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Re: incompleteness in RDFS closure rules

From: pat hayes <phayes@ihmc.us>
Date: Tue, 10 Jun 2003 11:58:37 -0500
Message-Id: <p05210603bb0bab07e1dd@[10.0.100.24]>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: www-rdf-comments@w3.org, jos.deroo.jd@belgium.agfa.com, gk@ninebynine.org

>From: pat hayes <phayes@ihmc.us>
>Subject: Re: incompleteness in RDFS closure rules
>Date: Mon, 9 Jun 2003 13:39:52 -0500
>
>>  >	rdfs:subClassOf rdfs:subPropertyOf xxx .
>>  >	xxx rdfs:domain yyy .
>>  >
>>  >RDFS-entails
>>  >
>>  >	rdfs:Class rdfs:subClassOf yyy .
>>  >
>>  >but this does not come out of the RDFS closure rules.
>>  >
>>  >
>>  >
>>  >	rdfs:subClassOf rdfs:subPropertyOf xxx .
>>  >	xxx rdfs:range yyy .
>>  >
>>  >RDFS-entails
>>  >
>>  >	rdfs:Class rdfs:subClassOf yyy .
>>  >
>>  >but this does not come out of the RDFS closure rules.
>>  >
>>  >
>>  >
>>  >	rdfs:subPropertyOf rdfs:subPropertyOf xxx .
>>  >	xxx rdfs:domain yyy .
>>  >
>>  >RDFS-entails
>>  >
>>  >	rdf:Property rdfs:subClassOf yyy .
>>  >
>>  >but this does not come out of the RDFS closure rules.
>>  >
>>  >
>>  >
>>  >	rdfs:subPropertyOf rdfs:subPropertyOf xxx .
>>  >	xxx rdfs:range yyy .
>>  >
>>  >RDFS-entails
>>  >
>>  >	rdf:Property rdfs:subClassOf yyy .
>>  >
>>  >but this does not come out of the RDFS closure rules.
>>
>>
>>  Yes, you are perfectly correct. The rule rdfs12 has been generalized
>>  to include these cases, as follows:
>>
>>  rdfs12a
>>
>>  ppp rdfs:subPropertyOf zzz .
>>  ppp rdfs:domain xxx .
>>  zzz rdfs:domain yyy .
>>  |-
>>  xxx rdfs:subClassOf yyy .
>>
>>  rdfs12b
>>
>>  ppp rdfs:subPropertyOf zzz .
>>  ppp rdfs:range xxx .
>>  zzz rdfs:range yyy .
>>  |-
>>  xxx rdfs:subClassOf yyy .
>>
>>  where in 12a, ppp is one of rdf:type, rdfs:subPropertyOf,
>>  rdfs:subClassOf, and in 12b only the last two are allowed (because an
>>  empty class need not be in the range of a superproperty of rdf:type).
>>  Including rdf:type in the 12a case covers the inference noticed
>>  earlier by Herman, though the rationale is somewhat different.  These
>>  rules are not valid more generally because of the inclusive nature of
>>  domain and range.
>>
>>  BTW, the URI of the current editors draft has changed somewhat: these
>>  changes are now visible at
>>
>>  http://www.ihmc.us/users/phayes/RDF_Semantics_Edit_nT.html
>>
>>  Thanks for noticing this.
>>
>>  Pat
>
>I do not believe that these rules are valid.

You are right, on reflection. I tend (still) to think of range and 
domain as having inverted bounding conditions, and seem to  have done 
so in this case. Sigh.

Let me get back to you on how best to handle these peculiar 
conditions.  It may be that the best one can do is to simply list the 
'odd' entailments explicitly, but they do seem to have a regular 
pattern which is shared with Herman's entailment.

>
>For example, if I say
>
>	rdfs:subPropertyOf rdfs:range rdfs:Resource .
>
>which seems like a benign thing to say,  then I get the conclusion
>
>	rdfs:Resource rdfs:subClassOf rdf:Property .
>
>from rule rdfs12b.

Well, that seems benign to me, even if it is not strictly valid. It 
says that anything can be a property; and since the RDF syntax allows 
one to write any URIref in the property 'position' of a triple, that 
is indeed always a possible option.

But your main point is taken, since the very loose semantic 
constraints on domain and range do indeed allow one to construct an 
interpretation satisfying the antecedents but not the conclusion.

Pat
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Received on Tuesday, 10 June 2003 12:58:46 GMT

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