Intelligent Backtracking in Plan-Based Deduction

This paper develops a method of mechanical deduction based on a graphical representation of the structure of proofs. Attempts to find a refutation(s) are recorded in the form of plans, corresponding to portions of an AND/OR graph search space and representing a purely deductive structure of derivation. This method can be applied to any initial base (set of nonnecessarily Horn clauses). Unlike the exhaustive (blind) backtracking which treats all the goals deduced in the course of a proof as equally probable sources of failure, his approach detects the exact source of failure. Only a small fragment of the solution space is kept on disk as a collection of pairs, each of which consists of a plan and a graph of constraints. The search strategy and the method of nonredundant processing of individual pairs which leads to a solution (if it exists) is presented. This approach is compared-on a special case-with a blind backtracking algorithm for which an exponential improvement is demonstrated. Some important implementation problems are discussed, and toplevel design of a mechanical deduction system implementing our algorithm is presented. It is proven that the algorithm is complete in the following sense: if for a given base a resolution refutation exists, then this refutation is found by the algorithm.