# Probabilistic Answer Set Programming with Discrete and Continuous Random Variables

arXiv: https://arxiv.org/abs/2409.20274 · HTML: https://mlsanity.com/paper/2409.20274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [An Introduction to Probabilistic Programming](https://mlsanity.com/paper/1809.10756/) (2018)
- [Edward: A library for probabilistic modeling, inference, and criticism](https://mlsanity.com/paper/1610.09787/) (2016)
- [Deep Probabilistic Programming](https://mlsanity.com/paper/1701.03757/) (2017)
- [Clingo goes Linear Constraints over Reals and Integers](https://mlsanity.com/paper/1707.04053/) (2017)
- [On the Semantics and Complexity of Probabilistic Logic Programs](https://mlsanity.com/paper/1701.09000/) (2017)
- [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)
- [PASOCS: A Parallel Approximate Solver for Probabilistic Logic Programs under the Credal Semantics](https://mlsanity.com/paper/2105.10908/) (2021)

## Abstract (arXiv)

Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming (HPASP). Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on the performance. Sampling allows handling larger instances, but sometimes requires an increasing amount of memory. Under consideration in Theory and Practice of Logic Programming (TPLP).