Complex Markov Logic Networks: Expressivity and Liftability
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:729-738, 2020.
We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and show that, unlike standard MLNs with real-valued weights, complex MLNs are"fully expressive". We then observe that discrete Fourier transform can be computed using weighted first order model counting (WFOMC) with complex weights and use this observation to design an algorithm for computing "relational marginal polytopes" which needs substantially less calls to a WFOMC oracle than an existing recent algorithm.