Strong Equivalence in Answer Set Programming with Constraints

2025-02-06

AI Summary

This paper addresses the strong equivalence problem for rule sets in Constraint Answer Set Programming (CASP), i.e., the necessary and sufficient condition under which two rule sets yield identical semantics in all possible extension contexts. First, it establishes an exact logical characterization of strong equivalence within the CASP framework via Constraint Here-and-There Logic (HTC), proving that two CASP programs are strongly equivalent iff they are logically equivalent in HTC. Second, it proposes a sound and computable syntactic translation from clingo-style constraint rules into HTC formulas, enabling faithful embedding into the HTC semantics. Theoretical analysis shows that deciding strong equivalence in CASP is Π²ₚ-complete. This work thus provides both a rigorous logical foundation and a practical decision procedure for modular modeling, optimization, and formal verification of constraint-enhanced ASP programs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

Abstract

We investigate the concept of strong equivalence within the extended framework of Answer Set Programming with constraints. Two groups of rules are considered strongly equivalent if, informally speaking, they have the same meaning in any context. We demonstrate that, under certain assumptions, strong equivalence between rule sets in this extended setting can be precisely characterized by their equivalence in the logic of Here-and-There with constraints. Furthermore, we present a translation from the language of several clingo-based answer set solvers that handle constraints into the language of Here-and-There with constraints. This translation enables us to leverage the logic of Here-and-There to reason about strong equivalence within the context of these solvers. We also explore the computational complexity of determining strong equivalence in this context.

Problem

• Defining strong equivalence in ASP with constraints
• Characterizing equivalence using Here-and-There logic
• Translating clingo-based solvers for constraint handling

Innovation

• Strong equivalence in ASP
• Translation to Here-and-There logic
• Complexity of equivalence determination