Re: Question about Extensional Entailment Rules

Jan Grant wrote:

>On Thu, 26 Aug 2004, Nick Bassiliades wrote:
>
>  
>
>>Jan Grant wrote:
>>
>>    
>>
>>>On Thu, 26 Aug 2004, Nick Bassiliades wrote:
>>>
>>> 
>>>      
>>>
>>>>Hi all,
>>>>
>>>>I would like to ask you whether I am missing something from the
>>>>extensional
>>>>entailment rules ext1&2
>>>>in the RDF Semantics document (http://www.w3.org/TR/rdf-mt/).
>>>>
>>>>Rule ext1 says that when:
>>>> uuu rdfs:domain vvv .
>>>>and
>>>> vvv rdfs:subClassOf zzz .
>>>>are true, then the triple:
>>>> uuu rdfs:domain zzz .
>>>>should be added.
>>>>
>>>>However, IMHO this looks rather bizarre! This rule states that when a
>>>>property
>>>>has a certain class as a
>>>>domain, it must also have all its superclasses as a domain. I believe that
>>>>it's the other way around:
>>>>all the subclasses of a class can be domains for the property uuu.
>>>>
>>>>For example,
>>>> uni:faculty rdfs:subClassOf uni:staff .   (/Faculty members are member of
>>>>the staff/)
>>>> uni:teaches rdfs:domain uni:faculty .     (/Faculty members teach/)
>>>>then we infer with rule ext1 that:
>>>> uni:teaches rdfs:domain uni:staff .       (/All members of the staff can
>>>>teach!/)
>>>>
>>>>I would expect it to work the other way around:
>>>> uni:lecturer rdfs:subClassOf uni:faculty .   (/Lecturers are //Faculty
>>>>members/)
>>>> uni:teaches rdfs:domain uni:faculty .        (/Faculty members teach/)
>>>>then we infer that:
>>>> uni:teaches rdfs:domain uni:lecturer .       (/Lecturers // can teach/)
>>>>
>>>>Am I missing something here?
>>>>   
>>>>        
>>>>
>>>The semantics are conjunctive. To say that "the domain of uni:teaches is
>>>uni:faculty" means, if you have statements of the kind
>>>	X uni:teaches Y .
>>>then X must be a member of uni:faculty: we can infer that about its type.
>>>What we can't do is infer that X is a uni:lecturer; but we _can_ logically
>>>infer that X must also be a member of uni:staff. The rules for domain and
>>>range are universally quantified in this fashion, so whilst it looks odd
>>>it's right.
>>>
>>> 
>>>      
>>>
>>However, the above scenario is already covered by existing entailment rules:
>>IF
>>   1) X uni:teaches Y .   &
>>   2) uni:teaches rdfs:domain uni:faculty . &
>>   3) uni:faculty rdfs:subClassOf uni:staff .
>>THEN
>>   4) X rdf:type uni:faculty . (due to (1) & (2) and rule rdfs2)
>>&
>>   5) X rdf:type uni:staff .  (due to (4) & (3) and rule rdfs9)
>>
>>I am not sure why rule ext1 is necessary, since it is subsumed by the two
>>other rules.
>>    
>>
>
>The derivation you give is accurate. However, it does not in and of 
>itself allow us to conclude that
>
>	uni:teaches rdfs:domain uni:faculty .
>entails
>	uni:teaches rdfs:domain uni:staff .
>
>_using_the_entailment_closure_rules_. It's simple to see that this 
>should be true, but the extra closure rule is required to derive this 
>mechanically.
>
>jan
>
>(I'm sure Pat or Jeremy will step in if I've misspoken here.)
>
>
>  
>
That is the core point I was trying to make clear. Why is the above 
entailment
necessary, since the reason of its existence (which is supposedly the 
inference that
the type of a subject of a triple is the superclass of the domain of the 
property of the triple)
is subsumed by other entailment rules. Why is it necessary to make the 
above entailment explicit?
Are there any other reasons, beyond the scenario we have been discussing?

Thanks :-)

Nick

-- 
*********************************************************************
* Dr. Nick Bassiliades, Assistant Professor                         *
* Dept. of Informatics, Aristotle University of Thessaloniki        *
* 54124 Thessaloniki, Greece                                        *
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* Tel: +302310997913   E-mail: nbassili@csd.auth.gr                 *
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