Foundations of Equational Logic Programming [1 ed.] 354051533X, 9783540515333
Equations play a vital role in many fields of mathematics, computer science, and artificial intelligence. Therefore, man
268 75 3MB
English Pages 256 [261] Year 1989
Table of contents :
Title Page
Copyright Page
Preface
Contents
1 Introduction
2 Preliminaries
2.1 Terms, Atoms, and Equations
2.2 Substitutions
3 Equational Logic Programming
3.1 Equational Logic Programs
3.2 Model Theory
3.3 Fixpoint Theory
3.4 Proof Theory
3.4.1 Unification
3.4.2 SLD-Resolution
4 Universal Unification
5 SLDE-Resolution
6 Paramodulation
6.1 Fixpoint Characterization
6.2 Paramodulation
6.3 Confluent Theories
6.4 Term Rewriting Systems
6.5 Narrowing
6.5.1 Canonical Term Rewriting Systems
6.5.2 Narrowing and Rewriting
6.5.3 Completely Defined Term Rewriting Systems
6.6 The Unification and Matching Problem for Canonical Theories
6.6.1 A Decidability Metatheorem
6.6.2 The Undecidability of the Unification and Matching Problem
6.7 Summary
7 Universal Unification by Complete Sets of Transformations
7.1 The Transformation Rules
7.2 Soundness of the Transformation Rules
7.3 Completeness of the Transformation Rules
8 Lazy Resolution and Complete Sets of Inference Rules for Horn Equational Theories
9 Conclusion
9.1 Summary
9.2 Discussion
E-resoIution
Resolution by Unification and Equality
Equality Graphs
Special Predicates
Flattening
EQLOG
Constraint Logic Programming
CHIP - Constraint Handling in PROLOG
Order-Sorted Horn Logic
LIFE
Theory Resolution
9.3 Open Problems
References
Index
The Inference Rules
Examples
Notations
Title Page
Copyright Page
Preface
Contents
1 Introduction
2 Preliminaries
2.1 Terms, Atoms, and Equations
2.2 Substitutions
3 Equational Logic Programming
3.1 Equational Logic Programs
3.2 Model Theory
3.3 Fixpoint Theory
3.4 Proof Theory
3.4.1 Unification
3.4.2 SLD-Resolution
4 Universal Unification
5 SLDE-Resolution
6 Paramodulation
6.1 Fixpoint Characterization
6.2 Paramodulation
6.3 Confluent Theories
6.4 Term Rewriting Systems
6.5 Narrowing
6.5.1 Canonical Term Rewriting Systems
6.5.2 Narrowing and Rewriting
6.5.3 Completely Defined Term Rewriting Systems
6.6 The Unification and Matching Problem for Canonical Theories
6.6.1 A Decidability Metatheorem
6.6.2 The Undecidability of the Unification and Matching Problem
6.7 Summary
7 Universal Unification by Complete Sets of Transformations
7.1 The Transformation Rules
7.2 Soundness of the Transformation Rules
7.3 Completeness of the Transformation Rules
8 Lazy Resolution and Complete Sets of Inference Rules for Horn Equational Theories
9 Conclusion
9.1 Summary
9.2 Discussion
E-resoIution
Resolution by Unification and Equality
Equality Graphs
Special Predicates
Flattening
EQLOG
Constraint Logic Programming
CHIP - Constraint Handling in PROLOG
Order-Sorted Horn Logic
LIFE
Theory Resolution
9.3 Open Problems
References
Index
The Inference Rules
Examples
Notations
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- Steffen Hölldobler (eds.)
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