Hypersequents and the proof theory of intuitionistic fuzzy logic

Baaz, Matthias, and Richard Zach. 2000. “Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.” In Computer Science Logic. 14th International Workshop, CSL 2000, edited by Peter G. Clote and Helmut Schwichtenberg, 187–201. LNCS 1862. Berlin: Springer. DOI:10.1007/3-540-44622-2_12

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.

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