First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation

Abstract

AbstractIn this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The approximation extends the signature and preserves unsatisfiability: if the simplified clause set is satisfiable in some model, so is the original clause set in the same model interpreted in the original signature. A refutation generated by a decision procedure on the simplified clause set can then either be lifted to a refutation in the original clause set, or it guides a refinement excluding the previously found unliftable refutation. This way the approach is refutationally complete. We do not step-wise lift refutations but lift conflicting cores, finite unsatisfiable clause sets representing at least one refutation. The approach is dual to many existing approaches in the literature.KeywordsAutomate ReasoningHorn ClauseGround InstanceLift StepPositive LiteralThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.