A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief

In this paper we deene two logics, KL n and BL n , and present tableau-based decision procedures for both. KL n is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BL n is somewhat similar; it is a temporal logic that contains connectives for representing the beliefs of agents. In addition to a complete formal deenition of the two logics and their decision procedures, the paper includes a brief review of their applications in AI and mainstream computer science, correctness proofs for the decision procedures, a number of worked examples illustrating the decision procedures, and some pointers to further work.