A note on the first‐order logic of complete BL‐chains |
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| Authors: | Petr Hájek Franco Montagna |
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| Institution: | Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy |
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| Abstract: | In 10] it is claimed that the set of predicate tautologies of all complete BL‐chains and the set of all standard tautologies (i. e., the set of predicate formulas valid in all standard BL‐algebras) coincide. As noticed in 11], this claim is wrong. In this paper we show that a complete BL‐chain B satisfies all standard BL‐tautologies iff for any transfinite sequence (ai: i ∈ I) of elements of B , the condition ∧i ∈ I (a2i ) = (∧i ∈ I ai)2 holds in B . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | First‐order fuzzy logics standard semantics complete BL‐chains |
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