Commodious Axiomatization of Quantifiers in Multiple-Valued Logic

We provide a concise axiomatization of a broad class of generalized quantiiers in many-valued logic, so-called distribution quantiiers. Although sound and complete axiomatizations for such quantiiers exist, their size renders them virtually useless for practical purposes. We show that for certain lattice-based quan-tiiers relatively small axiomatizations can be obtained in a schematic way. This is achieved by providing an explicit link between skolemized signed formulas and lters/ideals in Boolean set lattices.