5.4.2 Lexical Constraints

In this section, we define precisely the constraints governing assignment of lexical attributes. Consider the sequence of lexicon entries obtained for from the lexicon:

$\TUP{e_1,\ldots,e_n}=\Feature{lex}(\Feature{word}(w))$

let's write for the position of the one that is selected out of this sequence:

$I=\Feature{entryindex}(w)$

Abstractly, we can write to denote the selected entry and define it thus:

$E=\TUP{e_1,\ldots,e_n}[I]$

The lexical attributes assigned to are then obtained as explained in Section 5.3:

$\begin{array}{c} \Feature{cat}(w)\in\Feature{cats}(E)\\ \Feature{agr}(w)\in\Feature{agrs}(E)\\ \Feature{comps\_req}(E)\subseteq\Feature{comps}(w)\subseteq \Feature{comps\_req}(E)\UNION\Feature{comps\_opt}(E) \end{array}$

However, for practical reasons of implementation, the selection constraint cannot operate on arbitrary AVMs, but is only provided for finite domains and finite sets. This means that we cannot use the selection constraint directly on the sequence of lexicon entries to obtain . However, we only need to access its attributes, and we overcome the limitation we pointed out by pushing attribute access into the selection:

$\begin{array}{c} \Feature{cats}(w)=\TUP{\Feature{cats}(e_1),\ldots,\Feature{cats}(e_n)}[I]\\ \Feature{agrs}(w)=\TUP{\Feature{agrs}(e_1),\ldots,\Feature{agrs}(e_n)}[I]\\ \Feature{comps\_req}(w)=\TUP{\Feature{comps\_req}(e_1),\ldots,\Feature{comps\_req}(e_n)}[I]\\ \Feature{comps\_opt}(w)=\TUP{\Feature{comps\_opt}(e_1),\ldots,\Feature{comps\_opt}(e_n)}[I]\\[5mm] \Feature{cat}(w)\in\Feature{cats}(w)\\ \Feature{agr}(w)\in\Feature{agrs}(w)\\ \Feature{comps\_req}(w)\subseteq\Feature{comps}(w)\subseteq \Feature{comps\_req}(w)\UNION\Feature{comps\_opt}(w) \end{array}$