A Gödel Calculus for Linear Temporal Logic

05/10/2022

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by   Juan Pablo Aguilera, et al.

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We consider Gödel temporal logic (GTL), a variant of linear temporal logic based on Gödel–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 pspace-complete. In this paper we provide a deductive calculus for GTL, and show this calculus to be sound and complete for the above-mentioned semantics.