# Stone Duality for Modal Logic

(Leicester)

Since Goldblatt (1976) it is well-known how to account for Kripke's semantic of modal logic on the basis of Stone's duality of Boolean algebras and certain topological spaces. There is a general, simple principle underlying this phenomenon which is implicit in Abramsky's Domain Theory in Logical Form (1991): A duality between two categories A and X and two functors L:A->A and T:X->X, gives rise to a duality between the algebras for the functor L and the coalgebras for the functor T.

The aim of the talk is to show that this principle of constructing new dualities from old ones (i) accounts for a number of well-known dualities and (ii) helps to understand what appropriate specification languages for coalgebras are. The second item is motivated by understanding the theory of coalgebras as a theory of systems (Rutten 2000).

**Tuesday 19th October 2004, 14:00**

Robert Recorde Room

Department of Computer Science