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Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Matthew West" <dr.matthew.west@xxxxxxxxx>
Date: Wed, 17 Feb 2010 08:51:49 -0000
Message-id: <4b7bae23.1c07d00a.0623.ffffa813@xxxxxxxxxxxxx>
Dear John,    (01)

I think this is an important point.    (02)

> MW> For example, you could have a Linnean structure of living things
>  > that did not know about 3D or 4D, but could  take on either flavour
>  > when incorporated into those theories.
> My guess is that a conjunction of the Linnean theory with either
> a 3D or 4D theory of space & time would not cause any inconsistency.
> But you can test the consistency by a variation of the method above:
>   1. Start with a model for which one of the theories is true.
>      Store the data that represent that model in a relational DB.
>   2. Take the axioms of the theory that you want to combine it
>      with, convert each one to an SQL query, and check them
>      one at a time by executing the query.
> Note that the WHERE clause of an SQL query can express full FOL.
> Therefore, any axiom stated in first-order logic (or any subset
> of FOL) can be tested just by translating it to SQL.
> MW> This could have considerable value in achieving interoperability,
>  > and might well be the useful thing that arises from Pat C's vision
>  > of a common defining vocabulary, though I don't think there is any
>  > such vocabulary that is finite, but if we have extensibility, that
>  > does not matter too much, we just add what we need when we need it.
> Actually, the likelihood of inconsistency *increases* when you have
> a great deal of common vocabulary.  If two theories have nothing
> in common, it's unlikely that they disagree about anything.  But
> if they have a lot of terms defined in a common vocabulary,
> the likelihood of an inconsistency is greater.
MW: I think it is more than just a vocabulary, but I agree that great care
would need to be taken not to introduce into what I am calling abstract
theories axioms that did not contradict say the 3D and 4D axioms that would
be introduced when they were combined with those theories. However, having
such a theory would greatly simplify mapping between say 3D and 4D
ontologies. These would I think need to be carefully designed rather than
just picking something up, since it is casually almost certainly made some
upper ontology assumptions.    (03)

Regards    (04)

Matthew West                            
Information  Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
http://www.matthew-west.org.uk/    (05)

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