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Re: DTTF: How unasserted triples help

From: pat hayes <phayes@ai.uwf.edu>
Date: Thu, 23 May 2002 13:46:50 -0500
Message-Id: <p05111700b912e6a65290@ai.uwf.edu>
To: Dan Connolly <connolly@w3.org>
Cc: Jonathan Borden <jonathan@openhealth.org>, WebOnt WG <www-webont-wg@w3.org>
>On Wed, 2002-05-22 at 14:38, Jonathan Borden wrote:
>>  DanC raises the important question of how unasserted triples help OWL's
>>  problem.
>>
>>  http://lists.w3.org/Archives/Public/www-webont-wg/2002May/0177.html
>>
>>  My impression is that since certain triples are unasserted by the RDF MT,
>>  the OWL MT or axiomatic semantics etc. would be "free" to assert its own
>>  meaning. For example
>>
>>  First using "asserted" triples, the following:
>>
>>  intersectionOf( student, employee ) or in N3
>>
>>  _:c1 rdf:type owl:Class
>>  _:c1 owl:intersectionOf _:L1
>>  _:L1 rdf:type owl:List
>>  _:L1 owl:first <#student>
>>  _:L1 owl:rest _:L2
>>  _:L2 rdf:type owl:List
>>  _:L2 owl:first <#employee>
>>  _:L2 owl:rest owl:nil
>>
>>  which roughly translates to: "There exists a class having the intersectionOf
>>  property whose object is a List, whose first element is #student and whose
>>  rest is another List whose first element is #employee and whose rest is nil"
>>
>>  As "asserted" triples, these statements are said to be _truths_, which is a
>>  bit strange because this isn't what we really mean.
>
>It's not strange at all; it's exactly what we mean:
>
>"for intersectionOf(X, Y) read: X is the intersection of the classes in
>the list Y"
>  -- http://www.w3.org/2001/10/daml+oil

Well then, please someone write a model theory for DAML which makes 
it have this meaning. The DAML MT does not refer to lists.  English 
paraphrases are not reliable indicators of precise meaning.

For the record, I have never understood DAML to mean this (ie that 
daml:intersectionOf asserts that a list exists in the domain of 
discourse) and find this a slightly crazy way to interpret the 
language. In fact, if this really is the intended meaning of 
DAML+OIL, then I would urge that the decision to base OWL on DAML+OIL 
should be reconsidered at the earliest opportunity, before we waste 
any more time and effort.

>  > Instead we mean to say:
>>
>>  "There exists a class which is the intersectionOf #student and #employee."
>
>That's an informal corrollary of the above, but it can't be
>stated formally/directly using 2-place predicates.

True; binary relations are very limited. It can be expressed using 
binary functions, however. In KIF: (equal A (intersect B C)). Both 
intersect and equality are binary.

>  > So presumably the OWL MT would have a statement or axiom or 
>something to the
>>  effect that:
>>
>>  "intersectionOf(a , b) <=> intersectionOf( b, a)"
>
>Sorry, this is too hand-wavy to be convincing.
>
>
>>  In this way, having _unasserted_ triples allows the OWL MT to apply its own
>>  semantics to the triples (which we are using as syntax). The answer is that
>>  having unasserted triples:
>>
>>  1) prevents paradoxes
>>  2) allows the OWL MT to do its job of defining semantics for OWL statements
>
>I can imaging that it might; but I would be entirely more convinced
>if there were an existence proof showing *how* unasserted triples
>allows the OWL MT to do this.

Dark triples allow the OWL MT to do anything (that an MT can do). 
That is the point of them: the meaning of the triple is not 
constrained by any meaning that RDF(S) might impose on them, so that 
OWL can do what it likes. It follows therefore that if OWL can 
possibly be given a coherent semantics over a triples-based syntax of 
some kind, then it can be given one using dark triples.  Without dark 
triples, however, the situation is much murkier and the prospects of 
a coherent model theory much less hopeful.

>  > other examples would be
>>
>>  owl:import
>>
>>  etc. etc.
>>
>>  the idea being not that these statements would be lacking semantics, rather
>>  that the truths stated in these OWL statements would be defined by the OWL
>>  MT i.e.
>>
>>  "If it is true that John is a member of the intersectionOf(student,
>  > employee) then it necessarily follows that John is a member of the
>  > intersectionOf(employee,student)"
>  >
>  > Problem solved, etcetera.
>
>Not to my satisfaction.

What would satisfy you? Do you want more justification that there is 
a problem to be solved, or are you doubtful whether this proposal 
will constitute a solution?

Pat
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Received on Thursday, 23 May 2002 14:46:22 GMT

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