A Gödel Calculus for Linear Temporal Logic

Abstract

We consider Gödel temporal logic ($\mathsf{GTL}$), 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 {\sc pspace}-complete. In this paper we provide a deductive calculus for $\mathsf{GTL}$, and show this calculus to be sound and complete for the above-mentioned semantics.

arXiv admin note: text overlap with arXiv:2205.00574

References in corpus (1)

• A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables

Cited by in corpus (3)

• Time and Gödel: Fuzzy temporal reasoning in PSPACE
• Applications of Intuitionistic Temporal Logic to Temporal Answer Set Programming
• Tableaux for epistemic Gödel logic