On the independence of axioms in BL and MTL (Q1759710)
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scientific article; zbMATH DE number 6109488
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the independence of axioms in BL and MTL |
scientific article; zbMATH DE number 6109488 |
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On the independence of axioms in BL and MTL (English)
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21 November 2012
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The author proves that the multiplicative conjunction of two formulae implies the redundancy of the first one of them in the Hilbert-style calculi of the MTL logic of \textit{F. Esteva} and \textit{L. Godo} [Fuzzy Sets Syst. 124, No. 3, 271--288 (2001; Zbl 0994.03017)] and of the BL logic due to [\textit{P. Hájek}, Metamathematics of fuzzy logic. Dordrecht: Kluwer Academic Publishers (1998; Zbl 0937.03030)]. The independence of the remaining axioms in both logics is proved with suitable examples.
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basic fuzzy logic BL
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monoidal t-norm-based logic MTL
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Hilbert-style calculus
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0.805627703666687
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0.7579448819160461
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0.7561984062194824
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0.7518016695976257
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