Symmetry Breaking for Relational Weighted Model Finding

Symmetry breaking is a technique for speeding up propositional satisfiability testing by adding constraints to the formula that restrict the search space while preserving satisfiability. In this work, we extend symmetry breaking to the problem of model finding in weighted and unweighted relational theories, a class of problems that includes MPE inference in Markov Logic and similar statistical-relational languages. After describing the extension of symmetry breaking to weighted ground theories, we explore methods for finding and breaking symmetries directly in quantified theories. We introduce term symmetries, which are induced by an evidence set and extend to symmetries over a relational theory. We provide a detailed analysis of the important special case of term equivalent symmetries, showing that such symmetries can be found in low-degree polynomial time and can be completely broken by constraints that are linear in the size of the theory. Finally, we discuss connections between relational symmetry breaking and work on lifted inference in statistical-relational reasoning.

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