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## Bisimulation for weakly expressive coalgebraic modal logics

### November 28, 2016 @ 2:00 pm - 4:00 pm

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Speaker: Helle Hvid Hansen (TU Delft)

Abstract:

Bisimulation relations are a well known semantic tool for investigating the expressiveness and other properties of modal languages. When a class of T-coalgebras serve as the semantics of a modal language, the coalgebraic theory provides us with generic semantic equivalence notions, namely coalgebraic bisimilarity and behavioural equivalence (both parametric in T), and the perspective is usually that of finding a modal language which is able to distinguish semantically equivalent states. Such languages are often simply called "expressive". For certain applications, modal languages which are not expressive may nonetheless be of interest. The modal language of contingency logic (see e.g. Fan, Wang & Van Ditmarsch) is an example of such weakly expressive language. The question is, what is a suitable notion of bisimilarity for such languages?

In this informal talk, I will give a general coalgebraic proposal to answer this question by introducing a notion called lambda-bisimulation which is tailored to fit the expressiveness of a modal language regardless of its expressiveness. This notion is parametric in the coalgebraic semantics of the modal language (and thus implicitly also in the functor T). I will show some basic results and discuss its instantiation to contingency logic over Kripke models and neighbourhood models.