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

[Roger Frye]

Looks like results of previous classes were supposed to be written up at
the n-category-cafe.


On Mon, Jan 4, 2021 at 10:57 AM Frank Wimberly <wimberly3 at gmail.com> wrote:

> 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
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