Another fairly common type of NP is one containing a genitive:

(7) Garth's reply

This NP looks almost the same as the NPs above, but Garth is a proper noun, not a determiner. And yet Garth seems to occupy the same "slot" in the noun phrase. Notice that we can use either a determiner or the proper noun, but not both:

(7a) the reply
(7b) *the Garth's reply
(7c) *Garth's the reply

At this point, you may be ready to assume that Garth’s actually is a determiner, but that conclusion leads to some unfortunate consequences. First, we would have to say that any noun could change its part of speech simply by adding the genitive inflection. In other words, the category of determiner, which we have already described as containing a small number of words that have a principally grammatical function becomes an open-ended set. Further, this slot isn't just occupied by genitive nouns. It can be occupied by entire phrases:

(8) The President of Liberia's mistake

If we're going to call these determiners too, then we are saying that entire phrases can be described as a word category, making a mess of our descriptive system. The solution to this puzzle is to recognize that the contrast between (7) and (7a) is one of two different forms, a determiner on the one hand and a genitive noun on the other, that share a common function. We will call this function the determinative.[1] In its most basic semantic role, a determinative indicates the definiteness of a noun phrase. That is, it tells us whether the NP has a specific referent or not.

One interesting thing to note about the genitive inflection is that it doesn't behave like a normal inflection (for example plural -s).

(8a) *The President’s of Liberia mistake

The mistake was not that of Liberia but of its president, and yet we find the 's inflection at the end of the whole phrase and not attached to the head noun, president. Indeed, in informal varieties of English, the word to which the 's attaches doesn’t even have to be a noun:

(9) The guy I was talking to's resume
(10) The woman he plans to marry's opinion

In contrast, the plural -s inflection attaches to the head noun, not the end of the phrase.

(11) The Presidents of Liberia
(11a) *The President of Liberias

Because the genitive inflection appears at the end of the entire phrase when the phrase contains more than one word, and because phrases often contain only one word, there is no good reason to assume that the genitive behaves differently with individual nouns than it does with multi-word phrases. Nevertheless, we will keep our diagrams simpler by omitting the NP node when the genitive is a single word.[2] We will diagram genitive NPs this way:

Notice in the diagrams above that the genitives are labeled for their function. We will use "det." as an abbreviation for the determinative function. Don't confuse this with the word category label D, for determiner. Also note that in the music's beat, there are actually two determinatives. The music is the determinative for beat and the is the determinative for music. In other words, each NP has its own determinative slot. Because determiners prototypically fill the determinative function, we won’t bother to indicate this function in our diagrams when they are playing their ordinary role.

Pronouns fit easily into the above scheme. Since they are a type of noun, we treat them just like other one-word genitives:

Notice that the second example above, like the music's beat, also contains two determinatives, but in this instance we did label our as a determinative because it is not a determiner.

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Notes

[1] There is an unfortunate difference in terminology regarding the terms determiner and determinative. In The Comprehensive Grammar of the English Language, a work which was published in 1984 and which served as a major reference for a generation of other works on English grammar, the terms are used as they are in this text: determiner is a lexical category and determinative is a function. However, the major recent reference grammar, The Cambridge Grammar of the English Language, reverses the terms’ denotation. There, determiner is the function and determinative is the lexical category. The authors of the Cambridge Grammar provide no explanation for this switch, which is unfortunate as it is certain to breed confusion. As most other works use determiner for the lexical category, I have retained the more traditional terms here.

[2] If the inconsistency bothers you, see the aside "On Simplified Diagrams" at the end of chapter 7 for a detailed explanation of my reasoning.