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Mathematics > Logic

arXiv:math/0005183 (math)
[Submitted on 18 May 2000 (v1), last revised 27 Aug 2000 (this version, v2)]

Title:Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

Authors:Matthias Baaz, Richard Zach
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Abstract: 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.
Comments: v.2: 15 pages. Final version. (v.1: 15 pages. To appear in Computer Science Logic 2000 Proceedings.)
Subjects: Logic (math.LO)
MSC classes: 03B50 (Primary) 03B55, 03F05 (Secondary)
Cite as: arXiv:math/0005183 [math.LO]
  (or arXiv:math/0005183v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.math/0005183
Journal reference: 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

Submission history

From: Richard Zach [view email]
[v1] Thu, 18 May 2000 09:28:39 UTC (24 KB)
[v2] Sun, 27 Aug 2000 00:23:43 UTC (24 KB)
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