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Re: SEM: "natural" entailments

From: pat hayes <phayes@ai.uwf.edu>
Date: Tue, 17 Sep 2002 20:26:43 -0500
Message-Id: <p05111b10b9ad81b4e546@[65.217.30.172]>
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: www-webont-wg@w3.org

>On September 6, pat hayes writes:
>>
>>  >
>>  >I don't see any a priori reason why set theoretic truths have any
>>  >greater need to be included in Owl than arithmetic truths.
>>  >  Both set thery and arithmetic are really somebody else's concern.
>>  >
>>  >
>>  >Jeremy
>>
>>  One of the things that is so misleading about the entire
>>  description-logic way of thinking is that it treats some *logical*
>>  truths as set-theoretical truths. Look, to infer
>>
>>  John is a student and John is an employee .
>>
>>  from
>>
>>  John is a student.
>>  John is an employee .
>>
>>  is a *logical* matter. It has to do with the meaning of 'and'. It has
>>  nothing to do with sets or classes or any of this paraphanalia. But
>>  in the warped world of description logics, to assert a simple
>>  conjunction requires us to invent a conjunctive class (an
>>  intersection) and say that John is in it.  The reason for this
>>  intellectual warping goes back to an influential, but I think
>>  perverse, publication by Ron Brachman about 20 years ago, which
>>  invented the distinction between two 'kinds' of reasoning: that to do
>>  with meanings, which is supposed to be done in one place (the
>>  'A-box') and the other to do with facts, supposed to be done
>>  elsewhere (the 'T-box'). The same kind of distinction is sometimes
>>  expressed by the distinction between 'data' (mere facts, assertions
>>  which are true) and 'meta-data' (schemas; things that 'define the
>>  meanings' of the terms used in the facts.)  None of these
>>  distinctions make any logical sense or have even the slightest basis
>>  in semantics: they are pragmatic distinctions invented to facilitate
>>  effective use of database technology with simple reasoners. By using
>>  them as the basis for the *semantic* framework of the semantic web we
>>  are making the entire future of the Web hostage to the intellectual
>>  apparatus of a technology designed for the efficient use of
>>  regularized, commercial databases, not to the emergent world of a
>>  social semantic web.  We should be focussing on the issues that will
>>  matter, not on how to transfer old technology into a world where it
>>  is probably going to be largely irrelevant.
>
>Pat,
>
>I know that we can all get a bit overheated sometimes (at least I know
>that I can), but I think that it is a bit unfair to take it out on
>poor Ron Brachman.

I only took it out on that particular paper, and it really wasn't 
Ron's fault. Marx wasn't a Marxist, either. I agree that poor Ron 
(who now wields life-or-death power over us academic soft-money folk 
on this side of the pond) is a really, really Good Bloke.

>One of Ron's main contributions was to point out
>that KR languages are pretty useless unless they have a clear and
>unambiguous semantics - which is one of the few things that the WG
>seems to be in unanimous agreement about.

Well, that insight was hardly unique to Ron, even at that time.

>I should also correct a few factual errors. In modern DLs, if Tbox and
>Abox are talked about at all, it is only as a sometimes convenient way
>to group different kinds of axiom (by the way, in this context the
>Tbox is concerned with "meanings" and the Abox with "facts")

Sorry, I never could get that distinction straight.

>. No
>"logical" distinction is made between different types of axiom, and
>implemented reasoners for expressive DLs treat them in a completely
>uniform manner. In languages as expressive as OWL, the distinction is
>even more blurred as individuals can be used in class descriptions.

My point is that the 'distinction' was always 'blurred', because 
there never was any such distinction that was worth making. Im glad 
that after about 20 years, the DL community has come around to that 
point of view.

>Having said all that, I believe that in some applications it can still
>be conceptually useful to separate ontologies (which roughly
>correspond to a Tboxes) from assertions that use terms from those
>ontologies, e.g., in semantic annotations (which roughly correspond to
>an Aboxes).

Sure. There any many possibly such pragmatic distinctions that might 
be pragmatically useful. But one doesn't feel the need to erect an 
entire methodology based on a foundational distinction between, say, 
annotations and non-annotations.

>Finally, I would like to point out (again) that DLs are nothing more
>than decidable subsets of FOL with useful computational
>properties.

You keep saying this, but that isn't the impression I get. For 
example, the recent DQL document has to have a footnote pointing out 
that DAML doesn't have any notion of 'conjunction', strictly 
speaking.  So the inference

A, B |= (A and B)

which is about the simplest inference imaginable, so simple that 
Aristotle didn't bother to give it a name, apparently isn't supported 
by DLs.  And the 'strong' OWL semantics requires us to assert (or 
assume) that the class (union A B) must *exist* in order to validate 
the DL version of the inference

A |= (A or B).

That sure doesn't feel like a subset of FOL to me; it feels a lot 
more like a subset of ZF set theory. Those inferences are valid in 
propositional logic where there aren't any classes to exist in the 
first place. Union and intersection are *analogous* to disjunction 
and conjunction, but they are not the *same*.

>So, in as much as FOL is an old technology, yes, DLs are
>an old technology (and proud of it).

FOL isn't a technology, fortunately. I was referring to the 
implementation requirements of DLs.

Pat
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Received on Tuesday, 17 September 2002 21:26:48 GMT

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