[sc34wg3] The reflexiveness of isa

Robert Barta rho at devc.at
Mon Mar 30 14:37:00 EDT 2009

On Mon, Mar 30, 2009 at 09:35:11AM +0200, Lars Marius Garshol wrote:
> According to the current TMRM draft the isa relation is not reflexive.  
> (This issue was identified by Hannes Niederhausen, but I don't see a  
> post from him about it, so I'm writing it up myself.)

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".


The above constraint is by itself quite arbitrary. It only helps to
avoid that the world goes up in smoke (or crosses the road as a
chicken). If we assume that isa models an instance/class relationship,
then writing

   x isa x

means that a class is an instance of itself. I have no idea what that
means and I am definitely too uneducated[1] to understand the
consequences of making isa reflexive for *every* thing. Not sure what
the impact were on the finiteness of all involved sets.

It would certainly mean that all things are classes. All of them. Not
sure what that means, either.


>   - TMCL needs to be able to say
>       tmcl:topic-type isa tmcl:topic-type .
>     which means that we have a usecase for a reflexive isa.

Such a statement would in fact contradict TMRM.

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

>   - TMDM puts no restrictions on it, so the two are not exactly aligned.
>     Even worse, the TMDM is less restrictive, while if we are going to
>     have differences it's TMRM that should be less restrictive.

TMDM say this:

   A topic type is a subject that captures some commonality in a set
   of subjects. Any subject that belongs to the extension of a
   particular topic type is known as an instance of that topic type.

It talks about 'sets' and the 'extension of the set'. Although, it
does not commit itself to say what a set is (Zermelo, Kripke, Goedel,
...), so a naive reader (me) would think about the set and any of its
members NEVER being the same.


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

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