5.4.3 Valency Constraints

Every daughter set is a finite set of nodes in the tree:

$\forall w\in\VV,\ \forall\rho\in\setof{Roles},\quad\rho(w)\subseteq\VV$

The second principle of well-formedness requires that a complement daughter set $\rho(w)$ be non-empty only when $\rho$ appears in 's valency. Additionally, the first principle states that, when it is non-empty, the complement daughter set $\rho(w)$ must be a singleton:

$\begin{array}{l} \forall\rho\in\setof{Comps}\\ \quad \begin{array}{ll} &|\rho(w)|\leq 1\\ \wedge&|\rho(w)|=1\quad\equiv\quad\rho\in\Feature{comps}(w) \end{array} \end{array}$

In practice, the equivalence above will be enforced using reified constraints which are explained in Section 6.8.