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[ontolog-forum] What is an Ontology [was - Re: Is there something I miss

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Peter Yim <peter.yim@xxxxxxxx>
Date: Wed, 28 Jan 2009 23:20:45 -0800
Message-id: <af8f58ac0901282320l549eec20sb3bd4e7a309d5ec0@xxxxxxxxxxxxxx>
> [SeanBarker]   is there a formal definition of an ontology?    (01)

[ppy]  This community has actually adopted something previously ...
(ref. http://ontolog.cim3.net/cgi-bin/wiki.pl?ConferenceCall_2006_01_12#nidOHT )    (02)

See: http://ontolog.cim3.net/cgi-bin/wiki.pl?ConferenceCall_2006_01_12
plus http://ontolog.cim3.net/cgi-bin/wiki.pl?OntologySummit2007_Communique    (03)

--    (04)

On Wed, Jan 28, 2009 at 3:15 PM, Sean Barker <sean.barker@xxxxxxxxxxxxx> wrote:
> Folks
> Having followed this forum for some time, I have a feeling that I may have
> missed something so obvious that no-one has thought to mention it - that is,
> is there a formal definition of an ontology? An ontology cannot be just be a
> bowl of axiom soup, so how does one tell that a particular collection of
> axioms is an ontology - the question is posed on the analogy that
> mathematicians differentiate between a group, a ring and a field by the
> axioms they include. My naive guess for this would be based on set theory,
> and look something like:
> 1) A set S can be defined as S = {x s.t. x satisfies some combination of
> predicates};
> 2) Given a set of predicicates P = {p1, p2,...,pn} and a set of logical
> operaters L = {l1, l2,...,ln} (perhaps just AND, OR and NOT), then denote
> Spl as a set defined from some combination of predicates in P and operators
> in L, and Spl* is the set of all possible sets Spl (perhaps regularised to
> remove contraditions);
> 3) An ontology is constructed by taking a collection of sets from Spl* and
> identifying a partial ordering of those sets using the usual subset
> relationship.
> This would split the study of ontology into three area:
> 1) the formal problem of ontology as being concerned with the types of
> mappings (homomorphisms, homeomorphisms, etc) between different ontologies
> based on the choices from some Spl*
> 2)the practical problem as finding an ontology that supports the decision
> procedures in a particular process (I include classifying something as a
> decision procedure).
> 3) the computational problem of defining of terminating and efficient
> procedures for comparing ontologies and mapping between them.
> (Thanks to Pat Hayes for this suggestion - even his more acerbic comments
> can be quite enlightening.)
> I would then expect there to have been a number of competing definitions,
> and any number of arguements discussing the relative merits of these
> definitions. And possibly some argument demostrating that this whole
> approach is flawed.
> My question is, where are these definitions and the ensuing arguments? and
> is there a good summary of these?
> Sean Barker
> Bristol, UK    (05)

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