Generalized Quantifiers in Discourse Martin H. v.d. Berg

Introduction The last ten years have seen the development of theories of discourse semantics dealing with anaphoric referents introduced by indefinites and refered to by definites (including pronouns). Both Discourse Representation Theories as developed by Kamp [1981] and Heim [1984], and the more traditional, but essentially equivalent, approach developed by Groenendijk and Stokhof [1991] (Dynamic Predicate Logic) have been very successful. One big open question that still eludes these theories is the connection between them and the theory of Generalized Quantifiers. In the Dynamic Predicate Logic framework some success has been booked, in particular by Chierchia [1992] and van Eijck & de Vries [1991]. However, these approaches only deal with so called "closed" quantifiers, i.e. quantifiers that do not have dynamic properties but are only "tests". Interpreting Quantifiers in DPL In DPL formulas are interpreted as relations between assignments. Adding quantifi