First Order Model Counting

First-order model counting (FOMC) aims to efficiently compute the number of models (satisfying assignments) for a given first-order logic sentence. Current research heavily focuses on identifying tractable fragments of first-order logic, particularly extensions of the two-variable fragment with counting quantifiers (C²), and incorporating constraints representing real-world properties like acyclicity or connectivity. These efforts leverage techniques like dynamic programming and "counting by splitting" to develop polynomial-time algorithms for weighted FOMC, improving the efficiency of probabilistic inference in statistical relational learning and providing new tools for analyzing combinatorial structures.