Systematic Construction of Temporal Logics for Dynamical Systems via Coalgebra

TL;DR

This paper presents a systematic method for constructing temporal logics for dynamical systems by leveraging coalgebraic modeling and Moss's coalgebraic logic, enabling a unified understanding of temporal properties.

Contribution

It introduces a coalgebra-based framework for systematically deriving temporal logics tailored to dynamical systems, bridging coalgebra theory and temporal logic construction.

Findings

Coalgebraic modeling of dynamical systems as a basis for logic construction

Application of Moss's coalgebraic logic to generate temporal logics

Characterization of temporal properties expressed by the constructed logics

Abstract

Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems exists, and each candidate has its own pragmatic justification. Here, a systematic approach to the construction of temporal logics for dynamical systems is proposed: Firstly, it is noted that dynamical systems can be seen as coalgebras in various ways. Secondly, a straightforward standard construction of modal logics out of coalgebras, namely Moss's coalgebraic logic, is applied. Lastly, the resulting systems are characterized with respect to the temporal properties they express.