# smProbLog: Stable Model Semantics in ProbLog for Probabilistic Argumentation

arXiv: https://arxiv.org/abs/2304.00879 · HTML: https://mlsanity.com/paper/2304.00879/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 64 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## 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, 6 of 6)

- [A Compositional Atlas for Algebraic Circuits](https://mlsanity.com/paper/2412.05481/) (2024)
- [Understanding ProbLog as Probabilistic Argumentation](https://mlsanity.com/paper/2308.15891/) (2023)
- [Fast Inference for Probabilistic Answer Set Programs via the Residual Program](https://mlsanity.com/paper/2408.07524/) (2024)
- [Symbolic Parameter Learning in Probabilistic Answer Set Programming](https://mlsanity.com/paper/2408.08732/) (2024)
- [Solving Decision Theory Problems with Probabilistic Answer Set Programming](https://mlsanity.com/paper/2408.11371/) (2024)
- [Probabilistic Answer Set Programming with Discrete and Continuous Random Variables](https://mlsanity.com/paper/2409.20274/) (2024)

## Abstract (arXiv)

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics, which is, that probabilistic facts fully capture the uncertainty in the domain under investigation. The second contribution of this paper is then a novel PLP semantics for programs where a choice of probabilistic facts does not uniquely determine the truth assignment of the logical atoms. The third contribution of this paper is the implementation of a PLP system supporting this semantics: smProbLog. smProbLog is a novel PLP framework based on the probabilistic logic programming language ProbLog. smProbLog supports many inference and learning tasks typical of PLP, which, together with our first contribution, provide novel reasoning tools for probabilistic argumentation. We evaluate our approach with experiments analyzing the computational cost of the proposed algorithms and their application to a dataset of argumentation problems.