Thanks to Peter for the references on the forum. (01)
Thanks to the various contributors of informal definitions. (02)
Thanks to Pat Hayes for actually answering the question (pity there are no
pubs in Florida, I feel I must owe you a firkin or so for your answers). (03)
Following Pat's reply, I would like to add two comments: (04)
a) I have assumed that ontology is not the study of what one can say
about arbitrary collections of axioms - I guess that tends to send one
off down the description logic route. But my interpretation of Pat's
response is
- given your motivation is to produce an ontology -
there is no formal set of properties on the axioms that make it an
ontology. OK, then (05)
b)
one can move the goal and ask, are there certain classes of ontology
for which there is a formal definition, and for which it is interesting
to look at the mappings between them? (06)
For example, one might start with a directed graph of nodes N = {n1,
n2,...} and arcs A = (a1, a2,...) and define a hierarchy as a directed
graph which has a function f(N) -> natural numbers such that if ni is
related to nj by some arc in A, then f(ni) < f(nj);
Then a forest is a hierarchy where (n2 is related to n1) and (n3 is
related to n1) implies that (n2 equals n3);
A tree is a forest where there is exactly one node nk for which there is
no arc in A such that ni is related to nk (for all ni). (07)
One can then ask questions about whether one can map a particular
ontology onto a tree, or a forest or a hierarchy, and the classes of
ontologies a particular representation might support. For example, one might
decide that to be useful, an ontology written in RDF-Schema contains at
least two trees, one
for things and one for properties. (The common feature that everthing is a
URI is a fact about the
ontology of representation, not the ontology represented). (08)
One would also ask what systems of axioms are equivalent to an "interesting"
subclass of ontology -
I would be surprised if everyone used the same axioms as those above to
define a tree. (09)
I suppose this question is motivated by the concern that when
engineering a particular ontology, one needs to give comprehensible
guidelines to the engineer so that they don't accidentally produce an
incompatibility with any other ontology that their system may interact
with - particularly in aerospace with the ISO SC4 standards and the
ontologies they imply. (010)
Sean Barker
Bristol, UK (011)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: 29 January 2009 07:50
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Is there something I missed? (012)
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On Jan 28, 2009, at 5:15 PM, Sean Barker wrote: (015)
>
>
> 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 (016)
> - that is, is there a formal definition of an ontology? (017)
I think we spent about a year discussing this one :-) For myself, I use
the word to refer to a body of formalized knowledge in the form of
sentences (often called 'axioms') written in some widely recognized
formal notation, preferably one that is standardized in some way and
used by more than a handful of people or organizations. This usage is
quite common, I think fairly standard. (018)
> An ontology cannot be just be a
> bowl of axiom soup, (019)
Well, no, thats exactly what it is. (Why do you say "just" ?) (020)
> so how does one tell that a particular collection of axioms is an
> ontology (021)
I agree that ontologies are usually thought of as being purposeful,
organized, rational in some way, having a topic or focus, etc., - as
opposed to merely random collections of formal sentences - but as these
attributes are very hard to make precise, and as one person's rational
and focussed may be another person's loose and disorganized, there seems
to be very little utility in trying to legislate or precisely define the
boundaries of rationality or organization.
Technically, for example, the OWL standard asserts that any
syntactically legal collection of OWL axioms is an OWL ontology. (022)
> - the question is posed on the analogy that mathematicians
> differentiate between a group, a ring and a field by the axioms they
> include. (023)
... by the axioms that describe them, more accurately. One might say,
each kind of structure has a defining ontology, in fact. (024)
PatH (025)
> ------------------------------------------------------------ (026)
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