A STUDY OF NATURAL LANGUAGE QUANTIFICATION AND ANAPHORA
             THROUGH FAMILIES OF SETS AND BINARY RELATIONS

                         Master of Science 1995
                              Robert Lizee
                     Department of Computer Science
                         University of Toronto

                                Abstract

In this thesis, we study the use of families of sets and binary relations to 
represent natural language quantification and anaphora.  We focus on 
quantification in a dependency-free context (no variables) using the idea of 
Barwise and Cooper (1981) of expressing quantifiers as families of sets. 
A language where sentences are expressed as subset relations between 
generalized quantifiers is shown equivalent to the variable-free Montagovian 
syntax of McAllester and Givan (1992), relating their notion of obvious 
inference to the transitive closure.  To account for anaphora, we propose to 
use an extended algebra of binary relations (Suppes, 1976; Bottner, 1992), 
in practice, restricting the number of variables to one. We contribute to the 
formalism with a family of composition operators, allowing to account for 
sentences with determiners other than `every', `some', or `no'.  Moreover, we 
show how to handle some cases of long-distance anaphora, some cases involving 
the word `other', and some donkey-sentence anaphora.