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Tim Hosgood (Mar 17 2021 at 19:18):Wednesday, 20:00 UTC
Tim Hosgood (Mar 17 2021 at 19:19):Abstract:
This two-part talk is a tutorial on the use of coalgebraic techniques to model and reason about state-based dynamical systems.
The first part will introduce the basic concept of an F-coalgebra for an endofunctor F, and the derived notions of morphism, bisimulation, behavioural equivalence and coinduction. We will see examples where F is a polynomial functor as well as examples where F is a composition of a polynomial functor and a monad in order to model systems with, e.g., nondeterministic or probabilistic transitions.
The second part will be an introduction to coalgebraic modal logic, which is a framework for developing adequate and expressive modal logics for specifying properties of system behaviours. We will see that many results can be proved and studied parametric in the functor F. Time permitting, I will discuss some recent work on generalisations of the notion of coalgebraic bisimulation.
Uli Fahrenberg (Mar 17 2021 at 21:06):So let me repost my question here: What is the precise relation between the \nabla and characteristic formulae? It seems that the characteristic formula of a state/world s should be \nabla \Phi, where \Phi is the set of all v(t) for t reachable from s?