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# Re: The stupidest design I ever saw

From: Mikito Harakiri <mikharakiri_nospaum_at_yahoo.com>
Date: 10 Apr 2006 17:26:06 -0700

Neo wrote:
> > > > Mikito: Cartoon is a mammal ...
> > >
> > > Neo: Cartoon is not a mammal.
> >
> > Mikito: Look into the table on figure 1
> > which is the basis for the lattice on figure 2.
> > If you don't want cartoon to be classified as mammal,
> > which squares should be unchecked?
>
> First there is no systematic method that allows one to create the
> hierarchy (fig 2) on the basis of the table (fig1) (even after ignoring
> the top most and bottom most nodes which represent Universal and NULL
> respectively). If you know what that method is, please state it so that
> anyone can verify it.

The lattice nodes on figure 2 correspond to "cylindric sets" on figure 1. Each cylindric set is a cartesian product of some set of objects with some set of attributes. For example the unnamed node at the right of the "dog" corresponds to a set
{Socks,G Bobby}x{real,mammal}. Therefore, the formal method of transfoming figure 1 into the figure 2 is as follows: 1. Identify all the cylindric sets
2. Connect nodes with the partial order relation The partial order is defined as follows. If the set of attributes A1 is a subset of A2
and if the set of objects O2 is a subset of objects O1, then A1xO1 and A2xO2 are ordered. In the example {Socks} is subset of {Socks,G Bobby} and {real,mammal} is subset of {cat, real, mammal}. Therefore, the nodes {Socks,G Bobby}x{real,mammal} and {Socks}x{cat, real, mammal} are ordered -- in fact there is a lattice edge between this unnamed node and the object "Socks".

> Second, you can't unclassify cartoon as a mammal in the table because
> it isn't being classified as an mammal. Both cartoon and mammal are
> classifications listed across the top. And as the author states "The
> elements on the left side are formal objects; the elements at the top
> are formal attributes [aka classes]; and the relation between them
> [objects and classes] is represented by the crosses." Please state THE
> square/cell (and there should be only one, if any at all, otherwise why
> the redundancy) to uncheck which unclassifies cartoon as a mammal
> without also unclassifying Garfield and Snoopy as cartoons? A portion
> of the table shown below:
>
> ______ cartoon real dog cat mammal
> Garfield __X___ ___ ___ _X_ __X____
> Snoopy __X___ ___ _X__ ___ __X____

This is not big deal. Any classification system has to obey transitivity rule: if class A is a subclass of B and if B is subclass C then A has to be a subclass of C. Garfield, which is a cartoon is defined to be a cat. Cat is defined to be a mammal. Therefore, Garfield is a mammal, even though it is a cartoon. If you want a more realistic example where cartoon is not a subclass of mammal, or insist that these categories don't intersect at all, then you have to recategorize these cartoon characters as "cartoon cat" and "cartoon dog" which are not mammals. Received on Mon Apr 10 2006 - 19:26:06 CDT

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