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A Resolution Principle for a Logic with Restricted Quantifiers

  • Book
  • © 1991

Overview

Editors:
  1. H. -J. Bürckert
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Part of the book series: Lecture Notes in Computer Science (LNCS, volume 568)

Part of the book sub series: Lecture Notes in Artificial Intelligence (LNAI)

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Table of contents (6 chapters)

  1. Front Matter

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  2. Introduction

    Pages 1-16

  3. Preliminaries

    Pages 17-33

  4. Unification

    Pages 35-48

  5. A logic with restricted quantifiers

    Pages 49-77

  6. Equational constraint theories

    Pages 79-96

  7. Conclusion

    Pages 97-99

  8. Back Matter

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Keywords

About this book

This monograph presents foundations for a constrained logic scheme treating constraints as a very general form of restricted quantifiers. The constraints - or quantifier restrictions - are taken from a general constraint system consisting of constraint theory and a set of distinguished constraints. The book provides a calculus for this constrained logic based on a generalization of Robinson's resolution principle. Technically, the unification procedure of the resolution rule is replaced by suitable constraint-solving methods. The calculus is proven sound and complete for the refutation of sets of constrained clauses. Using a new and elegant generalization of the notion ofa ground instance, the proof technique is a straightforward adaptation of the classical proof technique. The author demonstrates that the constrained logic scheme can be instantiated by well-known sorted logics or equational theories and also by extensions of predicate logics with general equational constraints or concept description languages.

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