Factored Models for Probabilistic Modal Logic

Abstract

Modal logic represents knowledge that agents have about other agents ’ knowledge. Probabilistic modal logic further captures probabilistic beliefs about probabilistic beliefs. Models in those logics are useful for understanding and decision making in conversations, bargaining situations, and competitions. Unfortunately, probabilistic modal structures are impractical for large real-world applications because they represent their state space explicitly. In this paper we scale up probabilistic modal structures by giving them a factored representation. This representation applies conditional independence for factoring the probabilistic aspect of the structure (as in Bayesian Networks (BN)). We also present two exact and one approximate algorithm for reasoning about the truth value of probabilistic modal logic queries over a model encoded in a factored form. The first exact algorithm applies inference in BNs to answer a limited class of queries. Our second exact method applies a variable elimination scheme and is applicable without restrictions. Our approximate algorithm uses sampling and can be used for applications with very large models. Given a query, it computes an answer and its confidence level efficiently. 1