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Date: Tue, 5 May 1998 15:41:25 -0500 (CDT)
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To: Harold Boley <boley@informatik.uni-kl.de>
From: Pat Hayes <phayes@coginst.uwf.edu>
Subject: Re: WordNet treelike
Cc: Andreas.Reuter@eml.villa-bosch.de, 'BSpillers' <skydog@pacbell.net>,
'EHovy' <hovy@isi.edu>, 'GMiller' <geo@clarity.princeton.edu>,
'JSowa' <sowa@west.poly.edu>,
'KTschira' <Klaus.Tschira@ktf.villa-bosch.de>,
'LPolanyi' <polanyi@pal.xerox.com>, 'NGuarino' <guarino@ladseb.pd.cnr.it>,
'SPeters' <peters@csli.stanford.edu>,
'AFarquhar' <Adam_Farquhar@ksl.stanford.edu>,
'CFellbaum' <fellbaum@clarity.princeton.edu>,
'DSkuce' <doug@csi.uottawa.ca>,
'EFeigenbaum' <feigenbaum@ksl.stanford.edu>, 'FLehmann <fritz@cyc.com>,
'JMcCarthy' <jmc@cs.stanford.edu>, 'JPustejovski <jamesp@cs.brandeis.edu>,
'JTsujii' <tsujii@is.s.u-tokyo.ac.jp>, 'MvdBerg' <vdberg@us.ibm.com>,
'PHayes <phayes@nuts.coginst.uwf.edu>, 'PSimons' <p.m.simons@leeds.ac.uk>,
'WWahlster' <wahlster@dfki.uni-sb.de>
Greetings Harold
I agree that sort heirarchies are needed for nonunary predicates, however
things do get complicated rather rapidly. Take as an example the sorts
<human>, <man>, <lady> , with the first as the hypernym, and the binary
relation Married. In most states in the USA, the sort of Married is (man X
lady) U (lady X man), but excludes (man X man) and (lady X lady). In most
states of the USA one can be jailed for getting this wrong, so it is
important that the relational sort heirarchy keeps things straight.
We could allow a 'universal' Married relation with sort (human X human)
ie (man U lady) X (lady U man) to be the hypernym, but the relationship
between regular marriages and same-sex marriages is rather harder to state.
They are exclusive, for example, and neither of them can be determined by
specifying the sorts of their arguments; that is, there are no sorts S, T
such that the sort of these relations is S X T. Also, there are the sorts
(human X man) and (human X lady) and their reflections, which exist in the
abstract sort structure but are rarely discussed, presumably because their
sort structure is not preserved under the axiom of symmetry which is known
to be satisfied by the Married relation. (Contrast Parent, where we have a
collections of words for making exactly these distinctions: father, mother,
son, daughter.) This suggests that whether or not a combination of sorts is
to be allowed in the heirarchy must depend in part on what properties the
relation is supposed to have.
These issues have been discussed at length by others, in several contexts.
Sorted logics with disjoint-union sorts (like Married) were discussed at
length by Tony Cohn in his PhD thesis, and the theory of computation has
long had to deal with multiply-sorted languages in which functions and
relation sorting is 'overdetermined' in this way.
Pat Hayes
PS. Why do you say that
black-instrument(X:stringed-instrument^percussion-instrument)
is *more natural* than
black-instrument(X) /\ stringed-instrument(X) /\ percussion-instrument(X) ?
Does it have something to do with the stringedness and percussiveness of
the instrument being somehow more intrinsic to its functional role *as an
instrument* than its color? If so, is this something that could be
described in a theory of instruments (that they make sounds, say, and that
the sound of a string is different in musical quality than the sound of a
plate) sufficiently well that the naturalness of the former could be
figured out by examining the theory?
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