Publication Details

A Production System For Automatic Deduction

by Nilsson, Nils J.

Technical Note 148
Institution: AI Center, SRI International
Address: 333 Ravenswood Ave., Menlo Park, CA 94025
Jul 1977.

Note: This work was supported jointly by SRI International Project 6171, Office of Naval Research Contract No.NR049-405; and by the Stanford University Heuristic Programming Project, ARPA Order No. 2494.

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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.