Weighted Rules under the Stable Model Semantics

TL;DR

We introduce weighted rules into the stable model semantics to overcome its deterministic nature, enabling inconsistency resolution, ranking, probability assignment, and statistical inference.

Problem

The stable model semantics is deterministic, lacking flexibility when inconsistencies arise or when multiple models need selection. It also does not directly support probabilistic reasoning.

Approach

We adopt log-linear models from Markov Logic to assign weights to rules and define a probability distribution over stable models based on weights. This allows inconsistency resolution, model ranking, probability computation, and statistical inference.

Results & Contribution

The proposed framework demonstrates expressiveness and flexibility through formal comparisons with answer set programs, Markov Logic, ProbLog, and P-log. Weighted rules extend the applicability of stable model semantics, providing a practical tool that integrates uncertainty and statistical inference.