Reasoning and Learning with Probabilistic Answer Set Programming

Knowledge Representation (KR) is one of the prominent approaches to Artificial Intelligence (AI) that is concerned with representing knowledge in a form that computer systems can utilize to solve complex problems. Answer Set Programming (ASP), based on the stable model semantics, is a widely-used KR framework that facilitates elegant and efficient representations for many problem domains that require complex reasoning.

However, while ASP is effective on deterministic problem domains, it is not suitable for applications involving quantitative uncertainty, for example, those that require probabilistic reasoning. Furthermore, it is hard to utilize information that can be statistically induced from data with ASP problem modeling.

This dissertation presents the language LP^MLN, which is a probabilistic extension of the stable model semantics with the concept of weighted rules, inspired by Markov Logic. An LP^MLN program defines a probability distribution over "soft" stable models, which may not satisfy all rules, but the more rules with the bigger weights they satisfy, the bigger their probabilities. LP^MLN takes advantage of both ASP and Markov Logic in a single framework, allowing representation of problems that require both logical and probabilistic reasoning in an intuitive and elaboration tolerant way.

This dissertation establishes formal relations between LP^MLN and several other formalisms, discusses inference and weight learning algorithms under LP^MLN, and presents systems implementing the algorithms. LP^MLN systems can be used to compute other languages translatable into LP^MLN.

The advantage of LP^MLN for probabilistic reasoning is illustrated by a probabilistic extension of the action language BC+, called pBC+, defined as a high-level notation of LP^MLN for describing transition systems. Various probabilistic reasoning about transition systems, especially probabilistic diagnosis, can be modeled in pBC+ and computed using LP^MLN systems. pBC+ is further extended with the notion of utility, through a decision-theoretic extension of LP^MLN, and related with Markov Decision Process (MDP) in terms of policy optimization problems. pBC+ can be used to represent (PO)MDP in a succinct and elaboration tolerant way, which enables planning with (PO)MDP algorithms in action domains whose description requires rich KR constructs, such as recursive definitions and indirect effects of actions.