Takeuti and Titani have introduced and investigated a logic they
called intuitionistic fuzzy logic. This logic turns out to be 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 Godel 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.
