Differential Logic, Dynamic Systems, Tangent Functors

[Jon Awbrey]

CybCom Group,

People interested in category theory as applied to systems
may wish to check out the following article, reporting work
I carried out while engaged in a systems engineering program
at Oakland University.

The problem addressed is a longstanding one, that of building bridges
to negotiate the gap between qualitative and quantitative descriptions
of complex phenomena, like those we meet in analyzing and engineering
systems, especially intelligent systems endowed with a capacity for
processing information and acquiring knowledge of objective reality.

One of the ways this problem arises has to do with describing change
in logical, qualitative, or symbolic terms, long before we grasp the
reality beneath the appearances firmly enough to cast it in measured,
quantitative, real number form.

Development on the quantitative shore got no further than a Sisyphean
beachhead until the discovery/invention of differential calculus by
Leibniz and Newton, after which things advanced by leaps and bounds.

And there's our clue what we need to do on the qualitative shore, namely,
to discover/invent the missing logical analogue of differential calculus.

With that pre-ramble ...

• Differential Logic and Dynamic Systems 2.0
http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0

“This article develops a differential extension of propositional calculus
and applies it to a context of problems arising in dynamic systems. The
work pursued here is coordinated with a parallel application that focuses
on neural network systems, but the dependencies are arranged to make the
present article the main and the more self-contained work, to serve as
a conceptual frame and a technical background for the network project.”

NB: An earlier platform change messed up some of the Figures,
putting the graphic and text layers slightly out of alignment
with each other. A few other Figures were deleted altogether
and had to be replaced with ascii graphics for the time being.

Regards,

Jon

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