Reentrancy in feature structures

[Ash Asudeh]

(long)

Hello everyone

I'm sorry I'm entering this thread a little late, but I think this
discussion is very interesting. I just wanted to mention a phenomenon or
two that I don't think has been picked up on in the discussion (I haven't
read the messages carefully, so apologies in advance if these have been
mentioned) and to mention an alternative to coindexation (I think it's an
alternative, but it may be largely equivalent).

First, I don't think agreement and reflexive binding are the only places
where reentrancy is relevant. Another phenomenon is raising and also
possibly control (depending on how it's done). Note that type (i.e.
substructure) identity is insufficient for raising.

Second, in her recent book, Lexical Functional Grammar, Mary Dalrymple
proposes a Glue Semantics theory of pronominal binding/anaphora that I
think differs from what people on the list have been presupposing.

The theory in the book deals with both intra- and inter-sentential
anaphora, but I'll just sketch out the intra-sentential theory, which
avoids context-threading issues.

Basically, an anaphoric expression is an implication from the antecedent
to another copy of an antecedent conjoined with the pronoun (recall that
Glue is resource-sensitive, so the antecedent can't just be consumed to
get the pronominal semantics).

This looks something like this, where A is the antecedent and P is the
pronoun; -o is linear implication and @ is linear conjunction (tensor
variety):

A -o (A @ P)

On the meaning language side, this corresponds to a function from the
antecedent meaning to a pair (\ is lambda, x is product):

\Z. Z x Z

So putting it together: \Z. Z x Z: A -o (A @ P)

Now, the equivalent of coindexation is for two expressions to have the
same semantic-structure resource as the value of the feature ANTECEDENT,
which is a feature in semantic-structure, not functional-structure. If two
expressions have the same ANTECEDENT, then the "A"s above will get set to
the same resource. Binding restrictions are stated on the (^sigma
ANTECEDENT) equations.

Thus, we can have non-token identity in the syntax, but coindexation in
the semantics.

Coreference, as opposed to coindexation, occurs when the antecedent of a
pronoun just happens to be the same as another expression, in the meaning
language. Suppose we have a meaning constructor kim:K, another kim:K' and
a pronoun of the form \Z. Z x Z:K' -o (K' @ P). The pronoun will resolve
to kim x kim:K' @ P, which breaks down to kim:K' and kim:P. Thus, the
pronoun is coreferent with kim:K, but not (the equivalent of) coindexed
with it.

Going back to Luis's email, we can have the tree structure formalism he
was thinking about, without losing the distinction between coindexation
and coreference. It's just a matter of how things are factored out, I
think.

Dick Crouch and I presented a way of doing Glue for HPSG. It's in the 2001
proceedings.

Lastly, if you are working with a resource logic like linear logic for
semantic composition, as we do in Glue, the distinction between type and
token identity (EQ and EQUAL), is always relevant, because it affects
whether you have one resource or two contributed by the relevant item. Any
structure-sharing situtation is possibly worrying, as it usually leads to
multiple consumers for a single resource. For more on this, see our
NASSLLI lecture notes, day 4 (link on my webpage).

Hope this wasn't too confusing.

Best,
Ash

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