18.5.2 Noun Phrases

As we have already seen, the meaning representations for noun phrases can be either normal FOL terms or complex-terms. The following sections detail the semantic attachments needed to produce meaning representations for some of the most frequent kinds of English noun phrases. Unfortunately, as we will see, the syntax of English noun phrases provides surprisingly little insight into their meaning. It is often the case that the best we can do is provide a rather vague intermediate level of meaning representation that can serve as input to further interpretation processes.

Compound Nominals

Compound nominals, also known as noun-noun sequences, consist of simple sequences of nouns, as in the following examples:

(18.15) Flight schedule

(18.16) Summer flight schedule

As noted in Ch. 12, the syntactic structure of this construction can be captured by the regular expression $ Noun^{*} $, or by the following context-free grammar rules:

Nominal $ \rightarrow $ Noun

Nominal $ \rightarrow $ Nominal Noun

In these constructions, the final noun in the sequence is the head of the phrase and denotes an object that is semantically related in some unspecified way to the other nouns that precede it in the sequence. In general, an extremely wide range of common-sense relations can be denoted by this construction. Discerning the exact nature of these relationships is well beyond the scope of the kind of superficial semantic analysis presented in this chapter. The attachment in the following rule builds up a vague representation that simply notes the existence of a semantic relation between the head noun and the modifying nouns, by incrementally noting such a relation between the head noun and each noun to its left:

$$ Nominal\rightarrow Noun~Nominal $$

$$ \left\{\lambda x{\operatorname{N o m i n a l.s e m}}(x)\land\operatorname{N N}({\operatorname{N o u n.s e m}},x)\right\} $$

The relation NN is used to specify that a relation holds between the modifying elements of a compound nominal and the head Noun. In the examples given above, this leads to the following meaning representations:

$$ \lambda xisa(x,Schedule)\land NN(x,Flight) $$

$$ \lambda xIs a(x,Schedule)\land NN(x,Flight)\land NN(x,Summer) $$

Note that this representation correctly instantiated a term representing a Schedule, while avoiding the creation of terms representing either a Flight or Summer.

Genitive Noun Phrases

Recall from Ch. 12 that genitive noun phrases make use of complex determiners that consist of noun phrases with possessive markers, as in Atlanta's airport and Maharani's menu. It is quite tempting to represent the relation between these words as an abstract kind of possession. A little introspection, however, reveals that the relation between a city and its airport has little in common with a restaurant and its menu. Therefore, as with compound nominals, it's best to simply state an abstract semantic relation between the various constituents.

NP $ \rightarrow $ ComplexDet Nominal

$$ \{<\exists x N o m i n a l.s e m(x)\land G N(x,C o m p l e x D e t.s e m)>\} $$

$$ ComplexDet\rightarrow NP~^{\prime}s\qquad\{NP.sem\} $$

Applying these rules to Atlanta's airport results in the following complex-term:

$$ <\exists x I s a(x,A i r o p o r t)\land G N(x,A t l a n t a)> $$

Subsequent semantic interpretation would have to determine that the relation denoted by the relation GN is actually a location.

(18.17) I don't mind a cheap restaurant.

Adjective Phrases

English adjectives can be split into two major categories: pre-nominal and predicative. These categories are exemplified by the following BERP examples:

(18.18) This restaurant is cheap.

For the pre-nominal case, an obvious and often incorrect proposal for the semantic attachment is illustrated in the following rules:

Nominal $ \rightarrow $ Adj Nominal

$$ \{\lambda x{~N o m i n a l.s e m}(x)\land{I s a}(x,{A d j.s e m})\} $$

$$ Adj\rightarrow cheap\quad\{Cheap\} $$

This solution modifies the semantics of the nominal by applying the predicate provided by the adjective to the variable representing the nominal. For our cheap restaurant example, this yields the following not unreasonable representation:

$$ \lambda x\,Isa(x,Restaurant)\land Isa(x,Cheap) $$

This is an example of what is known as $ \underline{\text{intersective semantics}} $ since the meaning of the phrase can be thought of as the intersection of the category stipulated by the nominal and the category stipulated by the adjective. In this case, this amounts to the intersection of the category of cheap things with the category of restaurants.

Unfortunately, this solution often does the wrong thing. For example, consider the following meaning representations for the phrases small elephant, former friend, and fake gun:

$$ \lambda x\,Isa(x,Elephant)\land Isa(x,Small) $$

$$ \lambda x\,Isa(x,Friend)\land Isa(x,Former) $$

$$ \lambda x\,Isa(x,Gun)\land Isa(x,Fake) $$

Each of these representations is peculiar in some way. The first one states that this particular elephant is a member of the general category of small things, which is probably not true. The second example is strange in two ways: it asserts that the

person in question is a friend, which is false, and it makes use of a fairly unreasonable category of former things. Similarly, the third example asserts that the object in question is a gun despite the fact that fake means it is not one.

As with compound nominals, there is no clever solution to these problems within the bounds of our current compositional framework. Therefore, the best approach is to simply note the status of a specific kind of modification relation and assume that some further procedure with access to additional relevant knowledge can replace this vague relation with an appropriate representation (Alshawi, 1992).

Nominal $ \rightarrow $ Adj Nominal

$$ \{\lambda x{~N o m i n a l.s e m}(x)\land A M(x,A d j.s e m)\} $$

Applying this rule to a cheap restaurant results in the following formula:

$$ \exists x\,Isa(x,Restaurant)\land AM(x,Cheap) $$

Note that even this watered-down proposal produces representations that are logically incorrect for the fake and former examples. In both cases, it asserts that the objects in question are in fact members of their stated categories. In general, the solution to this problem has to be based on the specific semantics of the adjectives and nouns in question. For example, the semantics of former has to involve some form of temporal reasoning, while fake requires the ability to reason about the nature of concepts and categories.