A Gödel Calculus for Linear Temporal Logic

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.