Under the bed

[kaplan at parc.xerox.com]

There are now many threads to this discussion--a cynic might say that
the discussion is unraveling.  There are linguistic issues, philosophy
of science issues, mathematical issues, and even aethestic issues flying
around.   In this message I want to respond to a few of the linguistic
issues that were left hanging from last week--I'll get back to the
metatheory a little later, after another period of loin-girding.  Also,
you'll note that I changed the subject heading of this message:
"Filler-gap mismatches" is no longer discriminating.

In this message I'll stick to the (relatively concrete) linguistic
questions that Carl and Ivan asked as they tried to interpret how
categories and lexical selection work in LFG.  I had suggested that
"think of that..." was out because of the c-structure fact that
prepositional objects in English could not be realized as sentential
complements, but extraposed complements can be assigned
object-of-preposition functions (via functional uncertainty) and thus we
see the acceptable cases of categorial mismatch.  This account crucially
depends on the fact that a preposition like "of" does not select for the
c-structure category of its object-- if it did, then the the extraposed
sentence would be equally as bad as the non-extraposed version.  And it
crucially depends on where c-structure categories can appear and how
they can expanded--S-bar does not appear as the complement of a
preposition, but can be assigned the function object-of-preposition by a
functional uncertainty in topic position.

As the discussion unfolded, Carl at one point commented that "this
account seems based on a conception of category where the category of an
expression is determined externally (by what environments it can occur
in) rather than internally (what its internal structure is)."  He
pointed to sentences involving UNDER THE BED and DELIBERATELY
SLAUGHTERING RARE WARBLERS as examples of items that were internally
structured as categories other than NP but yet which seemed to appear in
typically NPcontexts.  Here are his UNDER THE BED examples:

>[1]  UNDER THE BED sure beats the commodities market if liquidity is
what matters to you.

>[2] I prefer UNDER THE BED to under the dresser.

>[3] I have always thought of UNDER THE BED as a stupid place to store
the good crystal.

Examples like this are discussed at some length in Joan's paper
"Locative inversion and the architecture of universal grammar"
(Language, 1994, starting on p 103 but especially on p 110--note that
the "think of" sentences are mentioned here as well--hard to get away
fromthem).   She gives lots of distributional arguments, and some
arguments based on agreement and interpretation, for why these
particular preposition phrases should be analyzed as NP's with missing
nominal heads  (she also cites some of Bob Levine's examples (Levine
1989) in making the argument).  Thus "under the bed" would be analyzed
as
	[NP (a place) [PP under the bed]]
where (a place) has been elided.  Her point in this paper is to
distinguish these cases from cases of locative inversion, where PP's are
assigned a subject function even though they don't appear in the
c-structure position where nominal subjects usually appear.   (I don't
think she is explicit about the f-structures for these NP-over-PP
phrases, but a plausible arrangement is that the f-structure would have
a dummy PRED (like 'place' or 'time'), provided by the construction, and
the PP would be an adjunct.

The formalism, of course, admits various alternatives in which the
patterns are accepted but where UNDER THE BED is a PP is not dominated
by NP.   And the modifications to the conventional grammar would be
relatively minor.  We would simply allow a PP as an alternative category
in the positions where the SUBJ and OBJ functions are usually assigned
to nominals.  It would not be a big deal from a formal or architectural
point of view, but it would not naturally account for as many properties
of these constructions (and the similarities/contrasts with Chichewa
that Joan examines).  So the NP over PP is more attractive, and
illustrates the point, also made later by Ivan, that both distributional
and internal properties are used to define categorial structures.
Indeed, on Joan's NP over PP account, the words "under the bed" are
categorized both as NP (characterizing a certain set of mostly
distributional properties) and PP (characterizing a certain set of
internal, realizational properties).  But the categories themselves are
not conflated in any way.

Note that whether or not UNDER THE BED in [3] is an NP or a PP is
irrelevant to the LFG account of the "think of" constrasts--that account
rests only on the claim that prepositions don't take sentential objects.
 [It is perhaps interesting to note that Quirk et al. use "doesn't take
a sentential object" as a defining characteristic of English
prepositions.]

The verbal gerund examples DELIBERATELY SLAUGHTERING RARE WARBLERS would
be handled in much the same way (NP over VP), I think, so that both
distributional and realizational properties can be captured.  Here I
think the NP and VP would map to the same f-structure, giving rise to
the mixed (functional) category phenomena that have already been
discussed.  There may be some other LFG'ers listening in  who might have
arguments for a different analysis (please speak up), but in any event I
don't think that fundamental architectural principles are at stake here.

I also want to comment on the kind of examples that Ivan brought up in a
later message:

"After you leave, John will finish the project"  (the example in Ivan's
message was a little garbled, I fixed it up)

This seems to indicate (and apparently Emonds has argued) that the
preposition "After" can take an S complement "you leave", not just an
NP.  And the fact that it is only some prepositions (after, before) that
can do this might be used as an argument that prepositions can select
lexically for specific categories.

This would run against the account of "think of" that we have proposed,
which involves the claim that prepositions don't take sententential
complements as a matter of c-structure realization, without lexical
selection for category.   What might we say?  Well, of course, if we
took this analysis on its face, we might still have an account of "think
of", merely by saying that "of", unlike "after", doesn't select for
sentential complements.   Or we might weasle and say that the
prohibition is against S-bars or CP's and not S's or IP's.

But I think the right thing to say is that [PP after S] is just not the
correct analysis of this construction (although I do wonder what Emonds
said).  Quirk et al, for example, analyze "after" and "before" as being
lexically ambiguous between conjunctions  and prepositions, and they are
acting as conjunctions or complementizers in these constructions, with a
[Sbar C S] or [CP C IP] analysis.

So the correct analog for "after you leave" is "while you leave", not
"after the game".  This analysis explains why you can't have another
complementizer, and probably a number of other things:
	*After that you leave...
	*While that you leave...
And it certainly means that these examples have no bearing on the "think
of" account.

Finally, Ivan also commented:

"I suppose some of these issues boil down to the fundamental question of
whether a grammatical theory should distinguish c-structure with monadic
categories (although some LFG work -- e.g. by Bresnan, Sells -- uses
feature
structures for c-structure categories as well) from f-structure with
feature
structure categories. HPSG would answer this negatively, saying that
there
are many kinds of (feature) structure categories, each with their own
properties, but no fundamental distinction between coarse-grained
c-structure
categories (NP vs. PP vs. A, etc.) and the various kinds of
f-structure."

In my mind the major contrast is not between monadic (I would say
unanalyzable) categories and feature structure categories.  It is only a
minor extension of the conventional LFG architecture to allow
c-structure categories that are realized as bundles of features, to
allow for certain subclassifications of c-structure derivations.
Indeed, our LFG implementations at Xerox include the possibility of
so-called complex categories, and they can be quite useful.  But our
complex features are formally analogous to GPSG categorial features and
not to the features that appear in HPSG feature structures or LFG
functional structures.  In particular, they only have values drawn from
finite sets (no hierarchy or recursion), they are associated with the
nodes in a one-to-one way, not a many-to-one way, and any dependencies
between them are purely local, resolved at compile-time by a finite
expansion of the c-structure grammar.  So I would put monadic and
complex categories together and contrast them with feature-structure
features.  The latter have much more expressive power--and require more
difficult computations to resolve.

--Ron