[Fwd: Fwd: "inverse" in owl-guide]

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-------- Original Message --------
Subject: 	Fwd: "inverse" in owl-guide
Date: 	Wed, 29 Aug 2007 00:27:05 -0400
From: 	Alan Ruttenberg <alanruttenberg@gmail.com>
To: 	Ivan Herman <ivan@w3.org>, Ian Horrocks <horrocks@cs.man.ac.uk>
References: 	<200708290352.l7T3qOvP008010@greengenes.cit.cornell.edu>

Begin forwarded message:

> *From: *Dave Matthews <matthews@greengenes.cit.cornell.edu
> <mailto:matthews@greengenes.cit.cornell.edu>>
> *Date: *August 28, 2007 11:52:24 PM EDT
> *To: *alanruttenberg@gmail.com <mailto:alanruttenberg@gmail.com>
> *Subject: **Re: "inverse" in owl-guide*
>
> Hi Alan,
>
>> Wouldn't the inverse of "Every legal OWL Lite ontology is a legal OWL  
>> DL ontology" be
>>
>> "Every not legal OWL Lite ontology is a not legal OWL DL ontology" [1]
>
> Well maybe I was fuzzy on the logic or the sentence.  Let's sort it out.
> The rules are:
>
> Statement:      a => b
> Inverse:        not a => not b
> Converse:       b => a
> Contrapositive: not b => not a
>
> Aha, yes you're right and I was wrong.  The inverse is what you say, or
> "An illegal OWL Lite ontology is an illegal OWL DL ontology".  Same thing
> simpler.  As you say it clearly doesn't hold.  And is equivalent to the 
> converse, "A legal OWL DL ontology is a legal OWL Lite ontology," which of
> course also doesn't hold.
>
> My issue was about the wording.  To me the (corrected) inverse description
> of the relationship isn't as clear about the what-isn't-true as the 
> converse version is.  But the _really_ clear and simple version would be 
> just "OWL Lite is a subset of OWL DL."  
>
> Anyway thanks for correcting me on this.  If I get time I'll try to fix it
> at http://lists.w3.org/Archives/Public/public-webont-comments/
>
> - Dave
>
>
>> From: Alan Ruttenberg <alanruttenberg@gmail.com
>> <mailto:alanruttenberg@gmail.com>>
>> Date: Tue, 28 Aug 2007 22:24:10 -0400
>>
>> Hi Dave,
>>
>> Wouldn't the inverse of "Every legal OWL Lite ontology is a legal OWL  
>> DL ontology"
>>
>> "Every not legal OWL Lite ontology is a not legal OWL DL ontology" [1]
>>
>> This doesn't hold[*], so technically the statement in the  
>> documentation is true.
>> In any case, isn't the converse logically equivalent to the inverse?
>>
>> -Alan
>>
>> [1] http://en.wikipedia.org/wiki/Contraposition
>> [*] A not legal OWL Lite Ontology could be created by taking any  
>> existing OWL Lite ontology and augmenting it with an additional  
>> cardinality 2 restriction, for example. This would, in fact, be a  
>> legal OWL-DL Ontology.
>>
>>
>> On Aug 26, 2007, at 4:27 PM, Dave Matthews wrote:
>>
>>>
>>> : Each of these sublanguages is an extension of its simpler
>>> predecessor, both
>>> : in what can be legally expressed and in what can be validly
>>> concluded. The
>>> : following set of relations hold. Their inverses do not.
>>> :
>>> : Every legal OWL Lite ontology is a legal OWL DL ontology.  ...
>>>
>>> I believe you mean "converses".  The converse is
>>>
>>>   Every legal OWL DL ontology is a legal OWL Lite ontology.
>>>
>>> The inverse is
>>>
>>>   Every legal OWL Lite ontology is not a legal OWL DL ontology.
>>>
>>>
>>> OWL is an advanced logic.  Not good to have a basic error like this
>>> in the
>>> documentation.
>>> A subset/superset relation might be more appropriate.
>>>
>>> - Dave
>


-- 

Ivan Herman, W3C Semantic Web Activity Lead
Home: http://www.w3.org/People/Ivan/
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