Approximate Weighted FirstOrder Model Counting: Exploiting Fast Approximate Model Counters and Symmetry
Abstract
We study the symmetric weighted firstorder model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted firstorder model count in the presence of an unweighted firstorder model counting oracle. The algorithm has applications to inference in a variety of firstorder probabilistic representations, such as Markov logic networks and probabilistic logic programs. Crucially for many applications, we make no assumptions on the form of the input sentence. Instead, our algorithm makes use of the symmetry inherent in the problem by imposing cardinality constraints on the number of possible true groundings of a sentence's literals. Realising the firstorder model counting oracle in practice using the approximate hashingbased model counter ApproxMC3, we show how our algorithm outperforms existing approximate and exact techniques for inference in firstorder probabilistic models. We additionally provide PAC guarantees on the generated bounds.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.05263
 Bibcode:
 2020arXiv200105263V
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Logic in Computer Science
 EPrint:
 Presented at StarAI 2020