Default unification: online vs. offline

[Raquel Fernandez]

Rob Malouf wrote:

> I don't think there are serious computational or formal problems with using
> persistent defaults.  The LKB implementation of Lascarides and Copestake's
> (1999) YADU operator is quite fast and robust, and for now at least it looks
> like if unification is fast enough for your purposes, then default
> unification probably will be fast enough too.

  Apparently, YADU (L&C 1999) can manage pretty well with default unification,
however it doesn't provide a good solution to deal with a
  multi-dimensional type hierarchy.

  According to YADU, a default TFS is calculated from a TDFS by unifying in the
maximal set of compatible elements of the
  union of the tails to the non-default TFS in *priority order*. The priority
order is given by the ordering in the type hierarchy. In the case
  where there is conflict between the default information, the specificity or
priority of the position of the root type in the type hierarchy
  determines which default information in the tail wins.

  The fact is that in a type hierarchy with multiple inheritance (like G&S 2001),
a subtype can inherit constraints from types belonging to
  different dimensions (which are not related in terms of specificity). So, in
the case where the supertypes contain (conflict) default
  information, it is not possible to calculate a default TFS according to the
specificity in the hierarchy. However, it's possible to use defaults
  and YADU `in some part' of the hierarchy as long as it behaves as a bounded
complete partial order (apparently a multidimensional
  inheritance hierarchy is not a BCPO, G. Erbach 1994). This seems to be the case
with the default GHFP: this default principle can only
  be overridden by constraints on types in the HEADNESS dimension of the
hierarchy.

  Maybe this is not too relevant for the previous discussion and probably the
problem can be solved without too much effort, but I think it's
  important to keep in mind that we still need a default unification for a
multidimensional typed hierachy.


 Best,
 Raquel

--
Raquel Fernández Rovira

NLP Group,
Dept of Computer Science
King's College London
The Strand,London WC2R 2LS,UK

phone: +44 (0)20 7848 2476
raquel at dcs.kcl.ac.uk


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