# Concrete Coalgebraic Modal Logic: Modalities beyond Set

(Birmingham)

Coalgebraic logic for Set coalgebras given by predicate lifting has been applied to different areas in computer science, e.g. modal logic, automata theory, and program verification. However, there are very few studies beyond Sets. Exceptions are, for example, the category of posets for positive modal logic (by Kapulkin, Balan, Kurz, Velebil) and the category of measurable spaces for stochastic coalgebraic logic . Although there are more general approaches applicable to abstract categories, it is not clear how to describe modalities explicitly.

In this talk, I will introduce a notion generalising predicate liftings, which can be defined for every concrete category with a dual adjunction. We prove the adequacy, discuss the one-step expressivity concretely and identify the logic induced by all predicate liftings for categories of descent type.

**Thursday 24th May 2012, 14:00**

Far-134 (Video Conferencing Room)

Department of Computer Science