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Re: [ontolog-forum] Is there something I missed?

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Mike Bennett <mbennett@xxxxxxxxxxxxxxx>
Date: Thu, 29 Jan 2009 15:20:55 +0000
Message-id: <4981C957.8070002@xxxxxxxxxxxxxxx>
A distinction I find useful (though not very formal) is that ontology 
(singular) is the study of what is, while ontologies (plural) are the 
representations of reality that exist - whether you know about it or not 
- within individual computer systems and databases, i.e. the local 
representation of the reality about which the computer is manipulating 
symbols, with varying degrees of success.    (01)

I don't know how well grounded or attested that working definition is 
though.    (02)

A formal modern ontology is a good tool for discovering some of that 
undocumented or implied ontology that is lurking around various systems 
and databases.    (03)

Mike    (04)

Ali Hashemi wrote:
> The following from Guarino (2008) is apt here, i think:
>
>         In the philosophical sense, we may refer to an ontology as a
>         particular system of categories accounting for a certain
>         vision of the world. As such, this system does not depend on a
>         particular /language:/ Aristotle's ontology is always the
>         same, independently of the language used to describe it. On
>         the other hand, in its most prevalent use in AI, an ontology
>         refers to an /engineering artifact,/ constituted by a specific
>         /vocabulary/ used to describe a certain reality, plus a set of
>         explicit assumptions regarding the /intended meaning/ of the
>         vocabulary words. This set of assumptions has usually the form
>         of a first-order logical theory, where vocabulary words appear
>         as unary or binary predicate names, respectively called
>         concepts and relations. In the simplest case, an ontology
>         describe a hierarchy of concepts related by subsumptions
>         relationships; in more sophisticated cases, suitable axioms
>         are added in order to express other relationships between
>         concepts and to constrain their intended interpretation.
>
> (Guarino 2008, pp14-15)
>
> Though i'm not sure why vocabulary words are restricted to unary or 
> binary predicate names, it seems there'd be a lot of useful things to 
> say with terms that range directly over /n/ variables.
>
> An observation on a lot of literature i've come across, a lot seems to 
> focus on the taxonomic component of ontologies, when they can be, as 
> Guarino notes/, /more sophisticated. I wonder if this might be a 
> reason there have been no /killer apps/ for the field yet.
>
> // Ali
>
> On Thu, Jan 29, 2009 at 9:33 AM, Pat Hayes <phayes@xxxxxxx 
> <mailto:phayes@xxxxxxx>> wrote:
>
>
>     On Jan 29, 2009, at 5:55 AM, Azamat wrote:
>
>     > On Thursday, January 29, 2009 1:15 AM, Sean aked:
>     > "is there a formal definition of an ontology?"
>     >
>     > 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".
>
>     That is the definition of ontology, the philosophical field. When the
>     word is used in this (original) sense, the construction "an ontology"
>     is ungrammatical. The sense of "ontology" agreed to in this forum
>     dates back less than two decades, and has its origin in AI, not
>     philosophy. While the two senses are related, its important not to get
>     them confused with one another.
>
>     PatH
>
>     > 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].
>     >
>     > Azamat Abdoullaev
>     > http://www.eis.com.cy
>     >
>     >
>     > ----- Original Message -----
>     > From: "Sean Barker" <sean.barker@xxxxxxxxxxxxx
>     <mailto:sean.barker@xxxxxxxxxxxxx>>
>     > To: <ontolog-forum@xxxxxxxxxxxxxxxx
>     <mailto:ontolog-forum@xxxxxxxxxxxxxxxx>>
>     > Sent: Thursday, January 29, 2009 1:15 AM
>     > Subject: [ontolog-forum] Is there something I missed?
>     >
>     >
>     >>
>     >>
>     >> 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
>     >>
>     >>
>     >>
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>      (05)


-- 
Mike Bennett
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