16.3.2 Head Features

To account for the way that compositional grammatical constituents such as noun phrases, nominals, and verb phrases come to have agreement features, the preceding section introduced the notion of copying feature structures from phrase structure children to their parents. This turns out to be a specific instance of a much more

general phenomenon in constraint-based grammars. Specifically, the features for most grammatical categories are copied from one of the children to the parent. The child that provides the features is called the head of the phrase, and the features copied are referred to as head features.

This idea of heads, first introduced in Sec. ??, plays an important role in constraint-based grammars. Consider the following three rules from the last section.

$$ VP\to Verb NP $$

$$ \langle V P{\mathrm{~a g r e e m e n t}}\rangle=\langle V e r b{\mathrm{~a g r e e m e n t}}\rangle $$

NP $ \rightarrow $ Det Nominal

$$ \langle D e t\ A G R E E M E N T\rangle=\langle N o m i n a l\ A G R E E M E N T\rangle $$

$$ \langle N P\ A G R E E M E N T\rangle=\langle N o m i n a l\ A G R E E M E N T\rangle $$

Nominal $ \rightarrow $ Noun

$$ \langle Nominal~AGREEMENT\rangle=\langle Noun~AGREEMENT\rangle $$

In each of these rules, the constituent providing the agreement feature structure to its parent is the head of the phrase. More specifically, the verb is the head of the verb phrase, the nominal is the head of the noun phrase, and the noun is the head of the nominal. As a result, we can say that the agreement feature structure is a head feature. We can rewrite our rules to reflect these generalizations by placing the agreement feature structure under a HEAD feature and then copying that feature upward as in the following constraints.

$$ \begin{aligned}&VP\rightarrow Verb NP\\ &\quad\langle VP\text{HEAD}\rangle=\langle Verb\text{HEAD}\rangle\\ \end{aligned} $$

$$ NP\ \to\operatorname{Det}\operatorname{Nominal} $$

$$ \langle N P\mathrm{~H E A D}\rangle=\langle N o m i n a l\mathrm{~H E A D}\rangle $$

$$ \langle D e t\ \mathrm{H E A D}\ \mathrm{A G R E E M E N T}\rangle=\langle\mathrm{N o m i n a l}\ \mathrm{H E A D}\ \mathrm{A G R E E M E N T}\rangle $$

$$ Nominal\ \rightarrow\ Noun $$

$$ \langle Nominal\ HEAD\rangle=\langle Noun\ HEAD\rangle $$

Similarly, the lexical entries that introduce these features must now reflect this HEAD notion, as in the following.

$$ \begin{aligned}Noun&\rightarrow flights\\\langle Noun\text{HEAD}&AGREEMENT\NUMBER\rangle=pl\end{aligned} $$

Verb $ \rightarrow $ serves

$ \langle Verb\ HEAD\ AGREEMENT\ NUMBER\rangle = sg $