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.
The registered version of this article, first published in Soft Computing, is available online at the publisher's website: https://doi.org/10.1007/s00500-011-0752-x
Notas adicionales
TheLa versión registrada de este artículo, publicado por primera vez en Soft Computing, está disponible en línea en el sitio web del editor: https://doi.org/10.1007/s00500-011-0752-x
