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A Resolution Principle for a Logic with Restricted Quantifiers by Hans-Jurgen Burckert

A Resolution Principle for a Logic with Restricted Quantifiers (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence) by Hans-Jurgen Burckert
English | Dec 23, 1991 | ISBN: 3540550348, 0387550348 | 122 Pages | DJVU | 1 MB

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.
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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