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RE: SEM: circular primitive

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 23 Apr 2002 06:32:10 -0400
To: jjc@hplb.hpl.hp.com
Cc: connolly@w3.org, jonathan@openhealth.org, www-webont-wg@w3.org
Message-Id: <20020423063210R.pfps@research.bell-labs.com>
I have annotated Jeremy's example.  

J: So, here is my attempt to capture the semantics of child
J: in DAML+OIL (as I read it).
J: Frankly, I have no idea whether this is intended to be
J: permissable under the current D+O spec. If it is then
J: it seems a ludicrously cryptic way of saying it. But perhaps
J: the constraint is complicated.
J: Note I use classes as instances here.
J: Note I think the following is sufficiently disgusting that
J: I would be quite happy to have it as illegal; but I don't
J: think Jonathan will be able to describe the notion
J: of inherited disease without something like it. (He can of 
J: course describe individual inherited diseases quite well 
J: enough).

J: # Let's not use child but parent.
J: # parent has the advantage that in general
J: # it's mincardinality is 1 not 0.

J: parent daml:inverseOf child .

J: InheritableClass rdfs:subClassOf daml:Class .

J: parent rdfs:domain _:ParentDomain .

_:ParentDomain is a class whose instances can have parents.
Let's consider one such instance, _:John

_:John rdf:type _:ParentDomain .

J: _:ParentDomain rdfs:subClassOf _:WithInheritableClass .

Now _:John is an instance of _:WithInheritableClass

J: _:WithInheritableClass rdf:type daml:Restriction .
J: _:WithInheritableClass daml:onProperty rdf:type .
J: _:WithInheritableClass daml:hasClass InheritableClass .

_:WithInheritableClass is a restriction, and consists of those individuals
whose types contain an instance of InheritableClass.

In particular, _:John has a type that is an InheritableClass, lets call
this type _:JohnsInheritableType

J: InheritableClass rdfs:subClassOf daml:Restriction .

As _:JohnsInheritableType is an InheritableClass it also is a daml:Restriction

J: InheritableClass rdfs:subClassOf _:par .
J: _:par rdf:type daml:Restriction .
J: _:par daml:onProperty daml:onProperty .
J: _:par daml:hasValue parent .

Now _:par is the class that consists of objects that have a daml:onProperty
relationship to parent.  However, this is *all* that it is, for *two*
reasons.  First, this is not sufficient to make a full DAML+OIL
restriction.  Second, even if is was, this would not be in the RDF *graph*,
and the RDF graph is all that counts in the DAML+OIL model theory.

J: # Saying the same in English is
J: # Within the class InheritableClass the
J: # property daml:onProperty has a local constraint
J: # restricting it to be present and with the value
J: # parent.


J: # Similarly we want to say that the minCardinality 
J: # is 1.
J: InheritableClass rdfs:subClassOf _:min .
J: _:min rdf:type daml:Restriction .
J: _:min daml:onProperty daml:minCardinality .
J: _:min daml:hasValue "1" .

As above.

Now Inheritable class has both parts required for minimum cardinality
restrictions, but this is insufficient to make any difference, because they
are not in the RDF *graph*.

J: # Now we want to restrict the class of the 
J: # parent property, so we introduce
J: # toClass.
J: InheritableClass rdfs:subClassOf _:to .
J: _:to rdf:type daml:Restriction .
J: _:to daml:onProperty daml:toClass .
J: _:to daml:cardinality "1" .
J: # The above forces every InheritableClass
J: # to have a daml:toClass property.


This says that there is exactly one daml:toClass relationship.

J: # Now we need to force that daml:toClass 
J: # property to locally be a subPropertyOf 
J: # identity.
J: # Well, this too is possible (at least in
J: # the cardinality = 1 case)
J: # Let's introduce a superProperty as a technical
J: # device.
J: daml:toClass rdfs:subPropertyOf _:superProp .
J: daml:sameClassAs rdfs:subPropertyOf _:superProp .

In the DAML+OIL model theory this does not have the meaning that one might
think with respect to restrictions.

J: # We now restrict the cardinality of both
J: # the superProp and daml:sameClassAs to 1
J: # on InheritableClass.
J: InheritableClass rdfs:subClassOf _:sup .
J: _:sup rdf:type daml:Restriction .
J: _:sup daml:onProperty _:superProp .
J: _:sup daml:cardinality "1" .
J: InheritableClass rdfs:subClassOf _:same .
J: _:same rdf:type daml:Restriction .
J: _:same daml:onProperty daml:sameClassAs .
J: _:same daml:cardinality "1" .

So an instance of InheritableClass 
- has a daml:onProperty relationship to parent
- has a daml:minCardinality relationship to "1"
- has a exactly one _:superProp relationship
  and thus at most one daml:toClass relationship
  and thus at most one daml:sameClassAs relationship
- has exactly one daml:sameClassAs relationship
So if it has a daml:toClass relationship to some object, then it also has a
daml:sameClassAs relationship to that same object.

However, this does not provide any interesting consequences, as all these
relationships do not have to be in the RDF *graph* and that is all that can
trigger restriction consequences in the DAML+OIL model theory.

Received on Tuesday, 23 April 2002 07:53:35 UTC

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