Type identity

[Viktor Tron]

Hello,

Correct me if I am wrong, but the way I conceptualized them, typed
feature structure frameworks do not offer a straightforward
interpretation for type equality. Since the signature is a lattice, it
is not immediately obvious how type equality is computed for two
objects, more specifically: types of what level of specificity are
checked for equality. As an extreme case all objects are type identical
since they are equivalent by virtue of being instances of type 'top'.

A way out may be to interpret type euality as equality of sorts (most
specific/maximal type). This makes more sense given that it also have a
couterpart (sort assignment function) in the model (at least in
description logic approaches to FSs, like King).
However: if your calculus is categorical (ie., every two objects in the
model is distinguishable, more simply, you have a way to
express/describe their difference), then different atomic structures
(for which no features are defined) must belong to different sorts. This
means that in a categorical calculus, atomic objects are token identical
if and only if they are sort identical, which makes type equality
uninteresting for them.
As for non-atomic ones, sort identity would only force features defined
for the given sort to be defined for the two objects as well as force
their values to have types enabled by the signature (sort
appropriateness conditions), and of course they should both obey all
constraints imposed on the sort by the grammar. More simply put, it
imposes identity between the two objects to the extent instances of the
resolved sort are identical.
This is crucially different from token identity, which requires (at
least) that values of all paths be identical for the two FSs.
Since features and values are arbitraily assigned to sorts, for
instance, agreement could be expressed as sort identity on the level of
cat/sign
(as opposed to structure sharing whithin the index) simply by making
subsorts of cat/sign corresponding to equivalence classes of the
agreement relation.

This might be appropriate, but I wonder if one can get rid of all
non-substantial (ie., (morpho)syntactic) features (which are not
set/list valued) this way: feature government constraints are conceived
of as equivalence relations and imposed by type equality on sorts in an
appropriately arranged multiple inheritance hierarchy of signs.

The problems with token-identity and related problem of total sort
resolution has been noticed as early as Ingria 1990 in connection with
agreement phenomena and coordination with morphologically ambiguous
forms. Some papers addressing this issue might be interesting to you.
Actually, I am not sure if type identity is in any direct way related to
this problem, though :-)

http://www.coli.uni-sb.de/~tron/ToRead/Agreement/bayer-jophnson.ps
http://www.coli.uni-sb.de/~tron/ToRead/Agreement/dalrymple-1998-1229.ps
http://www.coli.uni-sb.de/~tron/ToRead/Agreement/agree.ps
and a recent proposal in HPSG:
http://www.coli.uni-sb.de/~tron/ToRead/Agreement/daniels-feature-indeterminacy01.ps

Cheers,

Viktor Tron

--
Viktor Tron, PhD student                     www.coli.uni-sb.de/~tron
Europeaische Graduiertenkollieg              www.coli.uni-sb.de/egk
Dept of Computational Linguistics            www.coli.uni-sb.de
Saarland University (Saarbruecken, Germany)  www.uni-saarland.de
University of Edinburgh (Scotland, UK)       www.ed.ac.uk
use LINUX and FREE Software                  www.linux.org
tron at coli.uni-sb.de                          49.681.302-3829