Anti-quantifiers and a theory of distributivity

Abstract

This dissertation deals with distributivity or quantifier scope interactions in natural languages evidenced by a pair of sentences in the following: (1) Each child bought a balloon. (2) The children bought a balloon each. Both sentences mean that there is a certain number of x 's such that for every x, if x is a child, x has a balloon. I assume that the distributive reading comes as a result of certain dependency between each child or the children and a balloon (each). The dissertation first shows that the expression a balloon each in (2) has some interesting properties and poses an interesting problem in a current theory of distributivity or quantifier scope interactions. It contends that there is a significant group of expressions in natural languages that share the same interesting properties and proposes to call them "anti-quantifiers." The "anti-quantificational" particles include po in Polish and Russian, je in German, -ssik in Korean, as well as the "shifted" each in English shown in (2). This dissertation then develops a theory of distributivity. The theory is initially motivated by morphological patterns including those of anti-quantifiers, but it intends to present a coherent view of distributivity in general. The starting assumption of the proposed theory is that distributivity has its own module in the grammar. It takes a relational view of distributivity and proposes that distributivity is a relation between two arguments accessible to each other. The syntactic/semantic mechanism of the proposed theory are powerful enough to explain a wide range of distributivity, but constrained well enough to block the unacceptable outputs. Seen as a relation between two arguments, distributivity demonstrates many interesting properties that were neglected or were not clear in other theoretical treatments. This dissertation includes discussion on a locality condition on anti-quantifiers. The condition resembles the locality condition on bound anaphors, but it is pointed out that there is a significant difference between the two. It also includes discussion on two logical properties of distributivity. This dissertation includes some more arguments for the proposed theory, which are based on the per construction, and "dependent plurals."

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