Abstract
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.
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Acknowledgments
The research of the first author was partially supported by grant 2009SGR-1433 of the AGAUR of the Generalitat de Catalunya and by grant MTM2008–01139 of the Spanish Ministerio de Ciencia e Innovación, which includes EU FEDER funds.
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Jansana, R., Rivieccio, U. Residuated bilattices. Soft Comput 16, 493–504 (2012). https://doi.org/10.1007/s00500-011-0752-x
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DOI: https://doi.org/10.1007/s00500-011-0752-x