Reentrancy in feature structures

[Luis Casillas]

On Wed, Jul 03, 2002 at 01:32:28PM -0400, Jirka Hana wrote:

>
> > 4. A tree satisfies an atomic path equivalence PATH1 = PATH2 iff the
> >    the subtree rooted at the node reached by following PATH1, and the
> >    subtree rooted at the node reached by following PATH2, are identical.
>
> If I understand you well, you are loosing the distinction between type and
> token identity.

Yes.  But there is another distinction sneaking in here; 4. says that, no
matter what information you add, you'll never be able to make the two
paths not be type identical, even if the values rooted under them are
unboundedly large.  You can't do this with a finite set of type-identity
statements.  In standard HPSG, the way you would enforce a type identity
would be with something like this:

|PATH1   |t1             | |
|        |A     t2       | |
|        |B     |t3    | | |
|        |      |C  t4 | | |
|        |      |...   | | |
|        |...            | |
|                          |
|PATH2   |t1             | |
|        |A     t2       | |
|        |B     |t3    | | |
|        |      |C  t4 | | |
|        |      |...   | | |
|        |...            | |


If there is an upper bound on the size of the subgraphs rooted under
PATH1 and PATH2 you can write some AVM which can only be satisfied if
the two values are type-identical.  But take a type that has an instance
of itself as a feature:

|nelist                       |
|CAR     t1                   |
|CDR     |nelist            | |
|        |CAR     t2        | |
|        |CDR     |nelist | | |
|        |        |...    | | |

Since there is no longest list, in the standard feature logic you can't
write a constraint that forces two indefinitely long lists to be
type-identical; any such constraint has to be finitely large, and as
such can't enforce type identity beyond the nth member of the list for
some n.  However, the condition I give as (4) can do it.

--
Luis Casillas
Department of Linguistics
Stanford University
http://www.stanford.edu/~casillas/