A Natural Deduction System for Intuitionistic Fuzzy Logic

@inproceedings{Baaz2008AND,
  title={A Natural Deduction System for Intuitionistic Fuzzy Logic},
  author={Matthias Baaz and Agata Ciabattoni and Christian G. Ferm{\"u}ller},
  year={2008}
}
Intuitionistic fuzzy logic IF was introduced by Takeuti and Titani. This logic coincides with the first-order Gödel logic based on the real unit interval [0, 1] as set of truth-values. We present a natural deduction system NIF for IF . NIF is defined by suitably translating a first-order extension of Avron’s hypersequent calculus for Gödel logic. Soundness, completeness and normal form theorems for NIF are provided. 

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