ONT Re: Differential Logic B -- Discussion
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DLOG B. Discussion Note 2
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HT = Hugh Trenchard
HT: I should have added to my "radial tree" a description
that "stable" represented either x or y, and "active"
also either represented x or y, but "active" in either
case was a variable in the sense that all the "actives"
radiating around the "stable" represent dynamic change.
The number of actives in my illustration was purely
arbitrary and was set up to show that while one of
either x or y remained in stable state, around it
revolve either x or y in a state of change.
HT: So I'm not sure if this was already apparent -- but does my explanation
above change how you may have viewed my previous email? Of course I mean
it only as conceptual tool for me to understand how one unit remains stable
while another is changing.
HT: In any event, I think I take your point that your representation
already illustrates the point, and is simpler than mine (Occam's
razor being instructive).
Hugh,
Once upon a time in the kingdom of AI it wasn't considered sporting unless
you tried the methods of your own device out on many problems aside from
those of your own device. So I took up the dare of the Jets and Sharks
example in that spirit, and had to go along with the assumptions that
came with the turf. In this (West Side) story, complex propositions
are represented by pools of formal neurons that represent the basic
logical variables. It doesn't matter all that much what you call
the states, so long as you have two distinguishable states. And
because one is trying to imagine how a continuous dynamic system
can reliably embody or represent a discrete logical proposition,
there is plenty of room to play around with alternative models.
I was using the word "stable" for a state of dynamic equilibrium,
typically a lower state of activation than the other states that
are available to agents, and I was using the word "active" for a
higher state of activation, typically transient, that there must
be exactly one formal neuron occupying, at equilibrium, in these
specialized pools of mutually inhibitory units. And even though
the system passes through all sorts of intervening states before
it finally settles down, it is only the equilibrium state of the
neural pool as a whole that counts.
Whatever choice of words eventually works best, the connotation
that we do want to preserve is the similarity between the agent
at rest and the collective of agents in a state of equilibrium,
as this is what gives us a notion of logical value that makes
sense for both simple and complex propositions, and thus what
allows us to combine propositions in the proper logical way.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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