Conflict Resolution: a First-Order Resolution Calculus with Decision Literals and Conflict-Driven Clause Learning

TL;DR

This paper introduces a first-order conflict resolution calculus inspired by SAT-solver techniques, incorporating decision literals and clause learning, and proves its soundness and completeness.

Contribution

It extends the resolution calculus with decision literals and conflict-driven clause learning for first-order logic, bridging SAT techniques with first-order theorem proving.

Findings

The calculus is sound, as it can be simulated by natural deduction.

It is refutationally complete, capable of simulating resolution.

The paper provides detailed proofs of soundness and completeness.

Abstract

This paper defines the (first-order) conflict resolution calculus: an extension of the resolution calculus inspired by techniques used in modern SAT-solvers. The resolution inference is restricted to (first-order) unit-propagation and the calculus is extended with a mechanism for assuming decision literals and a new inference rule for clause learning, which is a first-order generalization of the propositional conflict-driven clause learning (CDCL) procedure. The calculus is sound (because it can be simulated by natural deduction) and refutationally complete (because it can simulate resolution), and these facts are proven in detail here.