[closed] Re: Question about Extensional Entailment Rules

Jan Grant wrote:

>On Thu, 26 Aug 2004, Nick Bassiliades wrote:
>
>[previous discussion cut for brevity, see thread archives]
>
>NB:
>
>  
>
>>>>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.
>>>>   
>>>>        
>>>>
>
>JG:
>
>  
>
>>>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.
>>>      
>>>
>
>NB:
>
>  
>
>>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?
>>    
>>
>
>The rdfs-entailment of
> 	uni:teaches rdfs:domain uni:staff .
>from
>	uni:teaches rdfs:domain uni:faculty .
>	uni:faculty rdfs:subClassOf uni:staff .
>
>is a direct consequence of the model-theoretic semantics: the model 
>theory already has this as a consequence.
>
>However, the closure rules are a (non-normative) recouching of the same 
>entailment rules. We would like every rdfs-entailment (according to the 
>model theory) to come out of the rdfs closure rules. Now, whilst the 
>closure rules already let us conclude facts from statements that use 
>"uni:teaches" as a property, without this particular rule they don't 
>have another way of supplying the conclusion above.
>
>
>
>  
>
OK - I think I understand your point - thanks.

I was just thinking in OO terms (i.e. presrciptive semantics)
where asserting that the domain of a property is Y means
that objects of class Y and below (in the class hierarchy) can have this
property, whereas the meaning of ext1 sounded to me like:
"classes above Y can also have that property", which is obviously wrong
in OO terms. However, the purpose of this rule must be understood
in terms of assertional (descriptive) semantics.

Thanks again for your time :-)

Nick


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