---
title: "Probabilistic Inference Modulo Theories"
authors:
  - "Rodrigo de Salvo Braz"
  - "Ciaran O'Reilly"
  - "Vibhav Gogate"
  - "Rina Dechter"
doi: ""
url: "https://ijcai.org/proceedings/2016/506"
pdf: "https://ijcai.org/proceedings/2016/0506.pdf"
venue: "Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence"
year: 2016
pages: "3591-3598"
track: ""
keywords:
---

# Probabilistic Inference Modulo Theories

Rodrigo de Salvo Braz, Ciaran O'Reilly, Vibhav Gogate, Rina Dechter

*Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence*, pages 3591-3598.

## Abstract

We present SGDPLL(T), an algorithm that solves (among many other problems) probabilistic inference modulo theories, that is, inference problems over probabilistic models defined via a logic theory provided as a parameter (currently, propositional, equalities on discrete sorts, and inequalities, more specifically difference arithmetic, on bounded integers). While many solutions to probabilistic inference over logic representations have been proposed, SGDPLL(T) is simultaneously (1) lifted, (2) exact and (3) modulo theories, that is, parameterized by a background logic theory. This offers a foundation for extending it to rich logic languages such as data structures and relational data. By lifted, we mean algorithms with constant complexity in the domain size (the number of values that variables can take). We also detail a solver for summations with difference arithmetic and show experimental results from a scenario in which SGDPLL(T) is much faster than a state-of-the-art probabilistic solver.