12.3.4 Agreement

In Ch. 3 we discussed English inflectional morphology. Recall that most verbs in English can appear in two forms in the present tense: the form used for third-person, singular subjects (the flight $ \underline{\text{does}} $), and the form used for all other kinds of subjects (all the flights $ \underline{\text{do}} $, I $ \underline{\text{do}} $). The third-person-singular (3sg) form usually has a final -s where the non-3sg form does not. Here are some examples, again using the verb do, with various subjects:

Do [NP all of these flights] offer first class service?

Do [NP I] get dinner on this flight?

Do [NP you] have a flight from Boston to Forth Worth?

Does [NP this flight] stop in Dallas?

Here are more examples with the verb leave:

What flights leave in the morning?

What flight leaves from Pittsburgh?

This agreement phenomenon occurs whenever there is a verb that has some noun acting as its subject. Note that sentences in which the subject does not agree with the verb are ungrammatical:

*[What flight] leave in the morning?

$ ^{*} $Does [NP you] have a flight from Boston to Forth Worth?

$ ^{*} $Do [NP this flight] stop in Dallas?

How can we modify our grammar to handle these agreement phenomena? One way is to expand our grammar with multiple sets of rules, one rule set for 3sg subjects, and one for non-3sg subjects. For example, the rule that handled these yes-no-questions used to look like this:

$$ S\rightarrow A u x N P V P $$

We could replace this with two rules of the following form:

$$ S\ \to\ 3sgAux\ 3sgNP\ VP $$

$$ S\ \to\ \mathsf{N o n3s g A u x}\ \mathsf{N o n3s g N P}\ \mathsf{V P} $$

We could then add rules for the lexicon like these:

$$ \begin{array}{l}3sgAux\to does|has|can|\dots\end{array} $$

$$ \mathbf{N o n3}s g A u x~\to~d o~|~h a v e~|~c a n~|~\ldots $$

But we would also need to add rules for 3sgNP and Non3sgNP, again by making two copies of each rule for NP. While pronouns can be first, second, or third person, full lexical noun phrases can only be third person, so for them we just need to distinguish

between singular and plural (dealing with the first and second person pronouns is left as an exercise):

$$ 3S g N P\ \to\ \mathsf{D e t}\ S g\mathsf{N o m i n a l} $$

$$ Non3SgNP\ \to\ Det Pl Nominal $$

$$ S g N o m i n a l\;\rightarrow\;S g N o u n $$

$$ P l N o m i n a l\;\to\;P l N o u n $$

$$ \begin{array}{l}SgNoun\rightarrow flight\mid fare\mid dollar\mid reservation\mid\ldots\end{array} $$

$$ \begin{array}{l}PlNoun\rightarrow flights|fares|dollars|reservations|...\end{array} $$

The problem with this method of dealing with number agreement is that it doubles the size of the grammar. Every rule that refers to a noun or a verb needs to have a “singular” version and a “plural” version. Unfortunately, subject-verb agreement is only the tip of the iceberg. We’ll also have to introduce copies of rules to capture the fact that head nouns and their determiners have to agree in number as well:

$$ \begin{array}{l l}{{t h i s~f l i g h t}}&{{*t h i s~f l i g h t s}}\\ {{t h o s e~f l i g h t s}}&{{*t h o s e~f l i g h t}}\end{array} $$

Rule proliferation will also have to happen for the noun's case; for example English pronouns have nominative (I, she, he, they) and accusative (me, her, him, them) versions. We will need new versions of every NP and N rule for each of these.

These problems are compounded in languages like German or French, which not only have number-agreement as in English, but also have gender agreement. We mentioned briefly in Ch. 3 that the gender of a noun must agree with the gender of its modifying adjective and determiner. This adds another multiplier to the rule sets of the language.

Ch. 16 will introduce a way to deal with these agreement problems without exploding the size of the grammar, by effectively parameterizing each non-terminal of the grammar with feature structures and unification. But for many practical computational grammars, we simply rely on CFGs and make do with the large numbers of rules.