RE: [OWLWG-COMMENT] Re: Cardinality Restrictions and Punning

>Hi, Pat!
>
>Pat Hayes wrote:
>
>>>>And I am
>>>>talking about real examples, not "research examples". Such as being
>>>>able to infer, from the fact that a taxonomy represented as a class
>>>>of classes contains only three members and that a thing is not in any
>>>>of them, that it is not classified by the taxonomy.
>>>
>>>I don't see how to express this example in OWL-DL.
>>
>>I think you will be able to in 1.1, using
>>punning: but you will not be able to draw the
>>right conclusions. So I would prefer to say, that
>>you will SEEM to be able to represent it in 1.1,
>>but this is in fact an illusion.
>
>While I did not succeed to build from your idea a working
>1.1-DL-consistent/Full-inconsistent example, I instead found this pretty
>simple one:

Perhaps Im not following your notation, but I 
fail to see how this works. However, I see how 
the general idea works and what your point is. 
And again, I do not see this as a problem to be 
resolved: on the contrary, I see it as inevitable 
that this kind of thing will happen. IMO, 
examples like this show that DL is too weak to 
detect (a) certain (class of) obvious 
inconsistencies, not that Full is broken.

>   (A1) <C> a owl:Thing
>   (A2) <D> a owl:Thing
>   (A3) <p> a owl:ObjectProperty
>   (A4) <p> rdfs:range [ oneOf (C) ]
>   (A5) <x> a owl:Thing
>   (A6) <x> <p> <D>
>   (A7) <C> a owl:Class
>   (A8) <D> a owl:Class
>   (A9) <C> owl:ComplementOf <D>
>
>Because of (A4), this ontology will entail from (A6):
>
>   (E1) <C> owl:sameAs <D>

Thats the part I don't follow. Perhaps I don't 
understand what A4 is saying exactly. Could you 
write this out in RDF, which is much easier to 
follow? Ignore the 'typing' information, which is 
irrelevant.

>both in DL[Punning] and in Full.
>
>Now, Full, but *not* DL[Punning], will further entail from (E1), (A7) and
>(A8):

Doesn't A7 follow from the use of oneOf in A4?

>   (E2) <C> owl:equivalentClass <D>
>
>(E2) directly contradicts (A9). Thus, the ontology is *inconsistent* in
>Full.

IMO, A9 already contradicts E1, in any rational 
or intuitive reading of E1. I cannot make 
intuitive sense of how these could be mutually 
satisfiable, given that the semantic meaning of 
E1 is that C = D. In fact, E1 is a stronger 
statement than E2, so to have {E1, A4} consistent 
but {E2, A4} inconsistent is, on the face of it, 
insane. I know that the punning semantics gives 
this result: to my mind, this is a ringing 
condemnation of the punning semantics.

>This ontology is *consistent* in DL[Punning]: To see this easily, just
>"un-pun" the ontology by substituting all occurrences of the *instance*
>names 'C' and 'D' with 'c' and 'd', respectively, in the axioms (A1), (A2),
>(A4) and (A6). It is then obvious that this is a satisfiable ontology.

Because it now says something completely 
different: it mentions 4 things instead of 2 
things.

>So, after Jeremy's data/object punning example, we now have an example where
>through *instance/class* punning an ontology gets DL-consistent, but
>Full-inconsistent.

As I always expected you would.

Pat


>
>Cheers,
>Michael
>
>--
>Dipl.-Inform. Michael Schneider
>FZI Forschungszentrum Informatik Karlsruhe
>Abtl. Information Process Engineering (IPE)
>Tel  : +49-721-9654-726
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>Email: Michael.Schneider@fzi.de
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>
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Received on Thursday, 3 January 2008 22:30:38 UTC