About Coalgebraic Logic
Category theory is a subject of mathematics mainly used to study mathematical structures uniformly. It provides a better understanding then the traditional set-theoretical mathematics on what constructions and transformations between mathematical structures are.
Modal logic is a logic reasoning about dynamical structures. It can be applied to different fields in computer science, e.g. program semantics and protocol verification. However different variations of modal logic, e.g. probability modal logic, linear temporal logic and intuitionistic logic, have been invented for different purposes, but they are all strongly related.
Therefore, a uniform way to study these variants is needed. Coalgebraic logic was invented around 2000 in a paper under the same title. It shows how infinitary modal logic can be derived by the powerset functor and a straightforward generalization parameterized by a certain class of set functors. This nova development has been further studied in different settings.
About My Work
I am interested at the generalization of coalgebraic logic over topological spaces. The representation theorem of Boolean algebras provides a characterization in terms of topology, i.e. the Stone duality. Moreover, in classical modal logic there is an extension of Stone duality which can be formalized as a dual equivalence between Boolean algebras with operators (modal algebras) and topological transition systems on Stone spaces (descriptive Kripke spaces). This equivalence is indeed a duality between Vietoris coalgebras and M-algebras where M is a certain functor on Boolean algebras shown by C. Kupke in 2006.
School of Computer Science
Birmingham B15 2TT