Differential Logic and Dynamic Systems

[Jon Awbrey]

Cf: Differential Logic and Dynamic Systems • Overview
https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

All,

In modeling intelligent systems, whether we are trying to understand
a natural system or engineer an artificial system, there has long been
a tension or trade-off between dynamic paradigms and symbolic paradigms.

Dynamic models take their cue from physics, using quantitative measures
and differential equations to model the evolution of a system’s state
through time.

Symbolic models use logical methods to describe systems and their agents in
qualitative terms, deriving logical consequences of a system’s description or
an agent’s state of information. Logic-based systems have tended to be static in
character, largely because we have lacked a proper logical analogue of differential
calculus. The work laid out in this series of posts is intended to address that lack.

Note: The links below will take you to the current OEIS Wiki version of a project
I began under the auspices of a Systems Engineering program at Oakland University.
I'm about to be shanghaied into a mess of long put off chores but some time this
summer I hope to get back to revising the text, redoing the graphics messed over
by long ago Mac to PC platform changes, and serializing the content to my blog.

Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1
Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2
Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3
Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4
Part 5 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5
Appendices : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Appendices
References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_References
Doc History : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Document_History

Regards,

Jon

[Jon Awbrey]

Cf: Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/

All,

I was never on Twitter but I saw a lot of people I follow elsewhere
on the web were moving from there to various places in the so-called
Fediverse, especially to Mathstodon where they have LaTeX formatting,
so I went ahead and tagged along. The 500 character limit was a bit
of a challenge but it was an interesting experiment to see if I could
get anything across in a channel like that. At any rate, Mathstodon
just upped their limit to 1729 characters, more like a decent-sized
paragraph, so I'm looking at revising and serializing a few basic
articles in chunks of that order.

For starters, the blog post linked above and the transcript below update
the introduction to my article on Differential Logic and Dynamic Systems.

⁂ ⁂ ⁂

In modeling intelligent systems, whether we are trying to understand
a natural system or engineer an artificial system, there has long been
a tension or trade-off between dynamic paradigms and symbolic paradigms.
Dynamic models take their cue from physics, using quantitative measures
and differential equations to model the evolution of a system’s state
through time. Symbolic models use logical methods to describe systems
and their agents in qualitative terms, deriving logical consequences of
a system’s description or an agent’s state of information. Logic-based
systems have tended to be static in character, largely because we have
lacked a proper logical analogue of differential calculus. The work
laid out in this series of posts is intended to address that lack.

Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview
Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1
Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2
Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3
Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4
Part 5 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5
Appendices : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Appendices
References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_References
Doc History : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Document_History

Mathstodon Links —
• https://mathstodon.xyz/@Inquiry

Differential Logic Tag
• https://mathstodon.xyz/tags/DifferentialLogic

Differential Logic and Dynamic Systems Thread
• https://mathstodon.xyz/@Inquiry/109910069319800532

Regards,

Jon