Differential Propositional Calculus • 28
•
https://inquiryintoinquiry.com/2023/12/20/differential-propositional-calcul…
Commentary On Small Models —
The consequence of dealing with “practically infinite extensions” becomes crucial in
building neural network systems
capable of learning and adapting, since the adaptive competence of any intelligent system
is limited to the objects and
domains it is able to represent. If we seek to design systems which operate intelligently
with the full deck of
propositions dealt by intact universes of discourse then we must supply those systems with
succinct representations and
efficient transformations in that domain.
Beyond the ability to learn and adapt, which taken at the ebb so often devolves into bare
conformity and confirmation
bias, the ability to inquire and reason makes even more demands on propositional
representation. The project of
constructing inquiry driven systems forces us to contemplate the level of generality
embodied in logical propositions —
we can see this because the progress of inquiry is driven by evident discrepancies among
expectations, intentions, and
observations, and each of those components of systematic knowledge takes on the fully
generic character of an empirical
summary or an axiomatic theory.
A compression scheme by any other name is a symbolic representation — and this is what the
differential extension of
propositional calculus is intended to supply. But why is this particular program of
mental calisthenics worth carrying
out in general?
The provision of a uniform logical framework for describing time‑evolving systems makes
the task of understanding
complex systems easier than it would otherwise be when we try to tackle each new system de
novo, “from scratch” as we
say. Having a uniform medium ready to hand helps both in looking for invariant
representations of individual cases and
also in finding points of comparison among diverse structures otherwise appearing to be
isolated systems. All this goes
to facilitate the search for compact knowledge, to apply what is learned from individual
cases to the general realm.
Resources —
Differential Logic and Dynamic Systems
•
https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Differential Logic • Commentary On Small Models
•
https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Regards,
Jon
cc:
https://www.academia.edu/community/Lb7Ygl