Quantifiers, Scope, and Pseudo‐Scope

Abstract

Generalized Quantifier Theory (GQT) is discussed as an analysis of quantifying expression (QE) in natural language. According to that theory, a quantifier denotes a relation between sets, and quantifying DPs are QEs that are defined as sets of sets. Such QEs require quantifier raising (QR) and an additional mechanism that provides for the binding of bound variable pronouns. Various restrictions for scope taking in sentences with two or more quantifiers seem to apply; an alternative to scope taking via QR is scope independence, which can be modeled by choice functions or Skolem functions and is informally described in terms of game theory. Various data seem to require scope extension in the sense that semantic scope is wider than syntactic scope via c‐command. Such extensions are Discourse Representation Theory (DRT) and dynamic logic. Further extensions of GQT deal with pluralities.