A duality for two-sorted lattices

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Colleges, School and Institutes


A series of representation theorems (some of which discovered very recently) present an alternative view of many classes of algebras related to non-classical logics (e.g. bilattices, semi-De Morgan, Nelson and quasi-Nelson algebras) as two-sorted algebras in the sense of many-sorted universal algebra. In all the above-mentioned examples, we are in fact dealing with a pair of lattices related by two meet-preserving maps. We use this insight to develop a Priestley-style duality for such structures, mainly building on the duality for meet-semilattices of G. Bezhanishvili and R. Jansana. Our approach simplifies all the existing dualities for these algebras and is applicable more generally; in particular, we show how it specialises to the class of quasi-Nelson algebras, which has not yet been studied from a duality point of view.


Original languageEnglish
Pages (from-to)851–868
JournalSoft Computing
Issue number2
Publication statusPublished - 5 Jan 2021


  • Twist-structure, Nelson algebra, Semi-De Morgan algebra, Priestley duality, Bilattice