# SMProbLog: Stable Model Semantics in ProbLog and its Applications in Argumentation

arXiv: https://arxiv.org/abs/2110.01990 · HTML: https://mlsanity.com/paper/2110.01990/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 5 Oct 2021.

## Builds on (most cited first, 5 of 5)

- [Epistemic Graphs for Representing and Reasoning with Positive and Negative Influences of Arguments](https://mlsanity.com/paper/1802.07489/) (2018)
- [On the Semantics and Complexity of Probabilistic Logic Programs](https://mlsanity.com/paper/1701.09000/) (2017)
- [Stable Model Counting and Its Application in Probabilistic Logic Programming](https://mlsanity.com/paper/1411.5410/) (2014)
- [On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach](https://mlsanity.com/paper/2008.02550/) (2020)
- [Negation in the Head of CP-logic Rules](https://mlsanity.com/paper/1312.6156/) (2013)

## Built on by (most cited first, 5 of 5)

- [Efficient Knowledge Compilation Beyond Weighted Model Counting](https://mlsanity.com/paper/2205.07496/) (2022)
- [Semirings for Probabilistic and Neuro-Symbolic Logic Programming](https://mlsanity.com/paper/2402.13782/) (2024)
- [dPASP: A Comprehensive Differentiable Probabilistic Answer Set Programming Environment For Neurosymbolic Learning and Reasoning](https://mlsanity.com/paper/2308.02944/) (2023)
- [plingo: A system for probabilistic reasoning in clingo based on lpmln](https://mlsanity.com/paper/2206.11515/) (2022)
- [Research Note on Uncertain Probabilities and Abstract Argumentation](https://mlsanity.com/paper/2208.10932/) (2022)

## Abstract (arXiv)

We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is given by the success probability of a query, which corresponds to the probability that the query succeeds in a randomly sampled program. It is well-defined when each random sample uniquely determines the truth values of all logical atoms. Argumentation problems, however, represent an interesting practical application where this is not always the case. SMProbLog generalizes the semantics of ProbLog to the setting where multiple truth assignments are possible for a randomly sampled program, and implements the corresponding algorithms for both inference and learning tasks. We then show how this novel framework can be used to reason about probabilistic argumentation problems. Therefore, the key contribution of this paper are: a more general semantics for ProbLog programs, its implementation into a probabilistic programming framework for both inference and parameter learning, and a novel approach to probabilistic argumentation problems based on such framework.