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)
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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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Richard Zach
University of Calgary


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