BibTeX
@MISC{Platzer_dynamiclogics,
author = {André Platzer},
title = { Dynamic Logics of Dynamical Systems},
year = {}
}
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Abstract
We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important for modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. Distributed hybrid systems combine distributed systems with hybrid systems, i.e., they are multi-agent hybrid systems that interact through remote communication or physical interaction. Stochastic hybrid systems combine stochastic dynamics with hybrid systems. We survey dynamic logics for specifying and verifying properties for each of those classes of dynamical systems. A dynamic logic is a first-order modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior. Due to their full basis of first-order modal logic operators, dynamic logics can express a rich variety of system properties, including safety, controllability, reactivity, liveness, and quantified parametrized properties, even about
Keyphrases
dynamical system dynamic logic hybrid system stochastic dynamic cyber-physical system first-order modal logic operator parametrized modal operator many application hybrid dynamical system state evolves physical interaction differential equation proof principle survey dynamic logic continuous dynamic difference equation remote communication mathematical model discrete step full basis discrete dynamical system discrete state transition relation transition behavior possible property first-order modal logic rich variety system property stochastic hybrid system continuous dynamical system multi-agent hybrid system
