2021-11-10: Sean Watters (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Sean Watters (MSP)

A Tour of Temporal Logic

Abstract

Modal logic can be applied to a diverse range of use-cases by fixing different notions of model and modality. Our motivation today will be the formal verification technique of model checking, and with this in mind, I will focus on temporal logic. In temporal logics, the models represent systems which change over time, and the modalities allow us to reason about exactly how they proceed in time.

I will first introduce basic relational modal logic, and show its limitations in this domain. We will then go on a tour of LTL, CTL, CTL*, and the modal 𝜇-calculus. Key destinations on the tour will include the respective expressive power and model-checking complexity of each, particularly in comparison to the 𝜇-calculus. I will end the tour with a closer look at the model-checking problem of the 𝜇-calculus, and its relationship to parity games.

2021-11-10 15:00:00 UTC
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