Probabilistic Inference Modulo Theories
This provides a foundational method for efficient probabilistic inference in domains with rich logic languages, such as data structures and relational data, though it appears incremental as it builds on existing lifted and modulo theories approaches.
The authors tackled the problem of probabilistic inference over models defined by logic theories by introducing SGDPLL(T), an algorithm that is lifted, exact, and modulo theories, and demonstrated it is much faster than a state-of-the-art solver in experiments.
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.