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On some Simplifications of the Axiomatization of Monoidal Logic

  • Siegfried Gottwald
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 90)

Abstract

The class of t-norms has gained central importance in considerations on fuzzy sets as well as in fuzzy logic, mainly because they are natural candidates for non-idempotent conjunction and intersection operations.

For an inferential, and therefore syntactical treatment of such t-norm based conjunction connectives one needs an axiomatic basis, either for some particular t-norm, or preferably for whole classes of t-norms. Monoidal logic was a first attempt to find a logical calculus designed to handle the case of left continuous t-norms. Here its axiomatization shall be simplified and transformed in such a way that it becomes easy to compare monoidal logic syntactically with other, more recent systems for the treatment of t-norm based logics.

Keywords

Residuated Lattice Axiom System Fuzzy Subset Axiom Schema Truth Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Siegfried Gottwald
    • 1
  1. 1.Institut für Logik und WissenschaftstheorieUniversität LeipzigLeipzigGermany

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