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Constructive dualities have been recently proposed for some lattice basedalgebras and a related project has been outlined by Holliday and Bezhanishvili,aiming at obtaining "choice-free spatial dualities for other classes ofalgebras [$\ldots$], giving rise to choice-free completeness proofs fornon-classical logics''. We present in this article a way to complete theHolliday-Bezhanishvili project (uniformly, for any normal lattice expansion) byrecasting recent relational representation and duality results in a choice-freemanner. These results have some affinity with the Moshier and Jipsen dualityfor bounded lattices with quasi-operators, except for aiming at representingoperators by relations, extending the J\'{o}nsson-Tarski approach for BAOs, andDunn's follow up approach for distributive gaggles, to contexts wheredistribution may not be assumed. To illustrate, we apply the framework tolattices (and their logics) with some form or other of a (quasi)complementationoperator, obtaining canonical extensions in relational frames and choice-freedualities for lattices with a minimal, or a Galois quasi-complement, orinvolutive lattices, including De Morgan algebras, as well as Ortholattices andBoolean algebras, as special cases.

Choice-free Dualities for Lattice Expansions: Application to Logics with a Negation Operator