Kristoffer Kalavainen: A Coalgebraic approach to Modal Logic

Abstract: In this work, we focus on two results regarding invariant properties of Kripke structures and, the more general neighborhood structures. Kripke structures being the semantic tool for normal modal logic while neighborhood structures are the standard semantics for non-normal modal logic. The first result states that the existence of a certain relation between states implies logical equivalence. The second result -- known as the Hennessey-Milner Theorem -- specifies whenever the converse hold, that is when logical equivalence guarantees such a relation between two states. These results are presented, for the Kripke structures, in the traditional context while the results for neighborhood structures are presented in a coalgebraic context. We also show how modal logics can be obtained from so-called predicate liftings