On Thursday, January 29, 2009 1:15 AM, Sean aked:
"is there a formal definition of an ontology?" (01)
Good question. It seems there are as many definitions as many schools,
researchers and developers.
But the right one is that involving the original nature and meaning of
ontology as:
"Formal Ontology is the formal study of Reality". The issue of issues is how
Reality is related with the whole world (the totality of entities and
relations), particular worlds, or possible worlds; and how it could be truly
and consistently represented and effectively reasoned [by humans and
machines]. (02)
Azamat Abdoullaev
http://www.eis.com.cy (03)
 Original Message 
From: "Sean Barker" <sean.barker@xxxxxxxxxxxxx>
To: <ontologforum@xxxxxxxxxxxxxxxx>
Sent: Thursday, January 29, 2009 1:15 AM
Subject: [ontologforum] Is there something I missed? (04)
>
>
> Folks
>
> Having followed this forum for some time, I have a feeling that I may have
> missed something so obvious that noone 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
>
>
>
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