Quasi logical form

Next: Construction of QLF's Up: Semantics Previous: The semantic representation language

Quasi logical form

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.

**Figure 13:** QLF for 'Ik wil om ongeveer vier uur vertrekken' (I want to leave at about four o'clock)
$\begin{figure} \begin{avm} \begin{displaymath}\avmspan{\em p\_form} \\ pred & ... ...playmath} \> \end{displaymath}\par\> \end{displaymath}\end{avm}\par\end{figure}$

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 QUANT⁵(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)).

**Figure 14:** The relation between an expression in QLF and a fomula of predicate logic
$\begin{figure} \par\begin{tabular}{lll} \par a. & \multicolumn{2}{l}{\em Everybo... ...\forall x.(person(x) \rightarrow speak(e_1,x,y)))$\end{tabular}\par\end{figure}$

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 (
$\begin{avm}\@5\end{avm}$
) of the two quantifiers is left unspecified. Resolving scope order amounts to instantiating
$\begin{avm}\@5\end{avm}$
to
$\begin{avm}[\@1,\@3]\end{avm}$
(for everybody there are two languages that s/he speaks) or to
$\begin{avm}[\@3,\@1]\end{avm}$
(there are two languages that everybody speaks).

Next: Construction of QLF's Up: Semantics Previous: The semantic representation language

2000-07-10