Finding Connections via Satisfiability Solving

2026-03-06

AI Summary

This work addresses the automation bottleneck in automated theorem proving for first-order classical logic by proposing a novel approach that integrates the strengths of ordered saturation and subgoal reduction. The method directly encodes the connection calculus as a SAT problem and, for the first time, incorporates symmetry-breaking techniques to devise three innovative SAT encoding schemes. These encodings transcend the conventional paradigm of reducing first-order logic to propositional logic through simplification. The resulting solver, upCoP, demonstrates the effectiveness and practicality of the proposed approach in empirical evaluations, achieving a significant improvement in proof search efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry breaking for connection calculi in first-order logic, with the purpose of further pushing the automation in first-order classical logic proofs. In contrast to classical ways of reducing first-order logic to propositional logic, our method encodes the structure of the proof search itself. We present three distinct SAT encodings for connection calculi, analyse their theoretical properties, and discuss the effect of using SAT/SMT solvers on these encodings. We implemented our work in the new solver upCoP and showcase its practical feasibility.

Problem

• automated theorem proving
• first-order logic
• connection calculi
• SAT solving
• proof automation

Innovation

• SAT encoding
• connection calculi
• symmetry breaking
• first-order logic
• automated theorem proving