In reading a paper by Anand & Hacquard, I've come across the term "witness world," where a witness world can verify a proposition, p. I haven't been able to google an easily understandable definition of a "witness world," (although this is probably due to poor detective work on my part). This leads to my question: What is a witness world (i.e., how is it defined), and how does it do this business of verifying propositions?
The closest thing that comes to my mind are witness sets, which, as I understand them, are the characteristic sets of generalised quantifiers, except that unlike characteristic sets for a GQ like [Q NP], which may have non-NP entities as members, witness sets only contain NP-entities. Szabolcsi (2010)'s example is "more than one robot," where a characteristic set includes non-robots (i.e., any set that has more than one robot), but a witness set is constrained so that it only contains robots.
I figured I could construct a sort of parallel, where a world would be a set of pairs, so a "witness world" would be a set of these pairs (for a modal, or attitude predicate), but these pairs are somehow restricted by the prejacent or embedded clause's assignment. But I wasn't sure how to proceed here (or whether I even should, in case there is no parallel, or I was going about the parallel in the wrong way). Which is my second related question - is the notion of "witness world" related to the notion of a "witness set," and if so, how?