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Weakly Implicative (Fuzzy) Logics I: Basic Properties

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Abstract

This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass–the class of weakly implicative fuzzy logics. It contains the majority of logics studied in the literature under the name fuzzy logic. We present many general theorems for both classes, demonstrating their usefulness and importance.

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Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, Prague 8, 182 07, Czech Republic

    Petr Cintula

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  1. Petr Cintula
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Correspondence to Petr Cintula.

Additional information

The work was supported by grant A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AVOZ10300504.

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Cintula, P. Weakly Implicative (Fuzzy) Logics I: Basic Properties. Arch. Math. Logic 45, 673–704 (2006). https://doi.org/10.1007/s00153-006-0011-5

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  • DOI: https://doi.org/10.1007/s00153-006-0011-5

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