Refutational Theorem Proving Using Term-Rewriting Systems

In this paper we propose a new approach to theorem proving in first-order logic based on the term-rewriting method. First for propositional calculus, we introduce a canonical term-rewriting system for Boolean algebra. This system enables us to transform the first-order predicate calculus into a form of equational logic, and to develop several complete strategies (both clausal and nonclausal) for first-order theories based on the Knuth-Bendix Completion Procedure. More importantly, our strategies can deal with predicate logic and built-in (equational) theories in a uniform and effecave way. We also describe an implementation and comparisons with some other first-order theoremproving methods. 0. Structure of the Paper This paper has five sections. The first section gives a brief account of the basic not ions of the term-rewrit ing method. In Section 2, we present a canonical term-rewri t ing system for Boolean algebra. This system is used as a basis for developing several comple te theorem-proving strategies for the first-order predicate calculus in Section 3. In Section 4, the strategies given in Section 3 are ex tended to deal with richer theor iesf i rs t -order logic with built-in equational axioms. A n implementa t ion of these methods is described in Section 5, together with some exper imental results and discussions.