Counting Answer Sets of Disjunctive Answer Set Programs

2025-07-15

AI Summary

Addressing the computational intractability of exact answer set counting in Disjunctive Answer Set Programming (DASP) and the poor scalability of existing tools, this paper introduces SharpASP-SR—a novel framework for precise answer set enumeration. Methodologically, it is the first to reduce DASP answer set counting to projected model counting (#PMC) over propositional logic, leveraging a newly devised polynomial-size answer set characterization and a subtraction-based reduction technique to avoid exponential blowup in intermediate representations. Furthermore, it integrates an efficient translation from disjunctive logic programs to propositional formulas with a hybrid enumeration strategy, enabling universal support for arbitrary disjunctive programs. Experimental evaluation demonstrates that SharpASP-SR significantly outperforms state-of-the-art counters on large-scale benchmarks. To our knowledge, it is the first DASP counting framework that simultaneously guarantees theoretical soundness and practical efficiency.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Answer Set Programming (ASP) provides a powerful declarative paradigm for knowledge representation and reasoning. Recently, counting answer sets has emerged as an important computational problem with applications in probabilistic reasoning, network reliability analysis, and other domains. This has motivated significant research into designing efficient ASP counters. While substantial progress has been made for normal logic programs, the development of practical counters for disjunctive logic programs remains challenging. We present SharpASP-SR, a novel framework for counting answer sets of disjunctive logic programs based on subtractive reduction to projected propositional model counting. Our approach introduces an alternative characterization of answer sets that enables efficient reduction while ensuring that intermediate representations remain of polynomial size. This allows SharpASP-SR to leverage recent advances in projected model counting technology. Through extensive experimental evaluation on diverse benchmarks, we demonstrate that SharpASP-SR significantly outperforms existing counters on instances with large answer set counts. Building on these results, we develop a hybrid counting approach that combines enumeration techniques with SharpASP-SR to achieve state-of-the-art performance across the full spectrum of disjunctive programs.

Problem

• Counting answer sets in disjunctive logic programs efficiently
• Reducing answer set counting to projected model counting
• Improving performance for programs with large answer sets

Innovation

• Subtractive reduction to projected model counting
• Alternative characterization for efficient reduction
• Hybrid approach combining enumeration and subtractive reduction