Weighted Rules under the Stable Model Semantics

2026-05-10

AI Summary

This work addresses the limitations of stable model semantics in handling inconsistency, model preference, and probabilistic reasoning by introducing, for the first time, the log-linear framework from Markov logic into answer set programming. The proposed weighted stable model semantics systematically extends deterministic reasoning to probabilistic inference by assigning weights to rules, thereby enabling quantitative comparison among inconsistent programs and their models. The resulting formalism unifies strengths from answer set programming, Markov logic, ProbLog, and P-log, supporting statistical inference and model selection over stable models. This integration significantly enhances the expressiveness and practical applicability of non-monotonic logic in uncertain environments.

Abstract

We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

Problem

• stable model semantics
• weighted rules
• answer set programming
• probabilistic reasoning
• inconsistency resolution

Innovation

• weighted rules
• stable model semantics
• Markov Logic
• answer set programming
• probabilistic reasoning