[sc34wg3] The reflexiveness of isa

[Lars Marius Garshol]

(Sorry for the late reply. My ISP has been blocking outgoing email.  
Only solved it today with an SSH tunnel.)

* Robert Barta
>
> To be precise, the current draft says this:
>
>   The isa relationship is non-reflexive, i.e. x isa x for no x \elem
>   m, so that no proxy can be an instance of itself.
>
> That is not the same as saying "the isa relation is not reflexive".

True. I was being imprecise. Let me try again.

The problem is that the current draft says:

> The isa relationship is non-reflexive, i.e. x isa x for no x \elem
> m, so that no proxy can be an instance of itself.

Whereas we really have a case where a topic is an instance of itself.

Could we live without it? Yes, I guess we could, but it would cause  
some difficulties, because we need to write a TMCL schema for TMCL,  
which will be used to verify that TMCL schemas are structured  
correctly. At least I think it would.

> If we assume that isa models an instance/class relationship,
> then writing
>
>   x isa x
>
> means that a class is an instance of itself.

Yes, it does.

> I have no idea what that means and [...]

The topic type of all topic types is a topic type, and so an instance  
of itself. Whether we allow this to be said or not is a different  
issue, but semantically there is no doubt that it is an instance of  
itself.

Similarly, tmdm:subject is the type of *everything*, and therefore  
also an instance of itself. There's nothing that isn't a subject, so  
it must be a subject.

> I am definitely too uneducated[1] to understand the consequences of  
> making isa reflexive for *every* thing.

So am I. That would be crazy.

No, what we want is to be able to have some very few types be able to  
do this.

> Is this really the same 'isa'? What _exactly_ are you trying to
> express with it?

Well, in TMQL we have wired the two together, so clearly we do think  
it is the same 'isa', and it would be a pretty messed up TMDM->TMRM  
mapping that didn't use this machinery.

> What I understand what you suggest is to drop the TMRM constraint "isa
> is non-reflexive", allowing someone to write x isa x.

Yes.

For two reasons:

  (1) We have use cases for it.

  (2) The TMRM aims to be a universal data model with no ontological
      commitments whatever.

Given the latter, isn't it a bit hard to defend this restriction?  
After all, I'm sure there are systems where isa can be reflexive. For  
example, RDF: http://www.w3.org/TR/rdf-schema/#ch_class

How universal is the TMRM really if it cannot support all of TMDM and  
RDF?

> From where I am sitting, I cannot say what the impact on TMRM
> semantics (or the mapping would be).


Maybe we should work that out, then.

--Lars M.
http://www.garshol.priv.no/blog/
http://www.garshol.priv.no/tmphoto/



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