A Schütte-Tait Style Cut-Elimination Proof for First-Order Gödel Logic
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Density Elimination and Rational Completeness for First-Order Logics
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Proof Theory for First Order Łukasiewicz Logic
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Herbrand Theorems and Skolemization for Prenex Fuzzy Logics
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Cut Elimination for First Order Gödel Logic by Hyperclause Resolution
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
A multiple-conclusion calculus for first-order Gödel logic
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Fuzzy Equilibrium Logic: Declarative Problem Solving in Continuous Domains
ACM Transactions on Computational Logic (TOCL)
Analytic Calculi for Monoidal T-norm Based Logic
Fundamenta Informaticae
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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.