Residuated bilattices

R Jansana, Umberto Rivieccio

Research output: Contribution to journalArticle

9 Citations (Scopus)


We introduce a new product bilattice construction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize the congruences of its members in terms of those of their lattice factors. Finally, we show how to employ our product construction to define first-order definable classes of bilattices corresponding to any first-order definable subclass of residuated lattices.
Original languageEnglish
Pages (from-to)493-504
Number of pages12
JournalSoft Computing
Issue number3
Publication statusPublished - 1 Mar 2012


  • Residuated lattice
  • Twist-structure
  • Product bilattice
  • Bilattice


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