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arXiv · 2205.05182

A G\"odel Calculus for Linear Temporal Logic

Juan Pablo Aguilera·Martín Diéguez·David Fernández-Duque·Brett McLean
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Abstract

We consider G\"odel temporal logic ($\sf GTL$), a variant of linear temporal logic based on G\"odel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natural semantics both as a fuzzy logic and as a superintuitionistic logic. Using semantical methods, the logic was shown to be {\sc pspace}-complete. In this paper we provide a deductive calculus for $\sf GTL$, and show this calculus to be sound and complete for the above-mentioned semantics.

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Juan Pablo Aguilera, Martín Diéguez, David Fernández-Duque, Brett McLean. 2022-05-10. A G\"odel Calculus for Linear Temporal Logic. https://doi.org/10.24963/kr.2022%2F1

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