Re: Cyclic Classes/Properties [was: Re: DAML Correction: Same Is Not A Sub Of Sub]

>[...]
> > > An additional problem is that if you let class hierarchies by
> > > cyclic, then you might start getting inconsistencies quite easily
> >
> > The last time this came up (late Feb/early March), a lot of heat
> > was generated.  The DAML+OIL approach is that a cycle in a
> > class hierarchy defines a set of equivalent classes --- so if A is a
> > subclass of B, B is a subclass of C, and C is a subclass of A,
> > then A, B, and C are equivalent.
>
>Cyclic classes worry me slightly simply because I don't think you have
>to enable them in order to state that two classes are equivalent.

Cyclic classes would worry me too, but nobody is talking about cyclic 
classes. The issue is rather how to understand 'subclass' ; is this 
like < or like =< ? Is a class considered to be a subclass of itself? 
RDFS seems to assume not (ie it understands 'subclass' to be strict 
subclass), but DAML says yes. The two notions of 'subclass' can 
coexist without interference. To assert RDFS:subclass is a stronger 
assertion than asserting DAML:subclass but it is not inconsistent 
with it, in much the same way that asserting 2<=3 is not inconsistent 
with the fact that 2<3. (Notice there is no need to make a 
distinction between integers and cyclic integers.)

>Surely a subClass is defined as:-
>
>   [ ( m + M ) M ]
>
>Where "something that is an M but not an m" may or may not exist? If
>it doesn't exist, then the two classes are equivalent, i.e. there are
>no members of either class which cannot belong to one another, and the
>only property you need to declare that is daml:equivalentTo.

Yes, but what it you don't know whether they are equivalent or not, 
but you do know that all A's are in B; and someone else knows that 
all B's are in A. Putting what you know together, shouldn't you both 
be able to infer that A is equivalent to B ?

>This is
>coming from a non-logician, but I don't see why unecessary levels of
>expression should be added to such a basic level of RDF structuring,
>when the devices for declaing equivalence are already there.

The issue is being able to infer equivalence from other assertions.

>In other
>words, if someone can come up with an practical real world example of
>why cyclic classes should be introduced over equivalence (or why
>cyclicity is required for equivalence... in Notation3!), then I would
>be very glad to hear it.

Nobody (except you) is talking about these 'cyclic classes', whatever 
they are. We are all talking about classes.

Pat Hayes

PS. You know, this little exchange is a lovely illustration of the 
utility of a formal semantics. "Subclass"  sounds like it means 
something, but exactly what it means needs to be spelled out in 
mathematical terms to avoid needless misunderstanding.

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Received on Thursday, 10 May 2001 19:03:08 UTC