[FRIAM] Applied Category Theory 2021 — Adjoint School – Azimuth

[Frank Wimberly]

Do I understand correctly that there are 4 or 5 projects and 4 members of
each project.  I think I'll leave this for younger people like you Jon.
Are the presentations and results available online?

Frank

On Mon, Jan 4, 2021 at 9:37 AM jon zingale <jonzingale at gmail.com> wrote:

> cool. This topic looks particularly good:
>
> Topic: Extensions of coalgebraic dynamic logic
> Mentors: Helle Hvid Hansen and Clemens Kupke
>
> Description: Coalgebra is a branch of category theory in which different
> types of state-based systems are studied in a uniform framework, parametric
> in an endofunctor F:C → C that specifies the system type. Many of the
> systems that arise in computer science, including
> deterministic/nondeterministic/weighted/probabilistic automata, labelled
> transition systems, Markov chains, Kripke models and neighbourhood
> structures, can be modeled as F-coalgebras. Once we recognise that a class
> of systems are coalgebras, we obtain general coalgebraic notions of
> morphism, bisimulation, coinduction and observable behaviour.
>
> Modal logics are well-known formalisms for specifying properties of
> state-based systems, and one of the central contributions of coalgebra has
> been to show that modal logics for coalgebras can be developed in the
> general parametric setting, and many results can be proved at the abstract
> level of coalgebras. This area is called coalgebraic modal logic.
>
> In this project, we will focus on coalgebraic dynamic logic, a coalgebraic
> framework that encompasses Propositional Dynamic Logic (PDL) and Parikh’s
> Game Logic. The aim is to extend coalgebraic dynamic logic to system types
> with probabilities. As a concrete starting point, we aim to give a
> coalgebraic account of stochastic game logic, and apply the coalgebraic
> framework to prove new expressiveness and completeness results.
>
> Participants in this project would ideally have some prior knowledge of
> modal logic and PDL, as well as some familiarity with monads.
>
>
>
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-- 
Frank Wimberly
140 Calle Ojo Feliz
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505 670-9918

Research:  https://www.researchgate.net/profile/Frank_Wimberly2
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