Zeta Functions and the (Linear) Logic of Markov Processes

Thomas Seiller (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LIPN - Laboratoire d'Informatique de Paris-Nord

In a series of papers, the author introduced models of linear logic known as ”Interaction Graphs”. These models generalise Girard’s various geometry of interaction constructions, providing a unifying framework for those. In this work, we exhibit how these models can be understood mathematically through a cocycle property satisfied by zeta functions of dynamical systems. Focussing on probabilistic models, we then explain how the notion of graphings used in the models captures a natural class of Markov processes. We further extend previous constructions to provide a model of second-order linear logic as a type system over the set of all (discrete-time) sub-Markov processes.

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]; Systèmes dynamiques [math.DS]; Probabilités [math.PR]

Thomas Seiller. Zeta Functions and the (Linear) Logic of Markov Processes. 2021. ⟨hal-02458330v3⟩