Archive for Mathematical Logic

, Volume 41, Issue 7, pp 643–667 | Cite as

Fuzzy logic, continuity and effectiveness

  • Loredana Biacino
  • Giangiacomo Gerla


 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).


Continuous Function Fuzzy Logic Closure Operator Deduction System Hilbert Style 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Loredana Biacino
    • 1
  • Giangiacomo Gerla
    • 2
  1. 1.Dipartimento di Matematica e Applicazioni, Via Cintia, 80134 Napoli, ItalyIT
  2. 2.Dipartimento di Matematica e Informatica, Via S. Allende, 84081 Baronissi (SA), ItalyIT

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