Re: clarifying clarifying ontologies

fritz@rodin.wustl.edu (Fritz Lehmann)
Date: Mon, 7 Aug 95 23:41:53 CDT
From: fritz@rodin.wustl.edu (Fritz Lehmann)
Message-id: <9508080441.AA08216@rodin.wustl.edu>
To: cg@cs.umn.edu, forbus@ils.nwu.edu, hovy@isi.edu
Subject: Re: clarifying clarifying ontologies
Cc: doug@csi.uottawa.ca, fritz@rodin.wustl.edu, phayes@cs.uiuc.edu,
        srkb@cs.umbc.edu
Sender: owner-srkb@cs.umbc.edu
Precedence: bulk

     Ken Forbus wrote:
---begin quote---
Presumably the taxonomies in the NL system are reasonably consistent with
whatever axiomatization is used in those areas with the deeper semantics.
It would seem to me that the form of the deeper semantics would seriously
constrain the taxonomies.  In your experience, (a) do such mismatches occur,
and (b) if they do, how are they resolved?
---end quote---

     I don't know how or whether constraining axioms are integrated into
Hovy/Knight/Luk's Pangloss hierarchy (I would like to know), but I can
comment on other KRep systems I've read about, written about or reviewed.

     Generally, the hand-built hierarchy and the hierarchy of classes induced
by definitions (including constraining axioms) constrain each other.  In
KL-ONE systems the former are made of "primitives" and both together
form the TBOX (terminological box) although certain axioms are relegated
to the ABOX (assertional box) if they exceed the expressive power of the
terminology.  In Conceptual Graphs, there is a hand-built type hierarchy
built with "TYPEA < TYPEB" statements, which together with defining graphs
induces the structure on all possible CGs.  Without types, CGs form the
same subsumption poset as do equivalence-classes of descriptions in 
predicate logic: a poset based on homomorphic embedding of directed
hypergraphs (which provides the ordering of the poset).  In CGs, if you
_define_ concepts A and B as graphs such that A properly subsumes B, and then
_declare_ that "A < B" contradicting the relation induced by the graphic
definitions, it's just a bug, and needs to be corrected.  In Order-
Sorted Logics (like Frisch's and Cohn's) the same subsumption can be
stated in the sort-lattice or as a logical axiom -- they deal with
how the two methods interact in some of their papers.

     I have not actually seen (or written) a program which correctly
builds the full poset of classes based both on the explict taxononmy-building
statements and also on the hierarchy induced by _all_ the axioms in
which the classes participate.  The closest are some KL-ONE programs,
some French Conceptual Graph programs, some Dynamic Case-Based papers, and work
by the students of Rudolf Wille at TH-Darmstadt.  It ought to be an easily
soluble technical problem so maybe someone has already done it right.
(I treated a sub-problem with my "Fret Product" in Ellis & Lehmann in
ICCS-95, Springer LNAI 835, 1994.)  Franz Baader and others will have 
relevant papers on this issue at the KRUSE conference at Santa Cruz in
three days.

                             Yours truly,  Fritz Lehmann