A quantifier for matroid duality

A quantifier is introduced on the elements of a matroid which, given an element e, says “for all elements (except possibly e) of some circuit containing e,…”. The matroid dual of this quantifier is shown to be identical with its logical dual, and this provides an elegant reformulation of Minty's self-dual axiomatization of matroids.This approach also provides a practical, and in a sense optimal, means of taking a statement in terms of circuits and constructing its dual, still in terms of circuits.