A Compiling Method of Propositional Knowledge Base for Abductive Generation of Lacked Knowledge

Abstract

In order to realize advanced AI functions, such as learning, common sence, abduction etc., it becomes necessary to manipulate incomplete knowledge. Truth maintenance systems including TMS, ATMS, CMS (Clause Management System) have been developed for the efficient management of hypothesis which is a type of the incomplete knowledge. Among these systems, CMS proposed by Reiter and de Kleer has a logical structure and suggests the important properties of knowledge compilation and abductive function. Although the generation of prime implicant clauses and minimal support clauses is important in the CMS processing, it is very expensive with respect to computing time and memory. This paper proposes a fast and efficient algorithm named "ordered clause-consensus method" for the generation of the prime implicant clauses, which allows the compilation of propositional knowledge-base. In this method, the prime implicant clauses are generated directly from axiom clauses, and the method is similar to the Tison's method in the theory of Boolean function. A compiled hypothesis-based reasoning system is constructed on the basis of this method in the Prolog language. The knowledge compiling speed of this system is 5 to 90 times faster than that of simple implementation using the basic function of Prolog. In case of generating unempty minimal support clauses with respect to a unit query clause, the inference of this compiled system is 10 to 100 times faster than an inference in interpretive mode, and 60 to 10000 times faster than a simple breadth-first inference.