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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Len Yabloko" <lenya@xxxxxxxxxxxxx>
Date: Thu, 15 Jan 2009 23:19:00 +0000
Message-id: <W6008623708275221232061540@webmail32>
Sean and John,     (01)

>All the ontologies that have been proposed so far have been
>collections of statements (often called axioms) in some
>version of logic.    (02)

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    (03)

> > I have noted the use of standard data models to exchange
> > incompatible data - incompatible not because the data
> > structures were different, but because the groundings
> > of the model were different.
>I don't know what you mean by the word "grounding" or the
>term "data model".    (04)

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.
What may be called a "grounding" is this context is another structure (may be 
lattice) that orders A-Boxes. Then the question may be: how do these different 
structures relate and what to call them. I don't know the answer.    (05)

>If by grounding, you mean 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.    (06)

If we accept T-Box/A-box distinction, the the statement above is not 
necessarily true.    (07)

>I don't know whether there is some confusion of terminology
>or a true disagreement.
>    (08)

Neither do I. May be Pat H can help us.    (09)

>    (010)

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