Weighted Rules under the Stable Model Semantics

TL;DR

This paper extends stable model semantics with weights inspired by Markov Logic, enabling probabilistic reasoning, inconsistency resolution, and ranking of models in answer set programming.

Contribution

It introduces weighted rules under stable model semantics, bridging deterministic logic programming with probabilistic inference methods.

Findings

Provides methods to assign probabilities to stable models

Enables ranking and resolving inconsistencies in answer set programs

Offers formal comparisons with related probabilistic logic frameworks

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.