KR2022Proceedings of the 19th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning

Haifa, Israel. July 31–August 5, 2022.

Edited by
  1. Gabriele Kern-Isberner
  2. Gerhard Lakemeyer
  3. Thomas Meyer

ISSN: 2334-1033
ISBN: 978-1-956792-01-0

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Published by

Copyright © 2022 International Joint Conferences on Artificial Intelligence Organization

A Gödel Calculus for Linear Temporal Logic

  1. Juan Pablo Aguilera(Ghent University, Vienna University of Technology)
  2. Martín Diéguez(University of Angers)
  3. David Fernández-Duque(Ghent University, ICS of the Czech Academy of Sciences)
  4. Brett McLean(Ghent University)
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BibTeX
https://doi.org/10.24963/kr.2022/1

Keywords

  1. Uncertainty, vagueness, many-valued and fuzzy logics
  2. Reasoning with time, space and perceptions

Abstract

We consider 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.