Filler-gap mismatches

[kaplan at parc.xerox.com]

Carl,

You asked for an example of the fuzziness that comes from inverse
correspondences.  The gerund is one illustration of categorial
fuzziness, as Yehuda also mentioned.  A gerund can be derived as an NP
that expands to a VP.  So it's f-category is a little fuzzy--it would
satisfy f-category restrictions both for N and for V.  It doesn't make
sense to say that it is one (functional) category or the other.

The original example of f-precedence fuzziness was Megumi Kameyama's
analysis of Japanese null anaphors.  There are certain
antecedent-pronoun ordering conditions that seem always to be satisfied
by null anaphors, no matter what the canonical position might be of a
real pronoun filling the same grammatical function.  Because null
anaphors are f-structure units that, by definition, are not the image of
any c-structure node, the inverse correspondence gives the empty set, so
they both f-precede and are f-preceded by everything.  In effect, null
anaphors are everywhere and they satisfy all the antecedent ordering
conditions if they are stated in terms of f-precedence.

Another fuzzy situation might come from scrambling languages (e.g.
Warpiri).  If the subject is realized by nodes that are interspersed
between a collection of nodes that represent the object (a sequence like
S O O S S O), then any condition that requires the subject to f-precede
the object (or vise versa) would not be satisfied.  The scrambling of
the nodes is reflected in the failure of f-precedence, even though some
(but not all) of the nodes of the subject might come before all of the
nodes of object.  If there were such a condition on grammaticality, it
would only be satisfied if all the subject nodes came before all the
object nodes.

You asked whether I was talking about semantic or syntactic "arguments".
 Not sure how to answer this.  In LFG the PRED semantic form gives a
mapping between grammatical functions and the arguments (or thematic
roles) of the underlying semantic predicate.  So if you look at the
grammatical functions in the list, you might think of these as syntactic
arguments.  If you look at the thematic roles, then you might think of
this as a semantic specification.  The issue with ARG1, ARG2 (or AGT,
THEME) is really whether or not you can refer to the fillers of the
slots of this syntax/semantic correlation by their semantic roles (i.e.
ARG1 or AGT) or only by their grammatical functions.  For the phenomena
dealt with in the LFG syntactic module, we claim that designation by
grammatical function is all that you need.  We separate out the
interesting questions of how semantic roles map to grammatical
functions--predicting the semantic form from the semantic roles of the
underlying predicate.  Separate theories  of argument structure or
lexical-mapping address this issue.  Does this help to clarify my
earlier point?

Finally, you commented that "at least the analog of `set' in some
interpretation of higher-order logic.
(For them to LITERALLY be sets would mean that the interpretation of the
grammar logic was a Henkin model, but that is another story.)"

Actually, my intention in setting up LFG was to use the simplest and
most naive mathematical structures I could think of, and indeed, I
really did intend that LFG sets would be, literally, the simple sets of
ordinary ZF set theory.   And the f-structures are naive tabular
functions, finite sets of ordered pairs (I think several years ago, when
Ivan and I were doing the LFG/HPSG comparison course, we had a
discussion about one difference in the underlying models, noting that in
LFG equivalent structures are considered to equal, whether or not they
are asserted to be equal, whereas this is not true of HPSG models).

I'm not sure whether I should be happy or sad if this means that we are
interpreting in a Henkin model.   It may be that we can get by with
simpler models (I presume the Henkin models are simpler than the
alternatives) for feature structures because we've divided the
discriptive work in different ways--some recursion is in the
c-structure, for example.  But maybe I just don't understand the
problem.  Can you say more about this?

--Ron