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