Construction of QLF's

During grammatical analysis QLFs are constructed compositionally (see also [5]). In head complement structures the head daughter is the syntactic as well as the semantic head of the structure. This means that the semantic content of the complement constituents is combined with the semantic content of the head. The value of the SEM feature of the head is passed up to the mother (see figure 1).

In head modifier structures the modifier is the semantic head. The semantics of the syntactic head of the structure is plugged into the MOD feature of the modifier. Below we will show how the semantics of the modifier is combined with the semantics of the constituent it modifies. The value of the SEM feature of the modifier is passed up to the mother.

**Figure 15:** Examples showing the semantics of determiners, nouns, and adjectives.
$\begin{figure} \par\begin{tabular}{ll} a. & \begin{avm} \mbox{\tt lex(alle,}\be... ...nd{displaymath} \> \end{displaymath}\mbox{).} \end{avm}\end{tabular}\end{figure}$

We now discuss the semantics of various linguistic categories. Determiners subcategorise for a noun (see Figure 15(a.)). The semantics of the noun is unified with restriction of the determiner. Nouns introduce a v_form (fig. 15(b.)) Note that it is also assumed that quantifiers may scope at this point. Adjectives are modifiers (fig.15(c.)). They operate on structures whose semantic content is of type v_form. The lambda variables of the two formulas are unified and the semantic content of the structure is the conjunction of the logical formula of the adjective and the logical formula of the structure it modifies.

The semantics of verbs corresponds with a v_form (see fig. 16a). The value of VAR is reentrant with the INDEX of the event introduced by the verb. The semantics of the subject is unified with the second element of the argument list of the verb. Intransitive verbs have two semantic arguments, corresponding to the event and subject, respectively. Transitive verbs have three arguments, where the third argument is unified with the semantics of the single element on SC.

**Figure 16:** Verbal semantics.
$\begin{figure} \begin{tabular}{ll} a. & \begin{avm} \mbox{\tt lex(vertrekken,}\... ...aymath} \end{displaymath} \> \end{displaymath}\end{avm}\end{tabular}\end{figure}$

Modal verb are subject-control verbs. This means that the subject of the VP-complement is controlled by the subject of the modal verb. Semantically, this means that the INDEX of the subject must be unified with the semantics of the subject of the VP-complement. Note also that we assume that assume that the SC-list of a modal verb may contain complements introduced by the VP-complement (as explained in section 2.4.3). These are not relevant for the semantics of the modal verb.

The semantics of adverbial phrases resembles that of adjectives. In figure (17) the semantics of prepositions heading a PP which acts as a verbal modifier is given. PP-modifiers introduce a conjunction, with the verbal semantics as first argument, and the prepositional semantics as second. The INDEX of the VP is the first argument of the predicate introduced by the preposition, the semantics of the NP-object of the preposition corresponds to the second argument.

**Figure 17:** Adverbial semantics for prepositions.
$\begin{figure} \begin{avm} \mbox{\tt lex(op,} \begin{displaymath}\avmspan{\it p}... ...4 \end{displaymath} \end{displaymath} \> \end{displaymath}\end{avm}\end{figure}$

Ik wil zondag vertrekken
I want to leave on Sunday

Ik wil drie januari naar Amsterdam
I want to go to Amsterdam on the third of January

Ik wil er uiterlijk drie uur zijn
I want to arrive at the latest at three o'clock

As NPs normally do not have a modifier semantics, there is a unary rule that transforms temporal NPs into modifiers (figure 18). The structure that is modified is specified in the MOD feature. The semantic content of the modifier is constructed as if it was a PP with P/SMALL>_FORM om (at). The semantic content of the (temporal) NP daughter is plugged into the second position of the argument list of the preposition.