A Natural Deduction System for Intuitionistic Fuzzy Logic
نویسندگان
چکیده
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.
منابع مشابه
Hypersequent 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 Gödel logic based on the truth value set [0, 1]. The logic is known to be axiomatizable, but no deduction system amenable to prooftheoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work o...
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