Swapping arguments in Intensional Inheritance?

[Nil Geisweiller]

Hi,

I wonder if the order of arguments in intensional inheritance shouldn't
be swapped. Let me recall the definitions of the various inheritances
(according to the PLN book [and coincidingly the opencog wiki])

1. Extensional Inheritance

ExtInh A B

is equivalent to

SubSet A B

2. Intensional Inheritance

IntInh A B

is equivalent to

ExtInh A_{PAT} B_{PAT}

where A_{PAT} is the (fuzzy) set of patterns of A (i.e. super sets of A,
that have discriminative power and low complexity).

3. Mixed Inheritance

Inh A B

is equivalent to

Or
ExtInh A B
IntInh A B

Here's the problem, if A intensional inherits from B, then it means that
A tends to have less patterns than B, meaning A is as abstract as B or
more, or equivalently B is as specialized as A or more.

However, in average the more something is specialized, the smaller its
extension will be. Thus it is expected that

ExtInh A B

will tend to be correlated with

IntInh B A

and anti-correlated with

IntInh A B

For that reason I think either the definition of mixed inheritance
should be redefined into

Or
ExtInh A B
IntInh B A

or the definition of intensional inheritance should be redefined into

ExtInh B_{PAT} A_{PAT}

Otherwise mixed inheritance will tend to be always half true, in average
regardless of A and B, because of the anti-correlation tendency between
ExtInh A B and IntInh A B.

Nil

[Linas Vepstas]

Hi Nil,

Yes, that sounds right to me.  You seem to be saying that "larger sets are easier to describe", which might typically be the case.  I can think of one counter-example:

Imagine a star-shaped set, or maybe some complicated fractal set -- say, the mandelbrot set. Several circles lie inside the mandelbrot set -- they are subsets, they are simple, easy to describe.  But also, the mandelbrot set also lies inside of several circles - again, the circles are easy to describe.

I cannot find any convincing variant of this example in the "universe of physical objects"

--linas

Nil

--
You received this message because you are subscribed to the Google Groups "opencog" group.
To unsubscribe from this group and stop receiving emails from it, send an email to opencog+unsubscribe@googlegroups.com.
To post to this group, send email to ope...@googlegroups.com.
Visit this group at https://groups.google.com/group/opencog.
To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/2cdf3d5b-fb0e-ac2a-c5d6-72c4a7cff0ba%40gmail.com.
For more options, visit https://groups.google.com/d/optout.

--

cassette tapes - analog TV - film cameras - you