# Weighted Rules under the Stable Model Semantics

arXiv: https://arxiv.org/abs/2605.09519 · HTML: https://mlsanity.com/paper/2605.09519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 2 of 2)

- [Probabilistic Inductive Logic Programming Based on Answer Set Programming](https://mlsanity.com/paper/1405.0720/) (2014)
- [First-Order Stable Model Semantics and First-Order Loop Formulas](https://mlsanity.com/paper/1401.3898/) (2014)

## Built on by (most cited first, 2 of 2)

- [CLARK: Closed-loop Learning for Adaptive Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2607.19996/) (2026)
- [How Rules Represent Causal Knowledge: Causal Modeling with Probabilistic Logic Programming](https://mlsanity.com/paper/2607.21208/) (2026)

## Abstract (arXiv)

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.