Quantification as Reference : Evidence from Q - Verbs 7 2 QUANTIFICATION AS REFERENCE : EVIDENCE FROM Q - VERBS

Formal semantics has so far mostly focused on three categories of quantifiers (Q)—to wit, Qdeterminers (e.g. every), Q-adverbs (e.g. always), and Q-auxiliaries (e.g. would). All three form constructions that can be analyzed in terms of tripartite logical forms (LFs), consisting of a quantifier, the restriction, and the nuclear scope. This view has been implemented, with varying details, by most formal theories of natural language quantification, including landmark studies by Montague (1973), Lewis (1973, 1975), Barwise and Cooper (1981), Kratzer (1981), Heim (1982), Kamp and Reyle (1993), Partee (1995), and Matthewson (2001). Heim (1982) develops a unified dynamic semantics for Q-determiners (1a), Q-adverbs (1b), Q-auxiliaries (1c), as well as what she takes to be a covert universal quantifier () in donkey conditionals (1d), by assigning all of these constructions parallel tripartite LFs (1′a–d).