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Hypersequents and the proof theory of intuitionistic fuzzy logic
In Clote Peter G. & Schwichtenberg Helmut (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Springer. pp. 187– 201 (2000)
Abstract
Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively.Author Profiles
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Citations of this work
First-order Gödel logics.Richard Zach, Matthias Baaz & Norbert Preining - 2007 - Annals of Pure and Applied Logic 147 (1):23-47.
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Completeness of a Hypersequent Calculus for Some First-order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In 36th International Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. Los Alamitos: IEEE Press.
Nested sequents for intermediate logics: the case of Gödel-Dummett logics.Tim S. Lyon - 2023 - Journal of Applied Non-Classical Logics 33 (2):121-164.
From Semantic Games to Provability: The Case of Gödel Logic.Alexandra Pavlova, Robert Freiman & Timo Lang - 2021 - Studia Logica 110 (2):429-456.
References found in this work
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Intuitionistic fuzzy logic and intuitionistic fuzzy set theory.Gaisi Takeuti & Satoko Titani - 1984 - Journal of Symbolic Logic 49 (3):851-866.
Logic with truth values in a linearly ordered Heyting algebra.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):395-408.
Completeness theorem for Dummett's LC quantified and some of its extensions.Giovanna Corsi - 1992 - Studia Logica 51 (2):317 - 335.
A Cut‐Free Calculus For Dummett's LC Quantified.Giovanna Corsi - 1989 - Mathematical Logic Quarterly 35 (4):289-301.
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