5 April 2005
OUTLINE: I shall first show how this combinatorial setting can be generalized to an order theoretic structure that has a non-boolean resource-sensitive nature and considers communication actions as fundamental operations of an algebra rather than concrete constructions on a Kripke model. The algebra consists of an \em epistemic system \em $(M,Q,\{f_A\}_{A \in {\cal A}})$, which is a quantale-module pair $(M,Q)$ endowed with a family of appearance maps" for each agent $f_A = (f_A^M:M \to M, f_A^Q:Q \to Q)$. The right Galois adjoint to the appearance map gives rise to the box" modality of epistemic logic (expressing knowledge or belief of some agent).