Algebraizability of the Logic of Quasi-N4-Lattices
| Autor: | Clodomir Silva Lima Neto, Thiago Nascimento da Silva, Umberto Rivieccio |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Electronic Proceedings in Theoretical Computer Science. 358:240-253 |
| ISSN: | 2075-2180 |
| DOI: | 10.4204/eptcs.358.18 |
| Popis: | The class of quasi-N4-lattices (QN4-lattices) was introduced as a common generalization of quasi-Nelson algebras and N4-lattices, in such a way that N4-lattices are precisely the QN4-lattices satisfying the double negation law (~~x = x) and quasi-Nelson algebras are the QN4-lattices satisfying the explosive law (x ^ ~x) -> y = ((x ^ ~x) -> y) -> ((x ^ ~x) -> y). In this paper we introduce, via a Hilbert-style presentation, a logic (L_QN4) whose algebraic semantics is a class of algebras that we show to be term-equivalent to QN4-lattices. The result is obtained by showing that the calculus introduced by us is algebraizable in the sense of Blok and Pigozzi, and its equivalent algebraic semantics is term-equivalent to the class of QN4-lattices. As a prospect for future investigation, we consider the question of how one could place L_QN4 within the family of relevance logics. In Proceedings NCL 2022, arXiv:2204.06359 |
| Databáze: | OpenAIRE |
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