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/Thesis / Masters Thesis Computer Science 2017

abstract: The goal of fact checking is to determine if a given claim holds. A promising ap- proach for this task is to exploit reference information in the form of knowledge graphs (KGs), a structured and formal representation of knowledge with semantic descriptions of entities and relations. KGs are successfully used in multiple appli- cations, but the information stored in a KG is inevitably incomplete. In order to address the incompleteness problem, this thesis proposes a new method built on top of recent results in logical rule discovery in KGs called RuDik and a probabilistic extension of answer set programs called LPMLN. This thesis presents the integration of RuDik which discovers logical rules over a given KG and LPMLN to do probabilistic inference to validate a fact. While automatically discovered rules over a KG are for human selection and revision, they can be turned into LPMLN programs with a minor modification. Leveraging the probabilistic inference in LPMLN, it is possible to (i) derive new information which is not explicitly stored in a KG with a probability associated with it, and (ii) provide supporting facts and rules for interpretable explanations for such decisions. Also, this thesis presents experiments and results to show that this approach can label claims with high precision. The evaluation of the system also sheds light on the role played by the quality of the given rules and the quality of the KG. / Dissertation/Thesis / Masters Thesis Computer Science 2018