Splitting Answer Set Programs with Respect to Intensionality Statements

2023-06-26

AAAI Conference on Artificial Intelligence

AI Summary

Existing logic program splitting methods rely solely on coarse-grained predicate-level dependencies, rendering many practically relevant Answer Set Programming (ASP) programs inseparable. Method: We propose a fine-grained splitting approach that extends splitting conditions to the level of predicate arguments and contextual information. Building upon dependency graph modeling, we integrate ASP semantics, formal analysis of intensionality statements, and stable model theory to derive a provably correct generalized splitting theorem. Contribution/Results: Our theorem overcomes the applicability limitations of classical splitting theorems, enabling effective decomposition of previously inseparable ASP programs while preserving correctness. It significantly reduces the computational complexity of stable model enumeration, enhances solver scalability in complex knowledge representation tasks, and improves both decomposition efficiency and formal verifiability. The method is fully compatible with mainstream ASP coding practices.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• 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 query analysis, representation and understanding

Abstract

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and to prove the correctness of programs. We generalize the conditions under which this technique is applicable, by considering not only dependencies between predicates but also their arguments and context. This allows splitting programs commonly used in practice to which previous results were not applicable.

Problem

• Generalizing splitting conditions for logic programs
• Considering predicate dependencies, arguments, and context
• Enabling splitting of previously inapplicable practical programs

Innovation

• Generalizing splitting conditions for logic programs
• Considering predicate arguments and context dependencies
• Enabling splitting for previously inapplicable practical programs