A Two-Watched Literal Scheme for First-Order Logic

2026-05-20

AI Summary

This work addresses the problem of efficiently detecting propagatable and falsified clauses in first-order logic relative to a given set of ground literals. To this end, it introduces a lifted dual-watched-literal algorithm—an extension of the highly effective dual-watched-literal scheme from propositional logic—formulated within a rule-based system that dynamically maintains clause states by integrating resolution and grounding techniques. The proposed method significantly outperforms standard dynamic programming strategies in identifying both propagatable literals and conflicting clauses, demonstrating superior computational efficiency and scalability, particularly when handling long clauses.

Abstract

The two-watched literal scheme, a core component of efficient CDCL (Conflict-Driven Clause Learning) implementations for propositional logic, is extended to first-order logic. Given a set of first-order clauses and a set of ground literals, our lifted two-watched literal scheme efficiently detects all propagating and false clauses with respect to the ground literals. We present the algorithm as a system of rules and prove its soundness and completeness. Additionally, we provide an implementation of the two-watched literal scheme, which outperforms a standard dynamic programming approach for detecting propagatable literals and conflicts, especially when dealing with long clauses.

Problem

• two-watched literal
• first-order logic
• CDCL
• clause propagation
• ground literals

Innovation

• two-watched literal
• first-order logic
• CDCL
• lifted inference
• clause propagation