Deduction methods for rst-order constrained clauses with equality are described within an abstract framework: constraint strategies, consisting of an inference system, a constraint inheritance strategy and redundancy criteria for clauses and inferences. We give simple conditions for such a constraint strategy to be complete (refutationally and in the sense of Knuth-Bendix-like completion). This...

We describe resolution proof systems for several modal logics. First we present the propo-sitional versions of the systems and prove their completeness. The first-order resolution rule for classical logic is then modified to handle quantifiers directly. This new resolution rule enables us to extend our propositional systems to complete first-order systems. The systems for the different modal lo...

We present an inference system for rst-order constrained clauses with equality modulo associativity (A). Our procedure is refutationally complete and reduces to Knuth-Bendix completion modulo A in the equational case. As an essential ingredient we present the rst |as far as we know| A-compatible reduction ordering total on the ground A-congruence classes.

Informally, a b s t r a c t i o n can be described as the process of mapping a representation of a problem into a new representation. The aim of the paper is to propose a theory of abstrac­ t ion. The generality of the framework is tested by formalizing and analyzing some work done in the past; i ts efficacy by giving a procedure which solves the '' false proof problem by avoid­ ing the use of ...

Lifting is one of the most important general techniques for accelerating dii-cult computations. Lifting was used by Alan Robinson in the early 1960's to accelerate rst order inference Robinson, 1965]. A complete inference procedure had been done by Martin Davis and Hillary Putnam a few years prior to Robinson's work Davis and Putnam, 1960]. Unfortunately, it was a ground procedure and suuered f...

This talk reviews those efforts in automatic theorem proving, during the past few years, which have emphasized techniques other than resolution. These include: knowledge bases, natural deduction, reduction, (rewrite rules), typing, procedures, advice, controlled forward chaining, algebraic simplification, built-in associativity and commutativity, models, analogy, and man-machine systems. Exampl...