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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 16 Jan 2009 16:55:28 -0600
Message-id: <43C23243-67C8-4C5A-BAAC-C37F5D7F2580@xxxxxxx>

On Jan 16, 2009, at 11:37 AM, John F. Sowa wrote:    (01)

> Len,
>
> 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.    (02)

Exactly. The contents of all these boxes are all logical axioms/  
sentences/ assertions/ whatever. John is perfectly correct here:    (03)

>
> 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.
>
+1    (04)

But, one quibble:    (05)

> 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.    (06)

It doesn't depend on the logic, but it is possible to read it in a  
wrong way. The point is that the logic itself, alone, does not fully  
determine how its symbols are to be interpreted in the actual world  
that the logic is supposed to be describing. It _constrains_ possible  
interpretations, but something outside the actual logic will need to  
be used to 'anchor' or 'ground' it to real actual cases. (I know John  
agrees with this as he has been one of the most tireless exponents of  
this point.) Given this fact, therefore, one could interpret what Sean  
is saying as the observation that one set of axioms may be 'grounded'  
- attached to the real world, interpreted - in two different ways, and  
would then have two different meanings, in some sense. And if one then  
thinks of an ontology as comprising not just the axioms but also some  
other, less formal but still important, aspect which determines this  
'grounding', then one set of axioms might be in common between two  
different ontologies (in this 'grounded' sense of the term  
"ontology"), so having the same axioms need not determine the identity  
of an ontology (in this sense). Now, this is just plain true, and we  
all have to learn to live with it. (And I don't think that John meant  
to deny it, above.) However, I would prefer that we reserve the word  
"ontology" for the axioms (or whatever we call the things in the  
various boxes), not for this more amorphous notion of "axioms plus  
grounding", as I have absolutely no idea how to make sense, with this  
latter interpretation, of the phrase "ontology engineering" :-)    (07)

PatH    (08)

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>    (09)

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