Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic

  • Matthias Baaz
  • Richard Zach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1862)


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.

2000 Mathematics Subject Classification

03B50 03B55 03F05 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Matthias Baaz
    • 1
  • Richard Zach
    • 2
  1. 1.Institut für Algebra und Computermathematik E118.2Technische Universität WienViennaAustria
  2. 2.Institut für Computersprachen E185.2Technische Universität WienViennaAustria

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