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
[19]. 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 [17], 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 term index,
^{4} - a constant term,
- an term-expression of type
*t_expr*and containing the features INDEX, RESTR and QUANT^{5}(see (13)), where INDEX is a variable, RESTR is an expression of predicate logic (possibly with lambda-abstraction) and QUANT is a generalised quantifier.

A QLF formula is one of the following:^{6}

- a predicate-argument formula of type
*p_form*, and with features PRED and ARGS (see (13)). Predicates may be higher order, arguments may be formulas or terms, - a formula of type
*v_form*with features VAR and FORM representing a formula with lambda-abstraction (see(14b)). This is an auxiliary level of representation, introduced to facilitate the interaction between grammar-rules and lexical entries, - a formula of type
*s_form*(see(14b)), with features SCOPE and FORM. The value of SCOPE is either a variable or a list of indices indicating the relative scope of term expressions (generalised quantifiers) (see (14c)).

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
order (

)
of the two quantifiers is left unspecified. Resolving scope order
amounts to instantiating

to

(for everybody there are two languages
that s/he speaks) or to

(there are two
languages that everybody speaks).