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importing and entialment

From: pat hayes <phayes@ai.uwf.edu>
Date: Wed, 9 Oct 2002 12:25:22 +0100
Message-Id: <p05111b1cb9c9b6066761@[192.6.10.203]>
To: www-webont-wg@w3.org

The final discussion of owl:imports at the f2f kind of melted down, 
for which I take much of the blame. Afterwards it occurred to me how 
to phrase the statement everyone wanted to make about owl:imports so 
as to avoid all the unwanted implications. Not surprisingly, it is 
easy, and it has to do with the model theory:

------------
owl:imports BBB

is true in an interpretation I just when the owl KB gotten by 
dereferencing BBB is true in I, OR if there is no such owl KB.
-------------

If there isn't any such document, therefore, this is just plain true, 
which makes it kind of vacuous in that case. But if there is, then 
the imports assertion amounts to the same as asserting that KB inside 
this KB.

So in this case:

A:
socrates rdf:type B:human .

B:
human rdfs:subClassOf mortal .

C:
owl:imports B
socrates rdf:type B:human

then A does not entail

D: socrates rdf:type B:mortal

but C does, provided of course that the imports worked; since in that 
case the imports statement is only true in interpretations which make 
B true. If the imports failed, then C wouldnt entail D, but not 
because 'entails' changes its meaning, but because in that case 
asserting C doesnt amount to saying as much as it does when the 
imports did work. In effect, C gets smaller when the imports fails.

Note, this uses the usual notion of entailment, so entailment is not 
subject to the whims of 404 errors. Also note, this does not say that 
anyone is under any obligation to do anything (such as load a file) . 
It only says what is being claimed to be true.

Pat

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Received on Wednesday, 9 October 2002 07:24:43 GMT

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