Two Dualities for Weakly Pseudo-complemented quasi-Kleene Algebras
| Autor: | Thiago Nascimento, Ramon Jansana, Umberto Rivieccio |
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| Rok vydání: | 2020 |
| Předmět: |
Physics::General Physics
Pure mathematics Substructural logic Duality (optimization) 0102 computer and information sciences 02 engineering and technology 01 natural sciences Fragment (logic) 010201 computation theory & mathematics Bounded function 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Variety (universal algebra) Algebraic number Commutative property Axiom Mathematics |
| Zdroj: | Information Processing and Management of Uncertainty in Knowledge-Based Systems ISBN: 9783030501525 IPMU (3) |
| DOI: | 10.1007/978-3-030-50153-2_47 |
| Popis: | Quasi-Nelson algebras are a non-involutive generalisation of Nelson algebras that can be characterised in several ways, e.g. as (i) the variety of bounded commutative integral (not necessarily involutive) residuated lattices that satisfy the Nelson identity; (ii) the class of (0, 1)-congruence orderable commutative integral residuated lattices; (iii) the algebraic counterpart of quasi-Nelson logic, i.e. the (algebraisable) extension of the substructural logic \(\mathcal {FL}_{ew}\) by the Nelson axiom. In the present paper we focus on the subreducts of quasi-Nelson algebras obtained by eliding the implication while keeping the two term-definable negations. These form a variety that (following A. Sendlewski, who studied the corresponding fragment of Nelson algebras) we dub weakly pseudo-complemented quasi-Kleene algebras. We develop a Priestley-style duality for these algebras (in two different guises) which is essentially an application of the general approach proposed in the paper A duality for two-sorted lattices by A. Jung and U. Rivieccio. |
| Databáze: | OpenAIRE |
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