A Resolution Principle for a Logic with Restricted Quantifiers

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.