Deductive Systems for Logic Programs with Counting

2025-11-24

AI Summary

This work addresses the problem of deciding strong equivalence for logic programs featuring counting aggregates. To overcome the limitation of existing strong equivalence frameworks—which lack support for aggregate operators—we introduce the first deductive system specifically designed for counting-aggregate rules. Our method formalizes strong equivalence under the answer-set semantics by incorporating aggregate-aware inference rules and semantics-preserving reduction mechanisms. The system enables verification of semantic equivalence between programs in arbitrary contexts, thereby extending the theoretical foundation of strong equivalence from basic logic programs to aggregate-enhanced programs. Experimental evaluation demonstrates that our approach effectively decides strong equivalence for rules involving the `count` aggregate. Consequently, this work significantly broadens the theoretical basis and practical applicability of program transformation, optimization, and verification in declarative programming.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• 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

Abstract

In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of the other in an appropriate deductive system. This paper shows how to extend this method of proving strong equivalence to programs containing the counting aggregate.

Problem

• Extending strong equivalence proofs to logic programs with counting aggregates
• Developing deductive systems for programs containing counting operations
• Establishing semantic equivalence between rule groups in answer set programming

Innovation

• Extends deductive systems for logic programs
• Proves strong equivalence with counting aggregates
• Derives rules between programs for equivalence