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.