This book synthesizes the author's work (1980s 2015) on the logical expressive
power of natural language. It extends the tools and concepts of model theory as
used in (higher order) predicate logic to the study of natural language
semantics. It focuses on boolean structure, generalized quantification
(separated from variable binding), covering some cases of anaphora. Different
categories predicates, adjective, quantifiers are modeled by non-isomorphic
boolean lattices. Of empirical linguistic interest is the expressibility of many
natural classes of quantifiers defined in terms of their logical (automorphism
invariant) properties. Some of these correlate with classes used syntactically
in generative grammar. In other cases we find general (possibly universal)
constraints on