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In 'File Change Semantics and the Familiarity Theory of Definiteness' by Irene Heim, she calls 'its' in 'Every cat ate its food' a type of definite NP. Could a possessive adjective be classified as a noun phrase???
- Every cat ate its food.
- John didn't see a cat.
(2) has a reading where "its", a personal pronoun, i.e. a type of definite NP, functions as a so-called "bound variable pronoun" and doesn't refer to any particular cat.
It's hard to match up your question with your examples. The "its" in "its food" is neither an adjective nor a noun phrase. It is a definite determiner. The usual analysis is that this determiner is formed by combining a noun phrase with the "-s" ending. The definite pronoun "it" is a noun phrase, so "its" is simply a special case where the noun phrase "it" has been suffixed with "-s".
Full noun phrases, not just definite pronouns, can take this same "-s" suffix to form such noun phrases as "[NP [NP the man]'s hat]", "[NP [NP a girl who I used to know]'s car]", "[NP [NP [NP the hat]'s brim]'s edge]".
Heim's expression is ambiguous, but I think the sense is, if not exactly clear, at least readily recoverable. What Heim means is that the it piece of its is a pronoun standing for a "definite" NP, yet has no specific referent—it refers to no particular cat.
I see three strategies for rescuing the expression:
