Re: On formal HAS-A definition

On May 13, 1:07 am, Nilone <rea..._at_gmail.com> wrote:
> On May 12, 6:26 pm, Tegiri Nenashi <tegirinena..._at_gmail.com> wrote:
>
> > On May 12, 12:53 am, Nilone <rea..._at_gmail.com> wrote:
> > > I consider x IS-A y as a relation named y with a unique constraint on
> > > x.  Your thoughts?
>
> > I'm lost. Example, please?
>
> 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.

> 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?

> Aren't those terms still used in UML, e.g.http://en.wikipedia.org/wiki/Class_diagram#Instance_Level_Relationships?
>
> I messed up 'aggregation' and 'association' there.  Let me try again:
> a lack of unique constraints imply aggregation, a unique constraint on
> x denotes the composition of y from x, and vice-versa for a unique
> constraint on y.  Unique constraints on both implies a binary
> association relation.  For example:
>
> // aggregation
> StudentClass = [x : Student, y : Class]
>         John, Math
>         John, Biology
>         Mary, Math
>         Mary, History
>
> // composition, unique constraint on y
> SubjectModule = [x : Subject, y : Module]
>         Math, Geometry 1
>         Math, Algebra 1
>         Biology, Evolution 1
>
> // association, unique constraint on (x, y)
> DepartmentHead = [x : Department, y : Professor]
>         Physics, Frank
>         History, Susan

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 still struggle to understand what are the things that you are trying to relate to. Are they relation attributes, attribute sets, or something else? Received on Thu May 13 2010 - 17:35:11 CEST