Knowledge, belief and time

In the conclusion of [7] Halpern and Moses expressed their interest in a logical system in which one could talk about knowledge and belief (and belief about knowledge, knowledge about belief and so on). We investigate such systems. In the first part of the paper knowledge and belief, without time, are considered. Common knowledge and common belief are defined and compared. A logical system and a family of models are proposed, a completeness result is proved and a decision procedure described. In the second part of the paper, time is considered. Different notions of beliefs are distinguished, obeying different properties of persistence. One interpretation of belief which obeys a very strong persistence axiom is put forward and used in the analysis of the "wise men" puzzle.