives rise to a further typological expectation as well. Namely, since the join operator in inquisitive semantics generates multiple alternatives and therefore gives rise to inquisitiveness (unlike the other basic algebraic operations, as witnessed by the examples involving conjunction and negation in Figure 6), it is to be expected that words which are used to express the join operation, i.e., disjunction words, may also function as question words. Interestingly, it has been observed that this is indeed the case in many languages (see, e.g., Jayaseelan, 2008; Cable, 2010; AnderBois, 2011; Slade, 2011; Szabolcsi, 2015). This is illustrated in (7) with Malayalam -oo and Japanese ka:

(7) Malayalam Anna-oo Peter-oo Anna wannu-(w)oo

Japanese

English translation

Anna-ka Peter-ka Anna wa kita-ka

Anna or Peter (disjunction) Did Anna come?(question)

AnderBois (2012) and Szabolcsi (2015) propose an account of this phenomenon in inquisitive semantics, suggesting that the inquisitive join operator can indeed be seen as the semantic common core of disjunction words and question words in languages like Malayalam and Japanese. Hurford disjunctions. Finally, the inquisitive treatment of disjunction has repercussions for the analysis of so-called Hurford disjunctions. These are disjunctions were one disjunct implies another, giving rise to infelicity (Hurford, 1974). An example is given in (8): (8) # Marie lives in Paris or in France.

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Such sentences have been discussed quite extensively in the recent literature (e.g., Chierchia et al., 2009; Katzir & Singh, 2013; Meyer, 2014). This line of work assumes a standard truth-conditional semantic treatment of disjunction, and provides a pragmatic explanation for the infelicity of examples like (8). The basic idea is that the stronger disjunct (in this case ‘in Paris’) is redundant: the weaker disjunct by itself has the same meaning as the disjunction as a whole. However, Hurford disjunctions also appear in questions (Ciardelli & Roelofsen, 2017): (9) # Does Marie live in Paris↑, or in France↓? Assuming that in questions disjunction cannot be treated as a truth-conditional operator, but rather has to be treated as introducing multiple alternatives, the redundancy-based accounts of Hurford disjunctions cited above do not directly account for the infelicity of (9). The question that arises, then, is how these accounts fare when re-implemented in alternative semantics or inquisitive semantics. Ideally, this would give us a uniform account of Hurford disjunctions both in declaratives and in questions. Now, interestingly, there is a difference here between the two frameworks. In inquisitive semantics, a Hurford disjunction is still predicted to be redundant: the weaker disjunct by itself has the same meaning as the disjunction as a whole. This is because propositions in inquisitive semantics are downward closed sets of states, and the alternatives in a proposition are its maximal elements. This means that one alternative can never be contained in another (otherwise it would not be a maximal element). By contrast, in alternative semantics one alternative may very well be contained in another. As a consequence, Hurford disjunctions are not predicted to be redundant in alternative semantics. In this case, the stronger disjunct makes a non-trivial contribution to the meaning of the disjunction as a whole. Thus, it seems that the inquisitive treatment of disjunction is advantageous here. For a more indepth discussion of this issue we refer to Ciardelli & Roelofsen (2017).

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Index additive particles 51, 78–79, 93–95 alternative questions 24, 271–272, 274 alternative semantics 11, 14, 39–40, 47, 97, 256–261, 267–271 alternatives 6, 10–18, 21–24, 28, 34–36, 39– 56, 64–85, 88–90, 93, 97–98, 151–152, 212–213, 251–273 American Sign Language 3, 96, 127–131 see also ASL anaphoric deaccenting 9, 29–30, 38–39 ASL 96, 98–108, 110–112, 116, 120–124, 126–131 assertion accommodation 221 association with focus 43, 68, 78, 94, 130, 273

embedding 56, 64, 97, 107, 111–115, 124, 173 emphasis 98, 101, 115, 123–126, 251 erotetic structure 196–199, 208–210, 217, 220, 226–242, 246–247

compact discourse trees 177 contrast 6–10, 18–34, 37, 43, 55–60, 65, 70, 72, 80, 95, 99, 110, 120, 126, 131, 143, 153– 156, 171–172, 185, 196, 203, 225, 231, 248, 250, 270 contrastive focus 8, 20–23, 29–32, 42–43, 98–100 conversational implicatures 161 coordination 173, 198–199, 204, 218, 227– 232, 236–239, 242, 244, 246, 271–272 counterfactuals 252–254, 260–261, 271– 274

givenness 5–33, 35–44, 91, 127, 174–179, 185, 190, 192 gradable adjectives 135, 146–149

d-trees 91, 161, 166–167, 190 deaccenting 6–10, 12, 17, 22, 26–33, 38–42 definite 45, 58–60, 91 dependent questions 169, 177, 210, 215–218 DGS 3, 96–99, 102–103, 106, 112–128, 130 discourse navigation 201 discourse representation 4, 164–165, 191, 194, 198–210, 218–223, 242 discourse structure 93, 95, 110, 164–167, 176, 183–186, 191–197, 219, 246– 249 disjunction 28, 136–137, 211, 213, 251– 274 disjunction in alternative semantics 256, 271 double focus 33–34, 37 doubling 3, 101, 104–115, 119–126

focus 5–11, 13–63, 68, 70–83, 90–103, 108– 112, 124–137, 148, 151, 155–166, 173–183, 190–192, 197, 218, 221, 249–250, 257, 271, 273 focus and questions under discussion 46 focus-sensitive particles 34, 56, 92, 127 focus-sensitivity and questions under discussion 51 free choice 252–254, 270–274

implicature 60, 63, 83–87, 134–137, 142, 145– 162, 249, 272 indirect answers 132–145, 147–157, 159, 161– 163 information structure 45, 91–95, 98, 125–131, 162–167, 170–186, 191–193, 198, 210, 223, 230–234, 247–250 inquisitive semantics 4, 212, 251, 253, 261– 271 interrogative 107, 111, 114, 130–131, 153, 248, 268 narration 168–171, 185, 195–204, 207, 226– 235, 244 Ngamo (west chadic) 45–95 non-at-issue 49, 180–184 polar question 105–106, 110, 114–115, 132– 154, 157, 211, 258, 264–265 potential questions 110, 129, 162, 191, 210– 228, 234, 236, 246, 249 prominence 5, 43, 130 prominent 158, 160, 208, 238, 253, 258 prosodic domain splitting 35 prosodic reversal 7–8, 12–18, 22, 36, 41 prosody 6, 12–13, 18, 33, 39–44, 128–137, 147– 155, 190, 192, 273

276 QUD constraints 177 QUD s 39, 46, 48, 79–80, 164–176, 179, 185– 186, 191 see also question under discussion question 14, 16–37, 41, 47–69, 74–77, 91, 96–99, 101–129, 135–160, 165–184, 189, 193, 196–199, 208–250, 257–259, 264– 272 question trees 199, 209, 220, 226, 229–234, 242–247 question under discussion 7, 47, 97, 153– 154, 182, 197, 208, 246–247 question-answer pair 96, 102–114, 118, 122– 125 result 10, 17, 26, 35–41, 76, 93, 108, 110, 124, 126, 146–147, 172, 191, 194–249, 251, 253, 268 rhetorical relations 93, 129, 164, 191–199, 201–239, 241–249 rise-fall-rise contour 3, 132, 134, 144–157, 163

index salience 175, 214 salient 9–11, 17–28, 30–38, 43–56, 72–78, 80–85, 90, 174–177, 184, 186, 237 scalar additives 56 scalar implicature 134–137, 142–148, 155– 157, 161–162 scalar particles 67, 74, 94–95 SDRT 165–172, 177, 185, 190, 194–209, 221, 226–241, 246–248 sign language 3, 96–99, 103–104, 116, 119, 127–131 sub-questions 153–154, 198, 210, 215–218, 223–225, 231 subordination 95, 198–199, 218, 228, 232, 234, 237, 244 unalternative semantics 11–16, 18, 22, 30, 39, 43, 98 until 45, 57, 81, 85–92, 148, 219 wh-cleft 97, 110, 126 wh-question 74, 98, 102–103, 113–118, 122– 123, 211 wh-word 106, 110, 112–117, 120–123, 180, 227