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Re: [ontolog-forum] FW: Lattice of theories

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Len Yabloko" <lenya@xxxxxxxxxxxxx>
Date: Fri, 16 Jan 2009 19:18:03 +0000
Message-id: <W3186316035192041232133483@webmail6>
John,     (01)

I think there is more to it than simple terminological differences.    (02)

>As I said, they are "often" called axioms.
>JFS>> All the ontologies that have been proposed so far have been
> >> collections of statements (often called axioms) in some
> >> version of logic.
>LY> I think that you are talking about different ontologies here.
> > Using Semantic Web terminology the set of axioms is called "T-Box"
> > (if I not mistaken "T" refers to taxonomy or terminology or both)
> > The is also so called A-Box http://en.wikipedia.org/wiki/ABox
>The terms T-box (Terminology statements) and A-Box (Assertion
>statements) were introduced with KL-ONE, an early definition logic.
>(But if you consider Aristotle's syllogisms the most widely used
>definition logic of all time, then everything else is late.)  Since
>many of the people who developed OWL came from the DL community,
>they tended to use that terminology.    (03)

T-Box/A-Box distinction is highly remenicent (to say the least) of 
class/individual or type/instance. I think these are the closest common 
ancestors to both terminologies - not syllogism. This had been discussed on 
this forum many times, but I still fail to see how all these different branches 
of logic relate.    (04)

When describing lattice of theories you used the term "type" seemingly 
interchangeable with "theory". According to your description the lattice of 
theories is simply ordering lattice for types. The question then is: what 
operation does this order corresponds to ( must be some sort of composition 
operator).     (05)

>LY> It seems that Sean is calling T-Box a "data model" and his concern
> > is that the lattice of T-Boxes is not useful for some reasoning with
> > A-Boxes.
>The term 'data model' comes from the database community, which is
>nearly disjoint from the DL-community.  That is one of my primary
>complaints about the Semantic Web:  they did not integrate both
>communities.  That is a serious deficiency, since the DB community
>is far and away the largest consumer and developer of logic-based
>technology for commercial applications.    (06)

I agree with you and have been listening to your complains very carefully. In 
fact for a long time now I am building a bridge between two communities in a 
form of open-source project called Ontobase 
(http://semwebcentral.org/projects/ontobase/)    (07)

>In the DB community, the statements in the T-box correspond to
>the database schema and the constraints on permissible updates.
>JFS>> If by grounding, [Sean] means some part of the world for
> >> which some set of statements (or axioms) are true, then two
> >> identical sets of statements would be true of exactly the
> >> same parts of the world.  Therefore, identical axioms would
> >> have identical grounding.
>LY> If we accept T-Box/A-box distinction, the the statement above
> > is not necessarily true.
>That statement is true for all versions of logic.  Therefore, it is
>true for description logics, database logics, and the Semantic Web.
>It is also true for the larger, more general logics used in large
>systems such as SUMO (the KIF language) and Cyc (the CycL language).
>All of them are versions of logic, but they use different terminology.
>Bottom line:  For the Foundation Ontology, we should use the more
>general terminology of logic instead of the specialized terms used
>for one special case after another.
>John Sowa.
>    (08)

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