# Stable Model Counting and Its Application in Probabilistic Logic Programming

arXiv: https://arxiv.org/abs/1411.5410 · HTML: https://mlsanity.com/paper/1411.5410/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2014.

## Built on by (most cited first, 8 of 8)

- [Efficient Knowledge Compilation Beyond Weighted Model Counting](https://mlsanity.com/paper/2205.07496/) (2022)
- [smProbLog: Stable Model Semantics in ProbLog for Probabilistic Argumentation](https://mlsanity.com/paper/2304.00879/) (2023)
- [SMProbLog: Stable Model Semantics in ProbLog and its Applications in Argumentation](https://mlsanity.com/paper/2110.01990/) (2021)
- [Counting and Reasoning with Plans](https://mlsanity.com/paper/2502.00145/) (2025)
- [Generation and Prediction of Difficult Model Counting Instances](https://mlsanity.com/paper/2212.02893/) (2022)
- [Techniques for Measuring the Inferential Strength of Forgetting Policies](https://mlsanity.com/paper/2404.02454/) (2024)
- [Answer Set Counting and its Applications](https://mlsanity.com/paper/2502.09231/) (2025)
- [Counting Answer Sets of Disjunctive Answer Set Programs](https://mlsanity.com/paper/2507.11655/) (2025)

## Abstract (arXiv)

Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.