Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

Details Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

2000-05-18

arxiv.org/abs/math/0005183v2

Clote, Peter G., and Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Fischbachau,

Mathematics

Logic

v.2: 15 pages. Final version. (v.1: 15 pages. To appear in Computer Science Logic 2000 Proceedings.)

Scientific paper

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Goedel 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 Goedel 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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