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Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic | | Matthias Baaz
; Richard Zach
; | | Date: |
18 May 2000 | | Journal: | Clote, Peter G., and Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Fischbachau, Germany, August 21-26, 2000. Proceedings, pp. 187-201. Springer, Berlin, 2000 | | Subject: | Logic MSC-class: 03B50 (Primary) 03B55, 03F05 (Secondary) | math.LO | | Abstract: | Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as 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 Goedel 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. | | Source: | arXiv, math.LO/0005183 | | Services: | Forum | Review | PDF | Favorites | |
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