Model-Intersection Problems and Their Solution Schema Based on Equivalent Transformation

Abstract

Model-intersection (MI) problems are a very large class of logical problems that includes many useful problem classes, such as proof problems on first-order logic and query-answering (QA) problems in pure Prolog and deductive databases. We propose a general schema for solving MI problems by equivalent transformation (ET), where problems are solved by repeated simplification. The correctness of this solution schema is shown. This general schema is specialized for formalizing solution schemas for QA problems and proof problems. The notion of a target mapping is introduced for generation of ET rules, allowing many possible computation procedures, for instance, computation procedures based on resolution and unfolding. This theory is useful for inventing solutions for many classes of logical problems.