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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?

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    I guess somebody has to ask. What is that you are intending to do with your construction, once you have constructed it; and of what are you intending to construct it? Is this a programming question, or a linguistic one? Or both? – jlawler Mar 14 '12 at 18:59
  • Oh, by 'construct' I was just trying to guess at what a 'witness world' could be, if it were parallel to a 'witness set.' The only thing I intended to do with the parallel is try to use it to understand the paper I was reading, and then maybe keep the concept in mind in case it ends up being handy in explaining some data. So definitely a linguistic question, not a programming one. – user177 Mar 14 '12 at 19:08
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    Why don't you just contact the authors in a case like this? – Mark Beadles Mar 14 '12 at 20:57
  • FWIW, my intuition is that by witness world they mean the epistemic universe of a witness (in contrast to, say, a belief world), quite a different direction than I think you're headed. – Mark Beadles Mar 14 '12 at 21:07
  • Can you link the paper, or quote the relevant passages? It is pretty easy to guess what they mean in general terms, but the specific usage will depend on the context they are using. A witness world is just an imaginary universe where the proposition P holds, but it depends on the logic and on the context what kind of imaginary constructions are allowed, and how they verify P. – Ron Maimon Mar 15 '12 at 6:59
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I too would like a link to the paper: a Google search for anand hacquard "witness world" turns up this thread and nothing else. But I can take a stab at a general answer.

The notions of possibility and necessity in modal logic are commonly treated as involving quantification over possible worlds. So "It's possible that P" is taken to mean that there exists a world where P is true, and "Necessarily P" is taken to mean that in all worlds, P is true. We can get different sorts of possibility and necessity by restricting the set of worlds we quantify over. So for instance, for deontic modals, we quantify over worlds that are in accordance with the rules. ("John is permitted to do x" means roughly the same thing as "there exists a world in which no rules are being broken, in which John does x") For epistemic modals, we quantify over worlds that are consistent with our current knowledge. ("For all I know, maybe P" means, roughly, "there exists a world that's consistent with what I know, in which P is true.")

The semantics of modal expressions in natural language can be modeled this way too, though there are some additional complications. Kratzer's 1991 paper "Modality" is the classic reference here, but unfortunately I can't find a copy online.

In this context, a "witness world for P" is just a world in which P is true. So for instance, we can say that for "possibly P" to be true, there must be at least one witness world for P within our domain of quantification. This is indeed similar to the way the word "witness" is used in talking about nominal quantification — it's just that here we're quantifying over worlds instead of entities.

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  • I've contacted one of the authors, and a witness world is meant as answered by @Ron Maimon and Dan Velleman. The paper is "Epistemics, Mood, and Attitudes" - It's a draft I think, though, so don't know if it is available online. – user177 Mar 16 '12 at 14:50

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