Quantifying Over Eventualities in Continuation Semantics

The paper explores the possibilities of representing the semantics of eventualities in continuation semantics framework. It focuses on providing an analysis for quantification over eventualities and for anaphora to eventualities. We give specific lexical entries for the adverbial quantifiers always and never and for a silent adverbial quantifier we consider responsible for the meaning of expressions with no overt adverbial quantifiers. We point out that quantificational adverbs usually have an implicit restriction (i.e. the contextually relevant eventualities), as opposed to the nominal quantifiers where the restrictor is the noun phrase. This eventuality restriction is a set of eventualities that cannot be completely specified or enumerated. Nevertheless, the human mind has no problem to operate with this kind of vagueness. Also, we argue that the Scope Domain Principle, which says that the eventuality quantifier always takes lowest possible scope with respect to other quantifiers, is too strong.