Referential Ambiguity
The interpretation of sentences also depends on the referential properties of the words and constructions contained in them.
Referential ambiguity arises when a word (e.g. a pronoun) or construction can refer to more than one entity in the same sentence, another sentence, or in the world.
In the example, the reduced construction "and so did Bill" may relate to Bill's own girl-friend or to John's. The ambiguity has to be resolved on the basis of the context, which will have to determine the exact relationship between John, Bill, and their girl-friends.