On Oct 7, 2008, at 2:44 AM, Rob Freeman wrote: (01)
> ... (02)
> My argument has been that for many systems there are more ways of
> generalizing examples than there are examples. This is a game changing
> assumption. Up to now it has always been assumed that there will be
> fewer generalizations than examples (rules, classes, etc.) At worst
> that you need to make one generalization per example (analogy.) If it
> is possible to make more generalizations than examples, the game
> changes completely. No one set of generalizations will suffice. (03)
OK, that sounds really interesting. But Im having trouble
understanding it. Can you make the point more concrete, perhaps with
an example/sketch? What leads you to this conclusion, that there will
be this overwhelming number of generalizations in many systems? What
kind of systems, and why will they have the top-heavy quality? (04)
>
> The only way to model that would be to base analysis on sets of
> examples. (05)
There is an old idea (due I believe to Whitehead in the early 20th
century) that may be relevant here. If all you have are categories
(generalizations, classes,..), then you can define individuals to be
maximal sets of intersecting categories. Mathematically, they are
ideals or ultrafilters (same thing looked at upside-down.) Its a very
elegant and powerful technique: I've used for example to show that any
notion of 'context' that satisfies some basic assumptions can be
reduced to sets of individual context-points. It can be used to define
time-point in terms of time-interval, and other apparently impossible
"backward" creations of individual- or concrete- ish objects from
clouds of vaguer ones. (06)
Anyway, just a thought for the thought-bin. (07)
Pat (08)
>
>
> I understand once you have retrieved graphs your processing varies,
> but have you tried generating analyses based on sets of graphs
> retrieved?
>
> -Rob
>
> On Mon, Oct 6, 2008 at 5:14 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
>> Rob,
>>
>> The basis for the analogy engine is a graph encoding that supports
>> efficient
>> storage
>> and retrieval of arbitrary graphs based on a semantic distance
>> measure.
>>
>> That encoding and the semantic distance measure support many
>> different
>> kinds of
>> applications, of which analogies are one important kind. But there
>> are an
>> open
>> ended
>> number of different ways of using the technology, and there are
>> more left
>> to
>> explore
>> than the ones we have implemented so far.
>>
>> In any case, I'm in travelling mode for the next two weeks, so I
>> will only
>> have
>> sporadic access to email.
>>
>> John
>
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> (09)
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