A linear exponential comonad in s-finite transition kernels and probabilistic coherent spaces

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摘要

This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonad arising properly in the measure-theory (ii) continuous orthogonality between measures and measurable functions. A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels. The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic coherent spaces. The orthogonality is formulated by a Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated. As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.

原文English
文章編號105109
期刊Information and Computation
295
DOIs
出版狀態Published - 2023 12月

All Science Journal Classification (ASJC) codes

  • 理論電腦科學
  • 資訊系統
  • 電腦科學應用
  • 計算機理論與數學

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