Abstract
Twist-structure representation theorems are established for De Morgan and Kleene lattices. While the former result relies essentially on the quasivariety of De Morgan lattices being finitely generated, the representation for Kleene lattices does not and can be extended to more general algebras. In particular, one can drop the double negation identity (involutivity). The resulting class of algebras, named semi-Kleene lattices by analogy with Sankappanavar’s semi-De Morgan lattices, is shown to be representable through a twist-structure construction inspired by the Cornish–Fowler duality for Kleene lattices. Quasi-Kleene lattices, a subvariety of semi-Kleene, are also defined and investigated, showing that they are precisely the implication-free subreducts of the recently introduced class of quasi-Nelson lattices.
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