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[ontolog-forum] Automated Ontology Mapping

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: Bart Gajderowicz <bgajdero@xxxxxxxxxx>
Date: Tue, 24 Mar 2009 01:49:36 -0400
Message-id: <6b20199d0903232249sc1e9e50ja0083ba0aa66f52c@xxxxxxxxxxxxxx>
Hello,    (01)

This is my first posting on this forum, so let me introduce myself.
My name is Bart Gajderowicz, and I'm a graduate student at the
Computer Science Department at Ryerson University, in Toronto, Canada.    (02)

I am researching automated ontology mapping, and have compiled several
options which span the different categories currently being developed.
 Let me formally define these as per (Choi, et al 2006). Based on this
work, I am currently looking at the several fields/ideas to introduce
partial consistency to automate the mapping process.    (03)

I welcome any comments, corrections, suggestions, criticisms from the
forum on the following analysis.    (04)

Some of the current techniques take a deductive approach, and
concentrate on the structures, axioms, and hierarchies of the
ontology.  Others take an inductive approach, and look at instances in
order to derive what objects are being modelled.  Others still are a
hybrid of the two.  At this point I'm looking at both approaches, to
see which direction is more appropriate for my research.    (05)

I'm currently concentrating my efforts on ontologies defined by first
order languages such as Common Logic. I'm  doing this to take
advantage of provers and inference engines, but also to limit my
domain to these languages, so compatible representation becomes less
of a headache.    (06)

At this point, I would also like to concentrate on structural and
taxonomic similarities, with a limited amount of lexical similarity
measures.  Preferably, no natural language processing would be
performed on terms at this time.  This may limit my ability to perform
schema or semantic mapping.  In FOL, however, I have the ability to
apply unification techniques on a set of axioms, to align free and
bound variables.    (07)

Because ontologies may, and will define the same concepts differently
(depending on the context, a subject matter expert's knowledge, their
modelling approach, etc.), checking for consistency will be necessary,
but also tricky, which I realize is a serious understatement.  Most
systems currently in place have some level of manual verification, but
if a system's domain is to expand to a large repository, with an
active community contributing often, a fully automated system would be
desirable.  This can naturally be extended to the web, and semantic
classification of documents.  My task now is to see how far an
algorithm can go before some level of partial consistency is
introduced, and how this introduction is executed.    (08)

To that end, I am currently looking at the following fields/ideas to
introduce partial consistency:    (09)

1) A similarity measure can be evaluated by looking at properties such
as isomorphism, injection, surjection, associativity, commutativity,
and distributivity between some classes, but not others, in different
ontologies.    (010)

2) Perhaps Prototype Theory will allow me to formally define some key
terms, as a type of local upper ontology.  In OntoClean (Guarino, et
al 2004), for example, the first process was to define a “backbone
taxonomy of terms” to which all other terms were grounded.    (011)

3) Fuzzy Logic may also be suitable, by creating membership functions
which include some sets of axioms attributes, or properties, but not
others, and overlapping relations may be true to some degree.  As was
pointed out to me, these would define a maximum entropy, which is used
in the data mining field, not logic.  This may still be worth looking
at, for inductive analysis.  Perhaps a redefinition of inconsistent
FOL clauses to Fuzzy Logic could be done in a such a way that intended
meaning of axioms are persevered, and theories are weakened to
accommodate the discrepancies.  This approach would greatly limit the
decidability of theories, but if key axioms are pointed out, with
corresponding degrees, perhaps this limitation is worth the gains.
GLUE, for example, uses a Naive Bayes  learner to analyse statements
of ontologies.    (012)

4) Perhaps adding Modal Logic into the mix, and saying that some set
of properties define a concept now, but not at a later time, could be
a way of quantifying differences between concepts in different
ontologies.  Think of a Wikipedia entry where the definition of a term
may change with popular opinion or when more information becomes
available.    (013)

5) Contexts may be generated where some axioms are added or removed.    (014)

References:    (015)

Choi, N., Song, I.-Y., Han, H., A survey on ontology mapping (2006),
SIGMOD Record, 35 (3), pp. 34-41.    (016)

Guarino, N., Welty, C., Evaluating ontological decisions with
ontoclean (2002), Communications of the ACM, 45 (2), pp. 61-65.    (017)

Thank you.
Bart Gajderowicz
MSc Candidate, '10
Dept. of Computer Science
Ryerson University
http://www.scs.ryerson.ca/~bgajdero    (018)

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