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Re: [ontolog-forum] orthogonal

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From: "Schiffel, Jeffrey A" <jeffrey.a.schiffel@xxxxxxxxxx>
Date: Wed, 5 Mar 2008 16:29:23 -0600
Message-id: <ECF42862FCA16D41BFA98F8C45F09554046FA141@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
A number of comments have shown up. Rather than responding as they
occurred, which would be confusing to follow, I've consolidated them for
my replies.    (01)

Originally,     (02)

> From: Alexander Garcia Castro     (03)

> Hopefully this is not so out of focus. I am looking for a definition
> for orthogonality. When are ontologies orthogonal? Any body who can
> recommend me some good papers about orthogonal ontologies? Is there
> a measure for orthogonality?     (04)

To which I suggested,    (05)

> From Jeffrey Schiffel    (06)

> An ontology is intended to define the terms of a domain, and the
> machine. It enables semantic interchange.
> If two agents, each using an ontology, cannot exchange terms that can 
> be fitted into the respective ontology each is using, then they must
be using 
> different, non-overlapping ontologies. These two ontologies would be 
> orthogonal. No term or relation in one ontology would have meaning in
> other. The ontologies would be mutually exclusive.    (07)

Pat Hayes then rightly noted,    (08)

> Careful. In one (widely accepted) sense of 'definition', most
> are written in languages which do not support definitions. 
> (Examples: RDF, UML, OWL, Common Logic)    (09)

Pat is correct. I should have stated not _define_ but _tag_. The
concepts of a domain
need to be tagged (or named, listed, rostered, etc.). So to the
relationships among them.    (010)

PH also adds,    (011)

> What exactly do you mean by 'fitted into'? OWL, RDF and CL *always* 
> allow for exchange of terms, so this notion of 'fitting' must mean 
> more than simply "adding to".    (012)

I mean only that if the ontologies are orthogonal, they share nothing in
common. This does
not mean that that situation cannot change. If a concept is added to
each and shared,
the two are no longer orthogonal.    (013)

> So 'orthogonal' simply means 'different' ? Is that really what you
mean to say?    (014)

No, I mean to say (and did) _mutually exclusive_, in the sense that in
set theory two sets are mutually exclusive if their intersection is an
empty set .    (015)

Ed Barkmeyer added this to the dialog,    (016)

> Well, having a shared ontology "enables semantic interchange" within
the limits of what 
> is actually shared.  In practice, many of the concepts required for an
interchange do not
>  have formal definitions, and the ontologies treat them as "primitive
concepts" with 
> natural language definitions and some formal properties that are
helpful in identifying 
> the intent (and useful in reasoning about them).
> If you think Cairo is a city in Egypt, and I think Cairo is a city in
> then we know we are talking about different places; but if the shared
> only tells us that Cairo is a city, we may think we are talking about
the same place.    (017)

Yes, but I am not talking about sharing. I'm defining orthogonality.
This is not to say,
however, that some third ontology -- an upper ontology -- could enforce
some sort of sharing, if thet were desired.    (018)

As for the Cairo example, two points. First, if both ontologies have
_city_ in them, then there is at least one shared concept, hence they
are not orthogonal. For that matter, the name _Cairo_ needs to be
disambiguated only when written. The Egypt and Illinois cities are
pronounced differently, so there is no conflict in the instances. There
remains, however, an overlap in the shared concept _city_.     (019)

The Cairo example brings up an additional point that was in Alexander
Garcia Castro's original question. It is: is there a measure for
orthogonality? My take is that if orthogonality is a matter of degree (I
stated it isn't), then the underlying question is one of semantic
This, then, raises the further question of the two kinds of tags in an
ontology, the tags for concepts, and the named instances of the concepts
in the ontology. I suspect the semantic distance is measured by the
instantiated elements.    (020)

Regards,    (021)

-- Jeffrey Schiffel    (022)

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