Sufficient triangular norms in many-valued logics with standard negation

Dan Butnariu, Erich Peter Klement, Radko Mesiar, Mirko Navara

Research output: Contribution to journalArticlepeer-review


In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem (in the case of strict t-norms), together with convenient sufficient conditions. We list several families of strict t-norms having this property and provide also counterexamples (the Hamacher product is one of them). Finally, we discuss the consequences of these results for the characterization of tribes based on strict t-norms.

Original languageEnglish
Pages (from-to)829-849
Number of pages21
JournalArchive for Mathematical Logic
Issue number7
StatePublished - Oct 2005


  • Admissible function
  • Involutive negation
  • Many-valued logic
  • Sufficient t-norm
  • t-norm-based tribe

ASJC Scopus subject areas

  • Philosophy
  • Logic


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