R221a  
Probabilistic Inference Modulo Theories
Rodrigo de Salvo Bras, Claran O'Reilly, Vibhav Gogate, and Rina Dechter

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, equalities and inequalities on discrete sorts). 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 that our proposed algorithm can leverage firstorder representations to solve some inference problems in constant or polynomial time in the domain size (the number of values that variables can take), as opposed to exponential time offered by propositional algorithms.
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