Hypersequents and Cut Elimination for Intuitionistic Fuzzy Logic

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the rst-order Godel 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 armatively.