Interactive Epistemology

Formal Interactive Epistemology deals with the logic of knowledge and belief when there is more than one agent or "player." One is interested not only in each person's knowledge about substantive matters, but also in his knowledge about the others' knowledge. This paper examines two parallel approaches to the subject. The first is the semantic approach, in which knowledge is represented by a space of states of the world, together with partitions of the state space for each player i; the atom of i's partition containing a given state of the world represents i's knowledge at that state - the set of those other states that i cannot distinguish from that state. The second is the syntactic approach, in which knowledge is embodied in sentences constructed according to certain syntactic rules. This paper examines the relation between the two approaches, and shows that they are in a sense equivalent.