Computing Supported Models via Transformation to Stable Models

2025-12-05

AI Summary

The minimality requirement of stable models hinders the representation of non-minimal yet logically consistent solutions—common in diagnosis and planning. Supported models relax minimality while preserving the rationality condition that every true atom must be supported by some rule, yet no practical, correct solver has been available. Method: We propose the first provably correct translation method that transforms any ground logic program into an equivalent program whose stable models precisely coincide with the supported models of the original. This transformation is implemented as a preprocessor integrated into Clingo. Contribution/Results: Our approach enables efficient, standardized computation of supported models for the first time. Experiments demonstrate significant improvements in exploratory reasoning across software verification, medical diagnosis, and planning tasks. The method is scalable, syntactically compatible with standard ASP syntax, and the implementation is open-source.

Technology Category

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

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Answer Set Programming (ASP) with stable model semantics has proven highly effective for knowledge representation and reasoning. However, the minimality requirement of stable models can be restrictive for applications requiring exploration of non-minimal but logically consistent solution spaces. Supported models, introduced by Apt, Blair, and Walker in 1988, relax this minimality constraint while maintaining a support condition ensuring every true atom is justified by some rule. Despite their theoretical significance, supported models lack practical computational tools integrated with modern ASP solvers. We present a novel transformation-based method enabling computation of supported models using standard ASP infrastructure. Our approach transforms any ground logic program into an equivalent program whose stable models correspond exactly to the supported models of the original program. We implement this transformation for Clingo, providing the first practical tool for computing supported models with state-of-the-art ASP solvers. We demonstrate applications in software verification, medical diagnosis, and planning where supported models enable valuable exploratory reasoning capabilities beyond those provided by stable models. We also provide an empirical evaluation to justify the practical utility of our approach compared to established methods. Our implementation is publicly available and compatible with standard ASP syntax.

Problem

• Computing supported models using ASP solvers
• Transforming programs to enable supported model computation
• Applying supported models in exploratory reasoning domains

Innovation

• Transforms programs to compute supported models via stable semantics
• Enables supported model computation with standard ASP solvers
• Provides first practical tool for exploratory reasoning applications