Compilation for Critically Constrained Knowledge Bases

Abstract

We show that many "critically constrained" Random 3SAT knowledge bases (KBs) can be compiled into disjunctive normal form easily by using a variant of the "Davis-Putnam" proof procedure. From these compiled KBs we can answer all queries about entailment of conjunctive normal formulas, also easily --- compared to a "bruteforce " approach to approximate knowledge compilation into unit clauses for the same KBs. We exploit this fact to develop an aggressive hybrid approach which attempts to compile a KB exactly until a given resource limit is reached, then falls back to approximate compilation into unit clauses. The resulting approach handles all of the critically constrained Random 3SAT KBs with average savings of an order of magnitude over the brute-force approach. Introduction Consider the task of reasoning from a propositional knowledge base (KB) F which is expressed as a conjunctive normal formula (CNF). We are given other, query CNFs Q 1 ; Q 2 ; : : : ; QN and asked, for each Q i ,...