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Re: CYCLES IN CLASS/PROPERTY HIERARCHIES

From: Wolfram Conen <conen@gmx.de>
Date: Fri, 26 Oct 2001 15:55:32 +0200
Message-ID: <3BD96B54.34263C49@gmx.de>
To: www-rdf-interest@w3.org
Vassilis and Karsten wrote:

Below, I try to consider your concerns with respect to the current
interpretation of range/domain constraints in the RDF Model Theory. The
bottom line is that it seems as if nothing harmful can be expected from
using subProperty-Cycles.

> ...
> Properties:
> 
> Also for properties a cycle would mean that we have different names
> for properties expressing the same.  But for properties cycles even
> make less sense. So fare the RDF WG does not even states how to handle
> different domain/range definitions for properties and their
> subproperties. When we allow cycles it should at least be constraint
> that the properties have equal domain/range definitions.

The "things" that you use with such properties will have all the types
that follow from the domain (resp. range) definitions that are used
along the subProperty-Chain (upwards usually, full-circle in a circular
chain). That (ie. the resulting types of "things") is what seems to
count when it comes to RDFS (which called Pat Hayes once a "theory of
rdf:type" (if I remember it correctly).

> 
> Example:
> 
> C1 --p1--> C2
> C3 --p2--> C4
> in the case p1 < p2 < p1
> C3 --p1--> C2 would be valid
> 
> There might be cases this would be ok. But there is a high risk that
> it ends up in a semantic mess.

(I assume that C1,C2,C3,C4 are classes and that the example is a
shorthand for proper domain/range definitions)

The Draft-MT suggests the following closure rules:

(2) aaa rdfs:subPropertyOf bbb AND bbb rdfs:subPropertyOf ccc 
        add:       aaa rdfs:subPropertyOf ccc 

(4) xxx aaa yyy  AND  aaa rdfs:subPropertyOf bbb
        add:       xxx bbb yyy

(5) xxx aaa yyy  AND  aaa rdf:domain zzz 
        add:       xxx rdf:type zzz 

(6) xxx aaa uuu AND   aaa rdf:range
zzz                                                       add:     uuu
rdf:type zzz 

The schema.closure of a set of RDF expressions which contain (a) triples
that define a subProperty-Cycle, say 
        
        P1 subPropertyOf P2
        P2 subPropertyOf P1

and (b) one or more range/domain "definitions", say

        P1 range C1
        P2 range C2

and (c) a triple that uses one of the properties, say 

        x P1 y

will contain (among other triples)

        x P2 y (from 4)
        x type C1 (from 6)      
        x type C2 (from 6)

In fact, with this "generative" interpretation of range/domain
constraints, nothing can ever be invalid (whatever this precisely may
mean above).  The only thing that is special about subProperty-Cycles in
the above example is that the presence of 

        x P2 y

in the above collection of triples instead of [x P1 y] would lead to
precisely the same schema-closure. As said, no harm can ever result from
range/domain "definitions" because they are not anymore treated as
constraints but as another (additional) way to assign types to "things".


In the other possible interpretation of range/domain definitions (as
constraints), some interesting things could happen (the "de-facto range"
of a subProperty would have to be a subset of the union of the declared
ranges of its superProperty, otherwise the range constraints of the
superproperties would be violated - this was observed earlier (Michel
Klein?) and is, for example, a logical consequence of the old
axiomatization in "Logical interpretatin..." (though not noted there)).
However, this discussion seems to be obsolete now with the "generative"
interpretation that is put forward in the Model Theory (which makes me a
little bit sad, because detecting the violation of constraints was at
least something useful to be done in our RDFS application ;)

Best,
        Wolfram
Received on Friday, 26 October 2001 09:56:04 GMT

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