On the Relationships Among Probabilistic Extensions of Answer Set Semantics

abstract: Answer Set Programming (ASP) is one of the main formalisms in Knowledge Representation (KR) that is being widely applied in a large number of applications. While ASP is effective on Boolean decision problems, it has difficulty in expressing quantitative uncertainty and probability in a natural way. Logic Programs under the answer set semantics and Markov Logic Network (LPMLN) is a recent extension of answer set programs to overcome the limitation of the deterministic nature of ASP by adopting the log-linear weight scheme of Markov Logic. This thesis investigates the relationships between LPMLN and two other extensions of ASP: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. The studied relationships show how different extensions of answer set programs are related to each other, and how they are related to formalisms in Statistical Relational Learning, such as Problog and MLN, which have shown to be closely related to LPMLN. The studied relationships compare the properties of the involved languages and provide ways to compute one language using an implementation of another language. This thesis first presents a translation of LPMLN into programs with weak constraints. The translation allows for computing the most probable stable models (i.e., MAP estimates) or probability distribution in LPMLN programs using standard ASP solvers so that the well-developed techniques in ASP can be utilized. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl’s Causal Models, that are shown to be translatable into LPMLN. This thesis also presents a translation of P-log into LPMLN. The translation tells how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers or MLN solvers.Dissertation/ThesisMasters Thesis Computer Science 201

On the Strong Equivalences for LPMLN Programs

LPMLN is a powerful knowledge representation and reasoning tool that combines the non-monotonic reasoning ability of Answer Set Programming (ASP) and the probabilistic reasoning ability of Markov Logic Networks (MLN). In this paper, we study the strong equivalence for LPMLN programs, which is an important tool for program rewriting and theoretical investigations in the field of logic programming. First of all, we present the notion of p-strong equivalence for LPMLN and present a model-theoretical characterization for the notion. And we investigate the relationships among the p-strong equivalence and other existing notions of strong equivalences for LPMLN. Then, we investigate several properties of the p-strong equivalence from the following four aspects. Firstly, we investigate two relaxed notions of the p-strong equivalence according to practical scenarios of program rewriting, and present corresponding characterizations for the notions. Secondly, we analyze the computational complexities of deciding strong equivalences for LPMLN programs. Thirdly, we investigate the relationships among the strong equivalences of LPMLN and two extensions of ASP: ASP with weak constraints and ordered disjunctions. Finally, we investigate LPMLN program simplification via the p-strong equivalence and present some syntactic conditions that decide the p-strong equivalence between a single LPMLN rule and the empty program. The contributions of the paper are as follows. Firstly, all of the results presented in this paper provide a better understanding of LPMLN programming, which helps us further explore the properties of LPMLN. Secondly, the relationships among the strong equivalences open a way to study the strong equivalences for some logic formalisms by translating into LPMLN. Thirdly, the program simplification can be used to enhance the implementations of the LPMLN solvers ..

Splitting an LPMLN Program

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