[om-list] use case #2: add property

[Luke Call]

*****add property [could be a relationship, or not]
******could at some point consider fuzzy sets as per Tom's old archived 
email #12 (aug 19 2000), and mark's reply of aug 26 2000 in arch#13:
*******We need to consider fuzzy sets, too.  If you change or add an 
attributejto a class, to a partial/fractional degree, that will also 
affect all
members of that class, but in an incomplete way: it will change or add the
probability-of-fractional-degree that such an attribute applies to any given
member of that class.  Or, if a member is a member to a fractional degree,
then any attribute added to its superclass, even one added completely to
that superclass, will only affect that member to the degree to which it is a
member of the superclass.  If both the attribute and the membership are
fractional, then some convention needs to be established for combining the
fractionality here, such as multiplication of the fractional value (a value
between 0 and 1).

     A fractional attribute to a class can be over-ridden by the member,
which would say that the degree to which that attribute affects it, the
individual member, is 100%.  Considering all members' degree-of-attribution,
and the degree of attribution of this attribute to the general class, we can
achieve a useful redundancy: you can compute the degree of attribution for
the entire class based on the degrees found in the individual members, and
see if these two number match.
*******To: One Model List <om-list at onemodel.org> CC: Rex Butler 
<rexbutler at hotmail.com> Subject: Re: Modeling Relations -- Re: use cases
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Tom and other Packers wrote:

 > We need to consider fuzzy sets, too.  If you change or add an attribute
 > to a class, to a partial/fractional degree, that will also affect all
 > members of that class, but in an incomplete way: it will change or 
add the
 > probability-of-fractional-degree that such an attribute applies to 
any given
 > member of that class.

Probability (or likelihood) is a special kind of fractional set membership
that must be carefully distinguished from the more general case. 
Probability
expresses the measure of confidence that a certain proposition is correct,
based on a correct accounting of missing information.  Fractional set
membership, on the other hand, expresses the general idea of degree of
membership in a set with ill defined boundaries.  The latter can still exist
even in a environment of perfect information, whereas probability becomes
relatively useless.

To combine the two ideas (degree of belief with degree of membership in an
arbitrary set) requires expressing the truth value of a set membership
proposition as a probability density function over a degree of set 
membership
axis.  This allows ideas to be expressed like "I completely sure it is
half-tiger" or "I am convinced it either is or isn't a tiger (but it is 
not a
mixture)".

You cannot combine probability and degree of set membership into the same
scalar value without throwing rigor out the window.  Unfortunately doing it
correctly is computationally expensive, so there needs to be judgement
exercised when using both together.

In my opinion, probability is a much more effective concept than more
arbitrary fuzzy set membership, primarily because it is defined 
rigorously in
the language of science on a class of largely man-made sets with distinct
boundaries.  Scientists, as a rule, eschew fuzzy sets whenever possible 
except
in cases where the degree of set membership can be given a rigorous
definition.  Expressions like "78% warm" are nearly meaningless, because 
there
are but the barest conventions for expressing fuzzy set membership in 
natural
language.

However, there are certainly enough cases where it is extremely useful to
distinguish between "slightly", "somewhat", and "mostly" that I agree that
fractional set membership should be supported.

 > Or, if a member is a member to a fractional degree,
 > then any attribute added to its superclass, even one added completely to
 > that superclass, will only affect that member to the degree to which 
it is a
 > member of the superclass.  If both the attribute and the membership are
 > fractional, then some convention needs to be established for 
combining the
 > fractionality here, such as multiplication of the fractional value (a 
value
 > between 0 and 1).

Unfortunately there is no rigorous way that you can do this.  If you say 
that
the superclass has attribute of degree X, then it follows that all 
members of
that class have the same attribute of degree X.

The only legitimate thing you can say is that the expected degree of the
attribute is X given a sufficiently large sampling of the members of the
class, which is short hand for specifying the expected value of the
probability distribution over the degree of attribute.  You could also go on
to add the standard deviation to give a more complete picture of the
distribution.

If a certain member of the set is only a member of degree 1/2, the only 
thing
you might possibly do (in desparation) is to use the 1/2 as a scale 
factor for
combining the parents classes probability distribution with all other
probability distributions of sets the member might be fractionally a 
part of.

What you cannot do is multiply the centroid value of the parents probability
distribution with the degree of set membership of the child.  If cement is
typically 90% sand, and my mixture is 10% cement, I have no basis for
concluding that my mixture is 9% sand.  What if the other component of the
mixture is 50% sand - then my mixture is actually 54% sand.

Now if I do not know what the other components of my mixture are, all I can
claim is that the probability that my mixture has less than 9% sand is
relatively low.  And this is assuming that the attribute degrees combine
linearly.  In the more general case that is purely guess work - unless you
explicitly specify how multiply inherited attribute degrees combine, 
assuming
that they combine linearly can lead to the worst logical errors 
imaginable.

For an inference engine to operate safely, it must assume that it can 
make no
such conclusions until specifically instructed otherwise.  In any case,
statistical information, including expected values or centroids of attribute
degrees, has no necessary bearing on a sub-class even if it of degree of
superclass membership 1.0.  Just because the human race is 50% male, 
does not
mean a typical physics class is.  And if it is only half human, the 
stretch is
much worse.

 > > A fractional attribute to a class can be over-ridden by the member,
 > which would say that the degree to which that attribute affects it, the
 > individual member, is 100%.  Considering all members' 
degree-of-attribution,
 > and the degree of attribution of this attribute to the general class, 
we can
 > achieve a useful redundancy: you can compute the degree of 
attribution for
 > the entire class based on the degrees found in the individual 
members, and
 > see if these two number match.

Again, you cannot override an actual attribute degree, unless the member
object is only fractionally a member.  An actual attribute degree has to 
apply
to all true subclasses as well.  And if the attribute degree is only a
statistically expected value, then it is only in desparation that you can
assume those statistics are followed by the subclass.

[end]