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Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic
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.Comment: v.2: 15 pages. Final version. (v.1: 15 pages. To appear in Computer
Science Logic 2000 Proceedings.
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