ncku-talk2024-06-06

Colloquium

DATE 2024-06-06　16:10-17:00

PLACE 數學系館 1F3174教室

SPEAKER Masahiro Hamano (濱野正浩) 教授（成功大學敏求智慧運算學院）

TITLE Categorical Semantics of Logic and Computation Stochastically

ABSTRACT The first part of the talk briefly discusses how category theory offers a mathematical framework for understanding logic and computation. Conceptually, this is founded by Curry-Howard isomorphism, while a monoidal category is presented technically as an illustration to provide both a static interpretation of computation and a dynamic understanding of its execution.
The second part delves into my recent research on stochastic extension for this semantics framework. The convolution of the transition kernels is shown to emerge through Giry monad (a fuzzy version of power-set monad) and the class of s-finiteness (rather than sigma-finiteness) is seen as a categorically consistent class for preserving the functorial monoidal product of Fubini-Tonelli.
On top of the mesuareg-theoretic exponential spaces for counting processes, a general categorical construction is outlined how to exponentialise the transition kernels. This construction, involving a categorical limit, enables a continuous modeling of logical exponential modality.

Colloquium

DATE	2024-06-06　16:10-17:00

PLACE	數學系館 1F3174教室

SPEAKER	Masahiro Hamano (濱野正浩) 教授（成功大學敏求智慧運算學院）

TITLE	Categorical Semantics of Logic and Computation Stochastically

ABSTRACT	The first part of the talk briefly discusses how category theory offers a mathematical framework for understanding logic and computation. Conceptually, this is founded by Curry-Howard isomorphism, while a monoidal category is presented technically as an illustration to provide both a static interpretation of computation and a dynamic understanding of its execution. The second part delves into my recent research on stochastic extension for this semantics framework. The convolution of the transition kernels is shown to emerge through Giry monad (a fuzzy version of power-set monad) and the class of s-finiteness (rather than sigma-finiteness) is seen as a categorically consistent class for preserving the functorial monoidal product of Fubini-Tonelli. On top of the mesuareg-theoretic exponential spaces for counting processes, a general categorical construction is outlined how to exponentialise the transition kernels. This construction, involving a categorical limit, enables a continuous modeling of logical exponential modality.