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 probabilistic-epistemic logic program language, PELP, by introducing probabilistic modal operators Kwand PL into LPMLNprograms, where w is a sub-interval of [0, 1]. Intuitively, a probabilistic epistemic literal Kwe denotes that e is known with a probability in w, and a probabilistic comparing literal PL(e1, e2) denotes it is known that the probability of e1is less than the one of e2. The semantics of the new language is based on the semantics of LPMLNand epistemic specifications. In this paper, we analyze the relationship between PELP and some other epistemic logic programming languages. We also propose an algorithm for solving PELP programs, and then investigate the application of PELP for modeling and solving the Monty Hall problem and a conformant planning problem with a threshold.

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.