The technique called splitting sets has been proven useful in simplifying the investigation of Answer Set Programming (ASP). In this paper, we investigate the splitting set theorem for LPMLN that is a new extension of ASP created by combining the ideas of ASP and Markov Logic Networks (MLN). Firstly, we extend the notion of splitting sets to LPMLN programs and present the splitting set theorem for LPMLN. Then, the use of the theorem for simplifying several LPMLN inference tasks is illustrated. After that, we give two parallel approaches for solving LPMLN programs via using the theorem. The preliminary experimental results show that these approaches are alternative ways to promote an LPMLN solver.

LPMLNextends 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 LPMLNrules, 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, LPMLNhas been employed in several real world applications. However, an LPMLNprogram 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 LPMLNsolver: 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.

This paper develops a logic programming language, GI-log, that extends answer set programming language with a new graded modality Kω where ω is an interval satisfying ω ⊆ [0, 1]. The modality is used to precede a literal in rules bodies, and thus allows for the representation of graded introspectio ns in the presence of multiple belief sets: KωF intuitively means: it is known that the proportion of the belief sets where F is true is in the interval ω. We define the semantics of GI-log, study the relation to the languages of strong introspections, give an algorithm for computing solutions of GI-log programs, and investigate the use of GI-log for formalizing contextual reasoning, conformant planning with threshold, and modeling a graph problem.