Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting
Abstract
In this paper we study lifted inference for the Weighted FirstOrder Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in firstorder logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a nontrivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #Phard in the size of the input domain; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. Third, we present several properties of the algorithm. Finally, we discuss limitations of lifted inference for symmetric probabilistic databases (where the weights of ground literals depend only on the relation name, and not on the constants of the domain), and prove the impossibility of a dichotomy result for the complexity of probabilistic inference for the entire language FOL.
 Publication:

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.3250
 Bibcode:
 2014arXiv1405.3250G
 Keywords:

 Computer Science  Artificial Intelligence;
 Computer Science  Databases;
 Computer Science  Logic in Computer Science