Introduction

This chapter contains a brief survey of the formal machinery employed in GQT, a theory which is generally considered as a further development of the treatment of quantification in Montague's PTQ. There is, however, a technically important difference between Montague's treatment of NPs and the GQT-treatment: the former uses the indirect method of translating expressions of natural language into type-logical expressions, which are then semantically interpreted as set-theoretical objects, whereas the latter uses the direct method. On the former, an English sentence like All children came in is translated into a logical formula, say f(All children came in), which is then interpreted. The essence of the direct approach is that all, children and came_in are directly taken as denoting semantic objects. This means that the syntactic structure of All children came in is mapped into constituents which are directly related to semantic objects of the domain. These objects belong to distinguished types (individuals, sets, functions, relations, etc.).

As its machinery will play an important role throughout the present study, I shall first introduce a type-logical language EL which itself is an extension of the standard predicate first-order logic including prepositional logic. EL will be used as a formal logical language representing (the denotations of) expressions of natural language. It will play a role throughout the following chapters as a sort of checkpoint with respect to which elaborations of the system can be measured.