Fuzzy logic, continuity and effectiveness |
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| Authors: | Loredana Biacino Giangiacomo Gerla |
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| Institution: | (1) Dipartimento di Matematica e Applicazioni, Via Cintia, 80134 Napoli, Italy, IT;(2) Dipartimento di Matematica e Informatica, Via S. Allende, 84081 Baronissi (SA), Italy, IT |
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| Abstract: | It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory
of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose
connectives are interpreted in 0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective
fuzzy deduction system, in general).
Received: 15 February 2001 / Revised version: 31 May 2001 / Published online: 12 July 2002 |
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