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Computer Science > Logic in Computer Science

arXiv:2204.06735v1 (cs)
[Submitted on 14 Apr 2022]

Title:Algebraizability of the Logic of Quasi-N4-Lattices

Authors:Clodomir Silva Lima Neto (Federal University of Rio Grande do Norte), Thiago Nascimento da Silva (Federal University of Rio Grande do Norte), Umberto Rivieccio (Federal University of Rio Grande do Norte)
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Abstract: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.
Comments: In Proceedings NCL 2022, arXiv:2204.06359
Subjects: Logic in Computer Science (cs.LO)
Cite as: arXiv:2204.06735 [cs.LO]
  (or arXiv:2204.06735v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2204.06735
Journal reference: EPTCS 358, 2022, pp. 240-253
Related DOI: https://doi.org/10.4204/EPTCS.358.18

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 14 Apr 2022 03:28:09 UTC (18 KB)
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