Fwd: linear and non-linear terms

[Jonathan Ginzburg]

Another perspective on the issue of vacuous/multiple abstraction---in Ivan
Sag's and my book _Interrogative Investigations_ we treat questions as
propositional abstracts.  We use abstraction over sets, which can be empty,
singleton, or multiple.  This makes for simplicity in two respects:
answerhood can be characterized uniformly and similarly retrieval/binding
across all interogative construction types, incl polar interrogatives.

Polar questions come out as 0-ary abstracts (crucially distinct from
propositions) and we derive some fairly interesting results by having our
schemas generalize to the vacuous abstraction case (e.g. "intonation
questions" are an instance of a construction type for wh-in-situ, which
arises by abstracting over no parameters, whereas cases like A: Who left?
B: Who left?  [=Are you asking who left?]  are an instance of a
construction type for echo questions, which arises by abstracting over no
parameters.)

The abstraction Ivan and I use is admittedly a somewhat non-orthodox
version (it is essentially the simultaneous abstraction operator
axiomatized in Seligman and Moss' _Situation Theory_ paper in the Handbook
of Logic and Language.), but Robin Cooper has recently showed me how this
can be recast in Martin L\"of Type Theory (a preliminary version is in an
appendix to our paper from this year's Edilog, `Clarification Ellipsis in
Dependent Type Theory'.).

Jonathan