Non-involutive twist-structures
| Autor: | Paulo Maia, Umberto Rivieccio, Achim Jung |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Logic Journal of the IGPL. 28:973-999 |
| ISSN: | 1368-9894 1367-0751 |
| DOI: | 10.1093/jigpal/jzy070 |
| Popis: | A recent paper by Jakl, Jung and Pultr (2016, Electron. Notes Theor. Comput. Sci., 325, 201–219) succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices (the algebraic counterpart of Nelson’s paraconsistent logic) to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We provide product representation theorems for these algebras, as well as completeness, algebraizability (and some non-algebraizability) results for the corresponding logics. |
| Databáze: | OpenAIRE |
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