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Fuzzy logic, continuity and effectiveness

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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).

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Via Cintia, 80134 Napoli, Italy, , , , , , IT

    Loredana Biacino

  2. Dipartimento di Matematica e Informatica, Via S. Allende, 84081 Baronissi (SA), Italy, , , , , , IT

    Giangiacomo Gerla

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  1. Loredana Biacino
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  2. Giangiacomo Gerla
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Received: 15 February 2001 / Revised version: 31 May 2001 / Published online: 12 July 2002

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Biacino, L., Gerla, G. Fuzzy logic, continuity and effectiveness. Arch. Math. Logic 41, 643–667 (2002). https://doi.org/10.1007/s001530100128

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  • DOI: https://doi.org/10.1007/s001530100128

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