6月演講

Colloquium, 成功大學敏求智慧運算學院 濱野正浩教授 Thursday, June 6, 16:10—17:00 數學系3174 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.