What keeps tripping me up about Chierchia's system is all the going back and forth between w's and p's. w's are assignment functions (to dynamic variables...the kind that can be co-bound across clause boundaries.) p's are sets of assignment functions. At any point in a discourse, there is a current w--a current assignment function. But also at any point in the discourse, there is a current p: this is a set of admissible continuations of the discourse. A sentence affects both: it can e.g. open up new 'card's in w, and it can also effect which ways the discourse can continue. A sentence may do each without the other. A plausible example of the first kind of sentence is "a thing_xi is self-identical". A plausible example of the second kind is "Bill smokes", or "I don't have any children."
We should ask ourselves, though, just how w is an assignment function. Typically a file (i) only records partial information about discourse referents (certainly, for example, not information that is uniquely identifying) and (ii) its domain is partial.
In order to get from our ordinary notion of an assignment to the more intuitive notion of a file (as described above), we could employ functions. A file like
1 = cat, black
2 = woman, tall, owner of 1
...could be associated with a *set* of assignment functions which satisfy it. If we called this a proposition p, then, for example,
and would both be in p. But I'm not sure whether this is done! Investigation into this preliminary point is required!!
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