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ANTI-QUANTIFIERS AND A THEORY OF DISTRIBUTIVITY
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." ^
CHOE, JAE-WOONG, "ANTI-QUANTIFIERS AND A THEORY OF DISTRIBUTIVITY" (1987). Doctoral Dissertations Available from Proquest. AAI8727027.