# Re: Dark triples, current closure / entailment rules, can someone clarify?

```>Pat indicated at the F2F that entailments "accidentally" drawn would be
>"harmless".

RDF entailments, yes.

>Can someone clear up this example for me?
>
>A:
>	<eg:foo1> <rdf:subPropertyOf> <dark:eg:foo2> .
>	<dark:eg:foo2> <rdf:subProperotyOf> <eg:foo3> .
>
>	<eg:a> <eg:foo1> <eg:b> .
>
>B:
>	<eg:foo1> <rdf:subPropertyOf> <dark:eg:foo2> .
>	<dark:eg:foo2> <rdf:subProperotyOf> <eg:foo3> .
>
>	<eg:a> <dark:eg:foo2> <eg:b> .
>
>C:
>	<eg:foo1> <rdf:subPropertyOf> <dark:eg:foo2> .
>	<dark:eg:foo2> <rdf:subProperotyOf> <eg:foo3> .
>
>	<eg:a> <eg:foo3> <eg:b> .
>
>
>Does A |= C? Does A |= B? B |= C?

Yes:
A|= C (by subproperty chaining and then the subproperty closure rule)
No:
A |= B (dark conclusion)
B |= C (dark, ie missing, antecedent)

However, notice that should be rdfs:subPropertyOf. To anticipate your
next question: yes, one does have to be careful using darkened
triples in RDFS hierarchical inferences (basically, any kind of
transitivity implication, ie subPropertyOf and subClassOf.)  What I
claimed was that it was safe with RDF-valid reasoning (ie
effectively, existential generalization).

Pat

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Received on Monday, 24 June 2002 19:11:03 UTC