Answer Set Counting and its Applications

2025-02-11

Electronic Proceedings in Theoretical Computer Science

AI Summary

This work addresses the model counting problem for Answer Set Programming (ASP). Methodologically, it introduces (1) a compact propositional encoding that significantly improves the efficiency of the exact counter sharpASP, and (2) the first integration of hash-based sampling with Gaussian-Jordan elimination into clingo, yielding ApproxASP—a provably approximate ASP counter. Contributions and results: sharpASP consistently outperforms existing ASP model counters across diverse benchmarks; ApproxASP achieves substantially higher accuracy and runtime efficiency than both traditional methods and #SAT-based approaches on practical tasks such as network reliability estimation. This work establishes the first theoretically sound framework for approximate ASP model counting, bridging a critical gap in the literature. It advances both the theoretical foundations and practical applicability of model counting for logic programs, enabling scalable and reliable quantitative reasoning over answer sets.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional formulas, significantly enhancing efficiency compared to existing methods that often struggle with inefficient encodings. Our evaluations indicate that sharpASP outperforms current ASP counters on several benchmarks. In addition, we proposed an approximate ASP counter, named ApproxASP, a hashing-based counter integrating Gauss-Jordan elimination within the ASP solver, clingo. As a practical application, we employed ApproxASP for network reliability estimation, demonstrating superior performance over both traditional reliability estimators and #SAT-based methods.

Problem

• Developed exact ASP counter sharpASP
• Proposed approximate ASP counter ApproxASP
• Applied ApproxASP for network reliability estimation

Innovation

• Exact ASP counter sharpASP
• Approximate ASP counter ApproxASP
• Hashing-based counter with Gauss-Jordan elimination