Reasoning about Belief and Knowledge with Self-Reference and Time

In two previous papers (Asher & Kamp 1986,1987), Hans Kamp and I developed a framework for investigating the logic of attitudes whose objects involved an unlimited capacity for self-reference. The framework was the daughter of two well-known parents-- possible worlds semantics and the revisionist, semi-inductive theory of truth developed by Herzberger (1982) and Gupta (1982). Nevertheless, the offspring from our point of view was not an entirely happy one. We had argued that orthodox possible worlds semantics was an unacceptable solution to the problem of the semantics of the attitudes. Yet the connection between our use of possible worlds semantics and the sort of representational theories of the attitudes that we favor remained unclear. This paper attempts to provide a better connection between the framework developed in the previous papers and representational theories of attitudes by developing a notion of reasoning about knowledge and belief that a careful examination of the model theory suggests. This notion of reasoning has a temporal or dynamic aspect that I exploit by introducing temporal as well as attitudinal predicates.