Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

We highlight our work on lifted inference for the asymmetric Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in first-order logic. This work is at the intersection of probabilistic databases and statistical relational learning. First, we discuss how adding negation can lower the query complexity, and describe the essential element (resolution) necessary to extend a previous algorithm for positive queries to handle queries with negation. Second, we describe our novel dichotomy result for a non-trivial fragment of first-order CNF sentences with negation.Finally, we discuss directions for future work.