# Declarative Probabilistic Logic Programming in Discrete-Continuous Domains

arXiv: https://arxiv.org/abs/2302.10674 · HTML: https://mlsanity.com/paper/2302.10674/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 76 references that are in the map.
- First posted on arXiv 21 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [A New Approach to Probabilistic Programming Inference](https://mlsanity.com/paper/1507.00996/) (2015)
- [Venture: a higher-order probabilistic programming platform with programmable inference](https://mlsanity.com/paper/1404.0099/) (2014)
- [SPPL: Probabilistic Programming with Fast Exact Symbolic Inference](https://mlsanity.com/paper/2010.03485/) (2020)
- [A Convenient Category for Higher-Order Probability Theory](https://mlsanity.com/paper/1701.02547/) (2017)
- [Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints](https://mlsanity.com/paper/1601.04943/) (2016)
- [Efficient Search-Based Weighted Model Integration](https://mlsanity.com/paper/1903.05334/) (2019)
- [Functional Tensors for Probabilistic Programming](https://mlsanity.com/paper/1910.10775/) (2019)
- [Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks](https://mlsanity.com/paper/1304.1504/) (2013)
- [Discrete-Continuous Mixtures in Probabilistic Programming: Generalized Semantics and Inference Algorithms](https://mlsanity.com/paper/1806.02027/) (2018)
- [Scaling Exact Inference for Discrete Probabilistic Programs](https://mlsanity.com/paper/2005.09089/) (2020)
- [Syntactic Requirements for Well-defined Hybrid Probabilistic Logic Programs](https://mlsanity.com/paper/2109.08283/) (2021)
- [Paradoxes of Probabilistic Programming](https://mlsanity.com/paper/2101.03391/) (2021)

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

- [Neural Probabilistic Logic Programming in Discrete-Continuous Domains](https://mlsanity.com/paper/2303.04660/) (2023)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Semirings for Probabilistic and Neuro-Symbolic Logic Programming](https://mlsanity.com/paper/2402.13782/) (2024)
- [Independence Is Not an Issue in Neurosymbolic AI](https://mlsanity.com/paper/2504.07851/) (2025)
- [MILP-SAT-GNN: Yet Another Neural SAT Solver](https://mlsanity.com/paper/2507.01825/) (2025)

## Abstract (arXiv)

Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming languages owes much of its success to a declarative semantics, the so-called distribution semantics. However, the distribution semantics is limited to discrete random variables only. While PLP has been extended in various ways for supporting hybrid, that is, mixed discrete and continuous random variables, we are still lacking a declarative semantics for hybrid PLP that not only generalizes the distribution semantics and the modeling language but also the standard inference algorithm that is based on knowledge compilation. We contribute the measure semantics together with the hybrid PLP language DC-ProbLog (where DC stands for distributional clauses) and its inference engine infinitesimal algebraic likelihood weighting (IALW). These have the original distribution semantics, standard PLP languages such as ProbLog, and standard inference engines for PLP based on knowledge compilation as special cases. Thus, we generalize the state of the art of PLP towards hybrid PLP in three different aspects: semantics, language and inference. Furthermore, IALW is the first inference algorithm for hybrid probabilistic programming based on knowledge compilation