LPMLNModels: A Parallel Solver for LPMLN

Abstract

LP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MLN</sup> extends the language of Answer Set Programming (ASP) by assigning a weight degree to each rule so that its stable models do not have to satisfy all LP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MLN</sup> rules, which is rooted in the manner of Markov Logic Networks (MLN) to handle the uncertainties and inconsistencies in knowledge representation and reasoning. Due to its expressibility, LP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MLN</sup> has been employed in several real world applications. However, an LP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MLN</sup> program is much harder to solve than its unweighted counterpart (an ASP program), and only some preliminary solvers have been implemented so far, which is preventing further studies in both theoretical and practical sides. There are three main contributions in this paper. Firstly, we present an LP <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MLN</sup> solver: LPMLNModels, which is able to run concurrently. Secondly, we present parallel methods in LPMLNModels. For splitting set method, we present an algorithm to generate a proper splitting set, which is an essential part of the method. For augmented subset method, we present a heuristic method to improve its performance. Finally, we present hybrid methods in LPMLNModels to better utilize the parallel methods. The experimental results show that our algorithms and improvements in this paper works and hybrid methods have better performance in general.