Abductive inference in probabilistic logic programs

Action-probabilistic logic programs (ap-programs) are a class of probabilistic logic programs that have been extensively used during the last few years for modeling behaviors of entities. Rules in ap-programs have the form "If the environment in which entity E operates satisfies certain conditions, then the probability that E will take some action A is between L and U". Given an ap-program, we are interested in trying to change the environment, subject to some constraints, so that the probability that entity E takes some action (or combination of actions) is maximized. This is called the Basic Probabilistic Logic Abduction Problem (Basic PLAP). We first formally define and study the complexity of Basic PLAP and then provide an exact (exponential) algorithm to solve it, followed by more efficient algorithms for specific subclasses of the problem. We also develop appropriate heuristics to solve Basic PLAP efficiently.