SCL(FOL) Revisited

TL;DR

This paper refines the SCL(FOL) calculus for first-order logic without equality by enhancing regularity, adding trail and model bounding for termination, and providing rigorous proofs of its properties.

Contribution

It introduces a stronger regularity notion, trail and model bounding for termination, and formal proofs, advancing the theoretical foundation of SCL(FOL).

Findings

Guarantees non-redundant clause learning

Achieves termination guarantees

Provides rigorous soundness and completeness proofs

Abstract

This paper presents an up-to-date and refined version of the SCL calculus for first-order logic without equality. The refinement mainly consists of the following two parts: First, we incorporate a stronger notion of regularity into SCL(FOL). Our regularity definition is adapted from the SCL(T) calculus. This adapted definition guarantees non-redundant clause learning during a run of SCL. However, in contrast to the original presentation, it does not require exhaustive propagation. Second, we introduce trail and model bounding to achieve termination guarantees. In previous versions, no termination guarantees about SCL were achieved. Last, we give rigorous proofs for soundness, completeness and clause learning guarantees of SCL(FOL) and put SCL(FOL) into context of existing first-order calculi.