Abstract.
Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.
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Received: 15 March 2000 / Revised version: 20 September 2000 Published online: 12 December 2001
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Bělohlávek, R. Fuzzy equational logic. Arch. Math. Logic 41, 83–90 (2002). https://doi.org/10.1007/s001530200006
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DOI: https://doi.org/10.1007/s001530200006