L**: A First-order Polarity Logic with Plural Domains

Abstract

An alternative formal language (L**) is constructed that better mirrors the structure of natural language (for example, by treating numerical expressions as predicates and thereby divorcing cardinality and quantification). It is shown how directional entailingness can be understood in terms of polarity, and how the properties of generalized quantifier theory can be cashed out within the formal structures of the new formal language.