A Production System for Automatic Deduction

A new predicate calculus deduction system based on production rules is proposed. The system combines several developments in Artificial Intelligence and Automatic Theorem Proving research including the use of domain-specific inference rules and separate mechanisms for forward and backward reasoning. It has a clean separation between the data base, the production rules, and the control system. Goals and subgoals are maintained in an AND/OR tree structure. We introduce here a structure that is the dual of the AND/OR tree to represent assertions. The production rules modify these structures until they "connect" in a fashion that proves the goal theorem. Unlike some previous systems that used production rules, ours is not limited to rules in Horn Clause form. Unlike previous PLANNER-like systems, ours can handle the full range of predicate calculus expressions including those with quantified variables, disjunctions, and negations. 1. BACKGROUND Logical deduction is a basic activity in many artificial intelligence (Al) systems. Specific applications in which deduction plays a major role include questionanswering, program verification, mathematical theorem-proving, and reasoning about both mundane and esoteric domains. Of the several different approaches to deduction pursued by Al research, we might mention two extremes. In one (see for example, Hewitt, 1971), deduction procedures are, based on more or less intuitive, ad hoc, and informal considerations. Such an approach derives its main advantage, namely efficiency, from the specialized, domain-dependent heuristics that can be tightly encoded in the system. The approach sometimes suffers, however, from excessive rigidity that frustrates the evolutionary development of systems. Most examples of designs based on this approach also exhibit deficient logical competence.