---
title: "Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey"
authors:
  - "Paolo Morettin"
  - "Pedro Zuidberg Dos Martires"
  - "Samuel Kolb"
  - "Andrea Passerini"
doi: "10.24963/ijcai.2021/617"
url: "https://ijcai.org/proceedings/2021/617"
pdf: "https://ijcai.org/proceedings/2021/0617.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "4533-4542"
track: "Survey Track"
keywords:
  - "Knowledge representation and reasoning: General"
  - "Uncertainty in AI: General"
  - "Constraints and SAT: General"
---

# Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey

Paolo Morettin, Pedro Zuidberg Dos Martires, Samuel Kolb, Andrea Passerini

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 4533-4542. DOI: [10.24963/ijcai.2021/617](https://doi.org/10.24963/ijcai.2021/617)

## Abstract

Real  world  decision  making  problems  often  involve  both  discrete  and  continuous  variables  and require  a  combination  of  probabilistic  and  deterministic  knowledge. Stimulated  by  recent  advances  in  automated  reasoning  technology,   hybrid  (discrete+continuous)  probabilistic  reasoning with  constraints  has  emerged  as  a  lively  and  fast growing  research  field.   In  this  paper  we  provide a  survey  of  existing  techniques  for  hybrid  probabilistic  inference  with  logic  and  algebraic  constraints.   We leverage weighted model integration as  a  unifying  formalism  and  discuss  the  different paradigms that have been used as well as the expressivity-efficiency trade-offs that have been investigated. We conclude the survey with a comparative  overview  of  existing  implementations  and  a critical discussion of open challenges and promising research directions.