Stochastic Reasoning with Action Probabilistic Logic Programs

Abstract

In the real world, there is a constant need to reason about the behavior of various entities. A soccer goalie could benefit from information available about past penalty kicks by the same player facing him now. National security experts could benefit from the ability to reason about behaviors of terror groups. By applying

behavioral models, an organization may get a better understanding about how best to target their efforts and achieve their goals.

In this thesis, we propose action probabilistic logic (or ap-) programs, a formalism designed for reasoning about the probability of events whose inter-dependencies are unknown. We investigate how to use ap-programs to reason in the kinds of scenarios described above. Our approach is based on probabilistic logic programming, a well known formalism for reasoning under uncertainty, which has been shown to be highly flexible since it

allows imprecise probabilities to be specified in the form of intervals that convey the inherent uncertainty in the knowledge. Furthermore, no independence assumptions are made, in contrast to many of the probabilistic reasoning formalisms that have been proposed. Up to now, all work in probabilistic logic programming has focused

on the problem of entailment, i.e., verifying if a given formula follows from the available knowledge. In this thesis, we argue that other problems also need to be solved for this kind of reasoning. The three main problems we address are: Computing most probable worlds: what is the most likely set of actions given the current state

of affairs?; answering abductive queries: how can we effect changes in the environment in order to evoke certain desired actions?; and Reasoning about promises: given the importance of promises and how they are fulfilled, how can we incorporate quantitative knowledge about promise fulfillment in ap-programs?

We address different variants of these problems, propose exact and heuristic algorithms to scalably solve them, present empirical evaluations of their performance, and discuss their application in real world scenarios.