Residuated bilattices |
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Authors: | Ramon Jansana Umberto Rivieccio |
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Affiliation: | (1) Departament of Logic, History and Philosophy of Science, Faculty of Philosophy, University of Barcelona, c/ Montalegre, 6, 08001 Barcelona, Spain;(2) School of Computer Science, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK |
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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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Keywords: | |
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