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Re: [ontolog-forum] orthogonal

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Wed, 05 Mar 2008 18:56:48 -0500
Message-id: <47CF3340.9010304@xxxxxxxx>
Jeffrey Schieffel wrote:    (01)

>> An ontology is intended to define the terms of a domain, and the
>> relationships ...  It enables semantic interchange.    (02)

>> 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.    (03)

I think we are talking past one another.  My email was directed at the 
inaccuracies in this characterization of "semantic interchange", as 
distinct from whether there was a usable definition of "orthogonality" 
somewhere in there.    (04)

My position is that two agents don't need to have non-overlapping 
ontologies to be unable to communicate effectively.  Their ontologies 
can have a 90% overlap, but if there is one critical idea that one has 
and the other does not understand, they can't do business.    (05)

The example:
>> If you think Cairo is a city in Egypt, and I think Cairo is a city in
>> Illinois, 
>> then we know we are talking about different places; but if the shared
>> ontology 
>> only tells us that Cairo is a city, we may think we are talking about
>> the same place.    (06)

Jeffrey wrote:
> Yes, but I am not talking about sharing. I'm defining orthogonality.    (07)

Surprise!  I presumed that a discussion of communication between agents 
and "semantic interchange" was about "sharing".  My error.    (08)

> 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.     (09)

Indeed.  My point was that it the existence of the common concept does 
not guarantee that any related term can be exchanged.  If there is one 
term that cannot be fitted into one agent's ontology, in this case the 
concept "Egypt", that is sufficient to cause communication failure.    (010)

In Pat's terminology, if there is ONE term in ontology O that does not 
have a "definition" that can be proved in ontology P, that is, if *one* 
term in ontology O 'is orthogonal to' P, then the communication between 
the agent using O and the agent using P is "impaired".  And if that term 
is critical to the reason for the communication (i.e., the 'joint 
business process'), then the communication between them is *critically 
impaired* -- they cannot safely or effectively execute the joint process.    (011)

(I should mention that this is precisely the focus of work in my group 
at NIST, which is why it is important to me to clarify this.)    (012)

> 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.     (013)

This is irrelevant.  In point of fact, the term needs to be 
disambiguated when written and when the characters are encoded in 
automated exchanges, which is a substantial majority of business cases. 
  When the communication is verbal, we are talking about the mental 
'ontologies' of the human agents, which is rather beyond our scope. And 
in that case, it is probably true that both names spelled "Cairo" in 
English have different pronunciations by different agents.  In 
Louisville and Natchez, they pronounce it Keruh, and in Egypt it is al 
Qairah.  So even human agents would have to sort out differences in 
pronunciation which are regional from differences in pronunciation 
intended to differentiate terms.  (I am reminded of the New Yorker who 
thought "Milla's Dock" was a Boston beer, while "Milla's Dawk" was made 
in Milwaukee, where of course, it was pronounced "Miller's Dark". :-))    (014)

> 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
> distance.    (015)

Well, the definition of orthogonality between ontologies as stated by 
Pat (which mirrored my less careful phrasing) is certainly yes/no.  But 
it makes use of the concept 'orthogonality' of a term to an ontology. 
The number of orthogonal terms between two ontologies might be a measure 
of "semantic distance".    (016)

> 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.    (017)

Ultimately, the communication between two agents will succeed if they 
both associate the 'things' that arise in their joint activity with the 
mutually agreed-upon behavioral concepts.  The universe of discourse for 
the joint activity is just the things at hand and the actions taken. 
The actual meaning of the concept in a larger world is not important.    (018)

And in a larger sense, coextension of concepts may be just as useful an 
indication of "semantic equivalence" as "provable definition".  But 
provable definition guarantees coextension, and the only other mechanism 
of proving coextension is total enumeration.    (019)

A priori, the two communicating agents only know some of the relevant 
instances -- the others are less predictable.  "Cairo" can be an element 
of the ontology that corresponds to a specific 'thing' in every/any 
related UoD, or it can be a 'thing' that arises in the active situation, 
where  both agents classify it as 'city' and 'destination', because of 
ontological alignment.    (020)

But Agent X and Agent Y both have internal ontologies that are *larger* 
than the *shared ontology* for the joint activity.  When all Agent X 
gets is "Cairo", because the concept "Country of destination" was not 
shared, his internal ontology may  implicitly supply the value "USA" (it 
is amazing how insular Americans still are).  And agent Y may understand 
"country" as a significant element of a destination, but be able to 
deduce it from the city identifiers in his normal universe of discourse, 
unaware that the designation "Cairo" isn't unique in the actual universe 
of discourse for the joint activity.  (This is yet another version of 
the problem Pat Hayes refers to as the "Horatio Principle" -- there are 
more things in heaven and earth, Horation, than are dreamt of in your 
philosophy.")  And that makes extensional measures of semantic distance 
quite tricky.    (021)

-Ed    (022)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (023)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (024)

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