Quantification as reference: Evidence from Q-verbs

In Lisa Matthewson (ed.), Quantification: A Cross-Linguistic Perspective. Emerald. pp. 7-66 (2008)
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Abstract
Formal semantics has so far focused on three categories of quantifiers, to wit, Q-determiners (e.g. 'every'), Q-adverbs (e.g. 'always'), and Q-auxiliaries (e.g. 'would'). All three can be analyzed in terms of tripartite logical forms (LF). This paper presents evidence from verbs with distributive affixes (Q-verbs), in Kalaallisut, Polish, and Bininj Gun-wok, which cannot be analyzed in terms of tripartite LFs. It is argued that a Q-verb involves discourse reference to a distributive verbal dependency, i.e. an episode-valued function that sends different semantic objects in a contextually salient plural domain to different episodes.
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