On the independence of axioms in BL and MTL
Copyright policy )On the independence of axioms in BL and MTL
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.
- Charles University Czech Republic
- National Library of Technology Czech Republic
- Czech Academy of Sciences Czech Republic
- Academy of Sciences Library Czech Republic
basic fuzzy logic BL, Hilbert-style calculi, basic fuzzy logic (BL), independence of axioms, Fuzzy logic; logic of vagueness, Hilbert-style calculus, monoidal t-norm based logic (MTL), monoidal t-norm-based logic MTL, automated theorem proving; Hilbert-style proof systems; independece of axioms; logic BL; logic MTL, non-classical logics
basic fuzzy logic BL, Hilbert-style calculi, basic fuzzy logic (BL), independence of axioms, Fuzzy logic; logic of vagueness, Hilbert-style calculus, monoidal t-norm based logic (MTL), monoidal t-norm-based logic MTL, automated theorem proving; Hilbert-style proof systems; independece of axioms; logic BL; logic MTL, non-classical logics
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