Applied Category Theory 2021 — Adjoint School – Azimuth

[Roger Frye-4]

https://johncarlosbaez.wordpress.com/2021/01/02/applied-category-theory-2021-adjoint-school/ 

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[jon zingale]

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-2]

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 <[hidden email]> 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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[Roger Frye-4]

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 <[hidden email]> 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 <[hidden email]> 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
Santa Fe, NM 87505
505 670-9918

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

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[Frank Wimberly-2]

Thanks, Roger, that works.  I also found a book by Leinster there called "Basic Category Theory" which looks ideal for me.  A PDF is available for free but I will probably order the hardcopy version.

Frank

On Mon, Jan 4, 2021 at 11:06 AM Roger Frye <[hidden email]> wrote:

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 <[hidden email]> 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 <[hidden email]> 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
Santa Fe, NM 87505
505 670-9918

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

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