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Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

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Computer Science Logic (CSL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1862))

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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 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.

Research supported by the Austrian Science Fund under grant P-12652 MAT

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Author information

Authors and Affiliations

  1. Institut für Algebra und Computermathematik E118.2, Technische Universität Wien, A-1040, Vienna, Austria

    Matthias Baaz

  2. Institut für Computersprachen E185.2, Technische Universität Wien, A-1040, Vienna, Austria

    Richard Zach

Authors
  1. Matthias Baaz
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  2. Richard Zach
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Department of Biology, Boston College, Fulton Hall 410B, Chestnut Hill, MA, 02467, USA

    Peter G. Clote

  2. Mathematisches Institut, Ludwig-Maximilian-Universität München, Theresienstr. 39, 80333, München, Germany

    Helmut Schwichtenberg

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© 2000 Springer-Verlag Berlin Heidelberg

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Baaz, M., Zach, R. (2000). Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic. In: Clote, P.G., Schwichtenberg, H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44622-2_12

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  • DOI: https://doi.org/10.1007/3-540-44622-2_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67895-3

  • Online ISBN: 978-3-540-44622-4

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