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Re: RDF Semantics: RDFS entailment lemma

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 14 Apr 2003 14:27:13 -0500
Message-Id: <p05111b01bac0b5fed59f@[]>
To: herman.ter.horst@philips.com
Cc: www-rdf-comments@w3.org

>I agree that my two examples follow from the new rule rdfs12, and that
>this rule is valid.
>And I agree with Graham Klyne that the new rule rdfs7a follows
>from the old rule rdfs7a, so can be replaced by it.

Right, Graham was correct about that.

>  >But your example has some
>>other consequences: in fact, it entails that Resource is a subClass
>>of Class, ie that everything is a class.
>How do you obtain this?

Hmm, I thought I knew last night, but I cannot now reproduce that 
result. Never mind, pretend I never said it.

>  >
>>In order to prove the closure lemma, I need to somehow show that this
>>is the *only* way that the above entailment rule could possibly be

Because the entailment rule I mentioned

(x type A |- x type B) |- A subClass B

is in fact valid, and follows from the 'iff' in the semantic 
condition on subClassOf. So in order to show that this rule can be 
omitted from a complete rule base I have to show that any possible 
application of it is already covered by some other inference path. 
There is in fact a valid such rule for subPropertyOf as well, but no 
way it could possibly be invoked by an RDFS subproof, so that one can 
be safely omitted.

>>The only way I can see how to do this at present is by an
>>exhaustive analysis of the rule base, but I bet there is some elegant
>>way to do it which I don't have time to think of.
>>The general pragmatic conclusion seems to be that it is definitely
>>not a good idea to try to say  things about superproperties of
>>rdf:type, for sure :-) I propose to add the following paragraph as a
>>'warning' and also a brief commentary on this new rule:
>>The rule rdfs11

that should be rdfs12

>is a technicality, required in order to ensure the
>>truth of the following lemma. It is unlikely to be used in practice,
>>and will normally only produce redundant inference paths for some
>>items in the closure. In general, the property rdf:type is best
>>considered to be part of the logical machinery; as this rule
>>illustrates, imposing gratuitous conditions on rdf:type can produce
>>unexpected entailments. Similar strange conclusions can arise from
>>asserting that rdfs:Resource is a subclass of another class, for
>>example, or asserting unintuitive properties of rdfs:Class.
>I'm not sure whether these last two paragraphs are justified.
>Couldn't you also say that the new rule rdfs12 shows that the
>rdfs does not enable one to make the domain of rdf:type
>or any of its superproperties any smaller than it is
>(i.e., rdfs:Resource) by adding other domain statements?

That might indeed be a better way of putting it, thanks for the 
suggestion. I will re-draft this paragraph.

Thanks again for your help.

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Received on Monday, 14 April 2003 15:27:16 UTC

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