In figure 13 we give a QLF as it is produced by the OVIS-grammar. It is a typed feature-structure, whose main components are predicative forms ( p_form), representing relations (which may also be higher order, such as not and and), and terms. Generalised quantifiers are represented by term expressions ( t_expr). The example in (13) contains two generalised quantifiers, corresponding to the (existentially quantified) event-variables introduced by the two verbal predicates . Note that these quantifiers appear as arguments of the predicates, and thus are unscoped with respect to each other.
Our implementation of QLF in the OVIS grammar follows roughly the presentation in , although some of the apparatus supplied for contextual resolution in that work has been omitted. As the OVIS-grammar uses typed feature-structures, QLF's are represented as feature-structures below.
A QLF is either a qlf-term or a qlf-formula. A qlf-term is one of the following:
A QLF formula is one of the following:6
The definitions can best be illustrated with a simple example in which
we compare a QLF expression with its corresponding formula in
predicate logic. In figure 14 the sentence Everybody
speaks two languages is given both a translation in QLF and in predicate
logic. In the QLF-translation of the full sentence the scope
) of the two quantifiers is left unspecified. Resolving scope order amounts to instantiating
(for everybody there are two languages that s/he speaks) or to
(there are two languages that everybody speaks).