Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

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dc.creatorBaaz, Matthias
dc.creatorZach, Richard
dc.date2000-05-18
dc.date2000-08-27
dc.date.accessioned2026-07-07T04:35:22Z
dc.date.available2026-07-07T04:35:22Z
dc.descriptionTakeuti 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.
dc.descriptionv.2: 15 pages. Final version. (v.1: 15 pages. To appear in Computer Science Logic 2000 Proceedings.)
dc.identifierhttps://arxiv.org/abs/math/0005183
dc.identifierhttp://arxiv.org/abs/math/0005183
dc.identifierClote, 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
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59228
dc.subjectLogic
dc.subject03B50 (Primary) 03B55, 03F05 (Secondary)
dc.titleHypersequents and the Proof Theory of Intuitionistic Fuzzy Logic
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