At 4:29 PM -0600 3/5/08, Schiffel, Jeffrey A wrote: (01)
>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.
>
>Originally,
>
>> From: Alexander Garcia Castro
>
>> 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?
>
>To which I suggested,
>
>> From Jeffrey Schiffel
>
>> An ontology is intended to define the terms of a domain, and the
>relationships
>> 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
>the
>> other. The ontologies would be mutually exclusive.
>
>Pat Hayes then rightly noted,
>
>> Careful. In one (widely accepted) sense of 'definition', most
>ontologies
>> are written in languages which do not support definitions.
>> (Examples: RDF, UML, OWL, Common Logic)
>
>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.). (02)
?? First, this makes no sense. Tagging is done to
non-semantic objects which resist classification,
typically images. What would be the point of
tagging an ontology concept (which already has a
perfectly good name, or it would not be in the
ontology in the first place) ? (03)
Second, what has tagging got to do with being 'orthogonal' ? (04)
> So to the
>relationships among them.
>
>PH also adds,
>
>> 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".
>
>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.
>
>> So 'orthogonal' simply means 'different' ? Is that really what you
>mean to say?
>
>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 . (05)
OK, sorry. They are orthogonal if they share no
concepts; in logical terms, if their vocabularies
are disjoint. Is that right? That is an admirably
simple and clear notion, although it does not
seem to support what you say about orthogonality
elsewhere in the message. For example, in this
case it is clearly possible to conjoin orthogonal
ontologies into a single merged ontology, right? (06)
Pat (07)
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