Re: On formal HAS-A definition

On May 13, 5:35 pm, Tegiri Nenashi <tegirinena..._at_gmail.com> wrote:
> On May 13, 1:07 am, Nilone <rea..._at_gmail.com> wrote:
> > This definition of IS-A differs from the one I previously gave in this
> > thread ("IS-A is an isomorphism between domains of entities").  
>
> That one didn't make sense: isomorphism is an equivalence [relation],
> and we are after an order. Homomorphism might do.

Right, I didn't keep in mind that you said you wanted to define subsets, and wavered between notions of IS-A. I didn't distinguish between subset relations and abstraction (e.g. the employees in a department vs employees as persons), subsets of relations (as implied by referential constraints), or relations over subsets (e.g. a marriage relation in a heterosexual society). Also, subset relations over infinite domains may yield either finite or infinite ranges.

>
> > The
> > two uses correspond to the 'is' of identity and the 'is' of
> > predication, resp (see Korzybski).  For example:
>
> > // 'is' of identity
> > Flower = [x: Name]
> >         Rose
> >         Violet
>
> > // 'is' of predication
> > FlowerColor = [x : Animal, y : Color]
> >         Rose, Red
> >         Violet, Blue
>
> I don't understand: 'IS-A' is a binary relation, what are the things
> you relate to with 'IS-A' in your examples?

In this example, I forgot the difference between domains and relations and I tried to express a domain (flowers) as a unary relation. Then I got confused with the domain of the x attribute of FlowerColor, since I thought I wanted to use the unary relation as its domain. The Animal domain you see in there resulted from an incomplete rewrite (my first example used animals), but when I tried to correct it in my subsequent post, I couldn't resolve x : Name in Flower with x : Flower in FlowerColor and then I realised my mistake. The symbols we use for things don't equate to the things themselves.

> Association is easy: it is unconstrained binary relation between two
> things. It doesn't have to be reflexive, irreflexive, symmetric,
> asymmetric, antisymmetric, transitive, total, trichotomous, or
> whatever.

I agree.

> I still struggle to understand what are the things that you are trying
> to relate to.

The form of your question allows me to answer on a different level than intended, and I choose to do so. I want to relate to abstraction in all its forms, and understand how to make and use abstractions correctly. Received on Fri May 14 2010 - 09:57:59 CEST