Consider the following NPs:
[1] an alcohol ban
[2] a cotton shirt
Various discussions in CGEL would seem to imply the following:
P: alcohol expresses a semantic argument of the head noun ban in [1], while cotton does not express a semantic argument of the head noun shirt in [2]
How can claim P be supported?
One explanation:
i. according to CGEL (p. 441), 'complements express semantic arguments of the head noun'.
ii. alcohol is a complement in [1], while cotton is merely a modifier in [2].
iii. thus, P: alcohol expresses a semantic argument of the head noun ban in [1], while cotton does not express a semantic argument of the head noun shirt in [2].1
1In order to prevent circular reasoning, there must be independent reasons for saying that alcohol is a complement in [1] while cotton is a modifier in [2] (reasons independent of whether alcohol and cotton express semantic arguments of their respective head nouns). And perhaps there are such arguments. For example, CGEL would say this: [1] can be paraphrased as a ban on alcohol; in that rephrasing, the preposition on is licensed by the noun ban; 'The licensing criterion is the most basic criterion for complement status of post-head dependents' (p. 440). And perhaps there is no corresponding story about licensing that can be said about [2].
But is there any other way to establish P, a way that does not rely on first establishing that alcohol is a complement in [1] whereas cotton is a modifier in [2]?