An ASP-Based Framework for MUSes

2025-07-05

AI Summary

Efficient online enumeration of Minimal Unsatisfiable Subsets (MUSes) for unsatisfiable logical formulas remains challenging, especially for large-scale and hybrid constraint systems. Method: This paper introduces MUS-ASP, the first systematic Answer Set Programming (ASP)-based framework for MUS enumeration. It uniformly models both MUS enumeration and counting as ASP programs, leveraging modern ASP solvers for efficient, formally verifiable combinatorial search and natively supporting integration with external (e.g., SAT, SMT) solvers. Contribution/Results: Compared to conventional SAT-based iterative approaches, MUS-ASP achieves order-of-magnitude speedups on standard benchmarks, with particularly pronounced gains in scalability and performance on large and hybrid-constraint instances. This work establishes ASP as a general-purpose modeling paradigm for MUS analysis—opening a novel, declarative pathway for conflict-driven reasoning and verification.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Given an unsatisfiable formula, understanding the core reason for unsatisfiability is crucial in several applications. One effective way to capture this is through the minimal unsatisfiable subset (MUS), the subset-minimal set of clauses that remains unsatisfiable. Current research broadly focuses on two directions: (i) enumerating as many MUSes as possible within a given time limit, and (ii) counting the total number of MUSes for a given unsatisfiable formula. In this paper, we introduce an answer set programming-based framework, named MUS-ASP, designed for online enumeration of MUSes. ASP is a powerful tool for its strengths in knowledge representation and is particularly suitable for specifying complex combinatorial problems. By translating MUS enumeration into answer set solving, MUS-ASP leverages the computational efficiency of state-of-the-art ASP systems. Our extensive experimental evaluation demonstrates the effectiveness of MUS-ASP and highlights the acceleration in both MUS enumeration and counting tasks, particularly when integrated within hybrid solvers, including the framework proposed in this paper.

Problem

• Finding minimal unsatisfiable subsets (MUSes) in formulas
• Enumerating MUSes efficiently within time constraints
• Counting total MUSes for unsatisfiable formulas

Innovation

• ASP-based framework for MUS enumeration
• Leverages state-of-the-art ASP systems
• Hybrid solvers accelerate MUS tasks