residuated lattices, Boolean algebras are special by virtue of having a complementation operation . This permits an alternative expression of the three inequalities
:

in the axiomatization of the two residuals in terms of disjointness, via the equivalence . Abbreviating to as the expression of their disjointness, and substituting for in the axioms, they become with a little Boolean manipulation
:

Now is reminiscent of De Morgan duality, suggesting that be thought of as

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