A Resolution Principle for a Logic with Restricted Quantifiers [Paperback]

This monograph presents foundations for a constrainedlogic scheme treating constraints as a very general form ofrestricted quantifiers. The constraints - or quantifierrestrictions - are taken from a general constraint systemconsisting of constraint theory and a set of distinguishedconstraints.The book provides a calculus for this constrained logicbased on a generalization of Robinson's resolutionprinciple. Technically, the unification procedure of theresolution rule is replaced by suitable constraint-solvingmethods. The calculus is proven sound and complete for therefutation of sets of constrained clauses. Using a new andelegant generalization of the notion ofa ground instance,the proof technique is a straightforward adaptation of theclassical proof technique.The author demonstrates that the constrained logic schemecan be instantiated by well-known sorted logics orequational theories and also by extensions of predicatelogics with general equational constraints or conceptdescription languages.Preliminaries.- Unification.- A logic with restricted quantifiers.- Equational constraint theories.- Conclusion.This monograph provides the formal basics of a scheme for predicate logic with restricted quantifiers taken as constraints. It gives the model theory and proof theory for this logic together with a sound and complete refutation calculus for constrained clauses.Springer Book ArchivesDE