Joint work with Dirk Pattinson, Ludwig-Maximilians-Universität, Munich.
In contrast to previous talks about the relationship between coalgebras and modal logic, the emphasis of this presentation is on finitary modal logics. That is, syntactically I focus on basic modal logic and semantically on finite approximations of infinite behaviours.
I begin with …
read moreSince there will be enough time, I will use the opportunity to start the talk with a general introduction to natural transformations and examples of applications in computer science.
The semantics of a modal formula is an operation assigning to any model (Kripke frame) A, to any valuation of atomic …
read moreJoint work with Jiri Rosicky, Brno.
Lawvere introduced the idea to consider as equations expressions t=t' where t,t' are natural transformations U^n-->U, U being the forgetful functor U:Alg-->Set. This idea is dualised to coalgebras, and differences and analogies to the algebraic case are dicussed …
read moreBasic notions of coalgebras and modal logic are reviewed.
A categorical description of coalgebraic semantics of modal logics is developed.
This description turns out to dualise algebraic semantics of equational logic as given by Banaschewski and Herrlich in the paper "Subcategories defined by implications" (1976). This gives a precise meaning …
read moreJoint work with Rolf Hennicker (University of Munich) and Michel Bidoit (Ecole Normale Sup351rieure de Cachan).
The properties of a system being "observable" or "fully abstract" (all internal states can be distinguished by an external observer) and of being "reachable" (all internal states are relevant, i.e., can be reached …
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