Fancy GQ
I thought I’d just make a real post in response to Lance’s comment on my last post to clarify on the “fancy generalized quantifier” type (name courtesy of Polly :-P).
[[every boy who left who came before John]] = λE(e,t)[λM(e,t)[ ∀x [(left’(x) & came’(x) & E(x) & boy’(x)) -> M(x)]]]
The idea here is that E is a domain restriction argument, which can be filled either by some contextually salient restriction or by a relative clause (or perhaps other restrictions, such as exceptives). Kai discusses motivations for domain restrictions in his thesis (in Section 2.2.2) and associates the restriction with the quantifier. If you pass up that argument to the whole GQ, it gives the relative clause a place to contribute to the whole meaning of the GQ. (This isn’t a totally new idea; Bach & Cooper 1978 have this extra argument in their approach to relative clauses.) My idea is that if there is always a domain restriction argument in the GQ, we can have the relative clause fill that spot – but, we’ll need to pass up a new argument slot once we combine the GQ with the RC, not just for stacking but to leave that open for any contextually salient domain restrictions.
emma :: Feb.24.2007 :: misc, semantics, linguistics :: 2 Comments »
Ah! A domain restriction. Yes, that certainly belongs in there. I suppose I’m more used to seeing it unbound, its value supplied by context, but the day Polly lets you have an unbound variable in your formula is the day Chomsky says, “You know, maybe those LFG people are onto something.” And, yes, having it there does give you an “in” for the RC meaning.
(Exceptives? Hm. Do exceptives belong in there? Maybe. I should read Gajewski’s dissertation at some point; I think there are exceptives in it.)
If it’s not in there…what happens. The thing that should be a restrictor ends up coordinated with M(x) in the formula, doesn’t it. And that would be, well, wrong. Hm.
Well, definitely interested to see where this leads. Sorry you’re not down here for the PLC (especially since Celeste mentioned last weekend that you’d sounded like you might’ve been interested)! One of these days, I tell you, I’ll have to get off the train one stop early and visit Polly in Providence….
One of these days, I tell you, I’ll have to get off the train one stop early and visit Polly in Providence….
Yes, you definitely should!
And, yes, I had been thinking about attending the PLC, but alas, time/money concerns. Ach, life! :-P