

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@[]>
To: "Ziv Hellman" <ziv@unicorn.com>
Cc: www-rdf-logic@w3.org
> >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
