Distributivity and quantification in discourse representation theory

Abstract

In this study, I designed a system of NP semantics in the frame work of DRT by adopting the following assumptions: (i) Every indefinite NP is translated into a variable. (ii) The determiner quantifier of an NP does not provide quantificational force, but is an indicator of how many atomic individuals the individual sum (i-sum) denoted by the NP has (the cardinality of the i-sum). For example, the NP every student denotes an i-sum consisting of all the individuals which are students. (iii) Quantificational forces are provided by existential closure or by the rule of distributivity. Then, sentence (1) is translated into (b) via (a). $\vert$student$\vert$ represents the number of atomic individuals of the set denoted by student.$$\eqalign{(1)\ &\rm Every\ student\ came.\cr(\rm a)\ &\rm\exists X\ \lbrack students\ (X)\ \&\ \vert X\vert{=}\vert student\vert\ \&\ \sp{\rm D}came\ (X)\rbrack\cr(\rm b)\ &\rm\exists X\ \lbrack students\ (X)\ \&\ \vert X\vert{=}\vert student\vert\ \&\ \forall x\ \lbrack x\ is\ an\ atomic\ i{-}part\ of\ X\cr&\sk{155}\rm\to\ came\ (x)\rbrack\rbrack}$$

To give evidence to my approach, I have dealt with the data concerning with anaphoric resolution, the mode of predication, the proportion problems (or asymmetric quantification), and the proper distribution which requires a non-atomic individual as an argument of a distributive predicate.