Re: Possible semantic bugs concerning domain and range

Summary: attempt to collect arguments about this issue.
(Also added justification for uniformity, and a new argument about mutually 
entailing ontologies).

>Range
>Domain(P,C) implies/iff (forall x,y P(x,y) -> C(x))

>TransitiveProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(y,z)) -> P(x,z))
>SymmetricProperty(P) implies/iff (forall x,y P(x,y) -> P(y,x))
>FunctionalProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(x,z)) -> y=z)
>InverseFunctionalProperty(P) implies/iff (forall x,y,z (P(y,x) ^ 
>P(z,x)) -> y=z)
>inverseOf(P,Q) implies/iff (forall x,y P(x,y) -> Q(y,x))

I hear Dan, Jos, myself, Peter and Ian being able to go either way here.

There seem to be various arguments:

- treat them all the same
(unarticulated)
 Less difficult for implementors,. less difficult to document, less difficult 
to learn. I suspect the Guide would be shorter with iff semantics.

- implies only
 Few implementation would actually implement iff.
 (However most of the implementors in the group seem to have come round to the 
possibility of implementing iff)

- natural usage
 Pat (so far unsupported) has opinions about natural usage that split domain, 
range and inverse off as intensional (implies) and the others as extensional 
(iff).

- rdf datatyping
 I think this argument is now dead - some versions of rdf:datatyping requried 
intensional reading of rdf:range.

- possibility of identifying identical ontologies (new argument)
 With extensional semantics then ontologies using these with identical 
semantics entail one another. With intensional semantics then it is not the 
case e.g.

<owl:FunctionalPropery rdf:ID="a">
   <owl:inverse rdf:resource="#b" />
</owl:FunctionalProperty>


<owl:InverseFunctionalPropery rdf:ID="b">
   <owl:inverse rdf:resource="#a" />
</owl:InverseFunctionalProperty>

either have identical meaning or not.
Seems potentially useful, to say that they do have identical meaning.

- argument by authority 
iff we take this style of argument seriously

- surprising entailments
An empty property is necessarily transitive, functional, inversefunctional, 
its own inverse,  etc.


I think consistency is what I feel strongly about.

Jeremy

Received on Tuesday, 15 October 2002 17:24:42 UTC