TY - JOUR

T1 - A linear exponential comonad in s-finite transition kernels and probabilistic coherent spaces

AU - Hamano, Masahiro

N1 - Publisher Copyright:
© 2023 The Author(s)

PY - 2023/12

Y1 - 2023/12

N2 - 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.

AB - 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.

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U2 - 10.1016/j.ic.2023.105109

DO - 10.1016/j.ic.2023.105109

M3 - Article

AN - SCOPUS:85177558679

SN - 0890-5401

VL - 295

JO - Information and Computation

JF - Information and Computation

M1 - 105109

ER -