# RE: rdf as a base for other languages

From: pat hayes <phayes@ai.uwf.edu>
Date: Thu, 7 Jun 2001 11:56:19 -0500
Message-Id: <v04210156b7454cb99c22@[205.160.76.219]>
To: "Ziv Hellman" <ziv@unicorn.com>

```> >I agree that would be a desirable goal. BTW, the 'A-/T-box'
> >terminology was originally used to distinguish assertions from
> >definitions (of concept vocabulary) , which isnt quite exactly the
> >same as the ground-fact/rule distinction.
> >
>
>Could you elucidate the distinction between definitions and
>assertions, and explain how this differs from ground-fact/rule?

Ah, now I have painted myself into a corner, since I never fully
understood the definition/assertion distinction myself, though it
seemed central to many folk (and still does). Although to be fair,
the idea of a definition is a pretty common one in mathematics and
life generally, in spite of its having no obvious logical content.
The intuition as I understand it is that saying that Foo is defined
by a certain assertion (eg a biconditional, say, but it could have
any logical form) is saying more than simply that the assertion is
true of Foo; it is saying that this condition is in some sense 'all
there is' to the meaning of Foo; that it completely defines the
meaning. This is not to say, of course, that the definition
completely specifies all the facts involving Foo, since the whole
point, usually, of defining concepts is so that they can be handily
used to state new facts. But it does imply a distinction between the
facts about Foo that are definitional in nature - that specify the
meaning of Foo, and moreover do so in some sense completely, ie
comprise a full account of that meaning - and facts about Foo that
are merely facts, which are stated using 'Foo' but which are not, as
it were, constitutive of the actual meaning. So for example, if the
defining condition were simply an assertion about the concept, then
to assert something that contradicts that definition would simply
generate a contradiction; but if it is taken to be definitional, then
one knows immediately that the contradicting assertion must be false.

Now, I can guess from your earlier emailings that you think of these
matters in a fairly strict model-theoretic way, as I do myself, and
within a strict extensional model theory there really is no
principled way to make this distinction on logical grounds. Certainly
it cannot be identified with anything as simple as a syntactic
distinction like ground-fact/quantified rule. Some ontology folk
argue that making the distinction logically requires the use of a
modal logic, so that definitions are not just true but necessarily
true, or that the terms so defined are 'rigid' (have the same
denotation in every possible world.) I have rather a jaundiced view
of this approach, but that is a topic which probably goes beyond the
purview of this mailing list. But in any case, many Krep systems have
tried to provide some way to make the distinction. (KIF for example
has an elaborate syntax for defining relations, functions and so on.)
The A-box/T-box distinction was one such attempt. The key operational
point, as I understand it, is that while both the Tbox and the Abox
consist of assertions, those in the Tbox are cast in stone and cannot
be altered, whereas those in the Abox are mere data, which if they
seem to contradict those in the Tbox must be faulty.

Pat Hayes

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Received on Thursday, 7 June 2001 12:56:22 UTC

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