Commodious axiomatization of quantifiers in multiple-valued logic

Abstract

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