Upside-down meta-interpretation of the model elimination theorem-proving procedure for deduction and abduction

Abstract

Typical bottom-up, forward-chaining reasoning systems such as hyperresolution lack goal-directedness while typical top-down, backward-chaining reasoning systems like Prolog or model elimination repeatedly solve the same goals. Reasoning systems that are goal-directed and avoid repeatedly solving the same goals can be constructed by formulating the top-down methods metatheoretically for execution by a bottom-up reasoning system (hence, we use the term upside-down meta-interpretation). This formulation also facilitates the use of flexible search strategies, such as merit-ordered search that are common to bottom-up reasoning systems. The model elimination theorem-proving procedure, its extension by an assumption rule for abduction, and its restriction to Horn clauses are adapted here for such upside-down meta-interpretation. This work can be regarded as an extension of the magic-sets or Alexander method for query evaluation in deductive databases to both non-Horn clauses and abductive reasoning.