Cost-based query answering in action probabilistic logic programs

Action-probabilistic logic programs (ap-programs), a class of probabilistic logic programs, have been applied 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 have addressed the problem of deciding if there is a way to change the environment (subject to some constraints) so that the probability that entity E takes some action (or combination of actions) is maximized. In this work we tackle a related problem, in which we are interested in reasoning about the expected reactions of the entity being modeled when the environment is changed. Therefore, rather than merely deciding if there is a way to obtain the desired outcome, we wish to find the best way to do so, given costs of possible outcomes. This is called the Cost-based Query Answering Problem (CBQA). We first formally define and study an exact (intractable) approach to CBQA, and then go on to propose a more efficient algorithm for a specific subclass of ap-programs that builds on past work in a basic version of this problem.