arXiv math/00051832000-05math.LO

Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

Matthias Baaz, Richard Zach

备注：: v.2: 15 pages. Final version. (v.1: 15 pages. To appear in Computer Science Logic 2000 Proceedings.)
发表信息：: Clote, Peter G., and Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Fischbachau, Germany, August 21-26, 2000. Proceedings, pp. 187-201. Springer, Berlin, 2000

英文摘要：

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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