This is to follow up on the discussion in the EMB students meeting on whether or not a head-compositional version of head-spec is needed to model some possessive strategies. The ERG uses a normal (non-head-compositional) head-spec rule to model possession, and so I am working to see if I can adapt their analysis for my library.
After looking at it today, I think my answer is still cautiously ‘no.’ Here’s the reason: the overall INDEX of the possessive phrase must be the INDEX of the head of the possessive phrase. In English, this can be built into the lexical entry for 's – it can simply identify its INDEX with the INDEX of the head of the possessive phrase.
How would this work in the case where the possessive marker is an affix on the possessor? Presumably, you’d have the lexical rule that adds the affix do the same thing that 's does – identify its INDEX with the INDEX of the possessum. As long as the lexical rule also puts the right indices into the poss_rel, it should work fine.
Here’s where things go wrong: the ERG analysis only works because in English, the possessor noun combines with its determiner before it combines with the possessive marking 's. So, in the sentence the dog’s cat, you get all the usual semantics for the NP the dog, where the ARG0 of dog is identified with the ARG0 of its determiner. In this analysis, the possessor affix must apply to the possessor noun before it combines with its determiner, meaning, it’s the INDEX value that it has by the time you get around to attaching the determiner is no longer its own. So you get this, where the determiner for dog has as its ARG0 the ARG0 for cat:
So, that’s where I’m at. I’m not convinced there’s absolutely no way around this, but the head-compositional head-spec rule certainly does the trick.