Fernández-Duque, David - The intuitionistic temporal logic of dynamical systems

lmcs:3280 - Logical Methods in Computer Science, July 20, 2018, Volume 14, Issue 3 - https://doi.org/10.23638/LMCS-14(3:3)2018
The intuitionistic temporal logic of dynamical systems

Authors: Fernández-Duque, David

A dynamical system is a pair $(X,f)$, where $X$ is a topological space and $f\colon X\to X$ is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems, giving rise to a natural intuitionistic temporal logic. We introduce a variant of Kremer's logic, which we denote ${\sf ITL^c}$, and show that it is decidable. We also show that minimality and Poincaré recurrence are both expressible in the language of ${\sf ITL^c}$, thus providing a decidable logic expressive enough to reason about non-trivial asymptotic behavior in dynamical systems.

Volume: Volume 14, Issue 3
Published on: July 20, 2018
Submitted on: April 24, 2017
Keywords: Mathematics - Logic


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