Varieties of interlaced bilattices |
| |
Authors: | F��lix Bou Ramon Jansana Umberto Rivieccio |
| |
Institution: | 1. Department of Probability, Logic, and Statistics, Faculty of Mathematics, University of Barcelona, Gran Via de les Corts Catalanes 585, Barcelona, E-08071, Spain 2. Department of Logic, History and Philosophy of Science, Faculty of Philosophy, University of Barcelona, c/ Montalegre, 6, Barcelona, 08001, Spain 3. Department of Philosophy, University of Genoa, Via Balbi 4, Genova, 16126, Italy
|
| |
Abstract: | The paper contains some algebraic results on several varieties of algebras having an (interlaced) bilattice reduct. Some of these algebras have already been studied in the literature (for instance bilattices with conflation, introduced by M. Fitting), while others arose from the algebraic study of O. Arieli and A. Avron??s bilattice logics developed in the third author??s PhD dissertation. We extend the representation theorem for bounded interlaced bilattices (proved, among others, by A. Avron) to unbounded bilattices and prove analogous representation theorems for the other classes of bilattices considered. We use these results to establish categorical equivalences between these structures and well-known varieties of lattices. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|