I've run into "semantic head parsing" and "syntactic head parsing" and while I think I have a feel for the difference, I was wondering if anyone could give a more concrete definition or reference to read up about the difference.
In particular I'm curious about the characteristics of parsing sentences with each method. What benefits does each one have? What aspects of the sentence do they highlight?
When you write down the semantic representation of a sentence (lambda calculus) you see that the determiner "consumes" the noun. Hence, it is the semantic head of a noun phrase. SEOP has a comprehensive overview of the phenomena that led to this, but Wikipedia is not bad either.
In syntax, the noun is considered the head of the noun phrase because it is the more "contentful" part, in the way people understand sentences.
In HPSG, the CAT derivation is somewhat like the regular phrase-structure derivation, with heads having a correspondence to phrase-structure (PS) heads. (Though, AFAIK, there is no need for the concept of "head" in PS.*) The CONT derivation is somewhat like the derivation in Montague semantics.
These are not two different types of parsing in HPSG (or anywhere else, AFAIK), but two (of the many) aspects of parsing with a rich grammar like HPSG.
Benefits: I don't think you can compare one with the other for benefits... if you go through the references I gave for quantifiers, you'll see that the mathematics would become very cumbersome and ugly (or maybe even impossible... I don't know) if you try to make the semantic heads correspond with PS heads.
* Though some parsing techniques find it useful to have heads of a PS marked.
