5.4.4 Role Constraints

For each role $\rho\in\setof{Roles}$ there is a corresponding binary predicate $\Gamma_\rho$ . The third principle of well-formedness requires that whenever the dependency tree contains an edge $w\EDGE\rho w'$ , then the grammatical condition $\Gamma_\rho(w,w')$ must hold in the tree. Therefore the tree must satisfy the proposition below:

$\forall w,w'\in\VV,\ \forall\rho\in\setof{Roles},\quad w'\in\rho(w)\Rightarrow\Gamma_\rho(w,w')$

In practice, the proposition will be enforced by creating a disjunctive propagator for each triple $(w,w',\rho)$ :

$w'\in\rho(w)\wedge\Gamma_\rho(w,w')\quad\textbf{or}\quad w'\not\in\rho(w)$

For illustration, let's consider some examples of $\Gamma_\rho(w,w')$ .

Subject.

The subject of a finite verb must be either a noun or a pronoun, it must agree with the verb, and must have nominative case. We write $\SET{nom}$ for the set of agreement tuples with nominative case:

$\Gamma_{\Feature{subject}}(w,w')\equiv \begin{array}[t]{ll} &\Feature{cat}(w')\in\{\Value{n},\Value{pro}\}\\ \wedge&\Feature{agr}(w)=\Feature{agr}(w')\\ \wedge&\Feature{agr}(w')\in\SET{nom} \end{array}$

Adjective.

An adjective may modify a noun and must agree with it:

$\Gamma_{\Feature{adj}}(w,w')\equiv \begin{array}[t]{ll} &\Feature{cat}(w)=\Value{n}\\ \wedge&\Feature{cat}(w')=\Value{adj}\\ \wedge&\Feature{agr}(w)=\Feature{agr}(w') \end{array}$