Differential Logic

[Jon Awbrey]

Re: Patterns of change in multi-dimensional boolean spaces ...

Here's a collection of resource links on Differential Logic:

* Differential Propositional Calculus
https://oeis.org/wiki/Differential_Propositional_Calculus
This is probably the best to read first.

* Differential Propositional Calculus : Appendices
https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Appendices
For reference and examples -- but needs some reformatting
due to recent changes in the MediaWiki version of LaTeX.

* Differential Logic
Part 1. https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1
Part 2. https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2

* Differential Logic and Dynamic Systems
Overview (Table of Contents with Links to Sections)
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

Regards,

Jon

[Jon Awbrey]

Cf: Survey of Differential Logic : 2
At: http://inquiryintoinquiry.com/2020/02/08/survey-of-differential-logic-%e2%80%a2-2/

All,

My old worksite at the InterSciWiki has gone down, looks like permanently,
so I've been updating links and formatting to my new digs at the OEIS wiki.

Here's a newly updated Survey ( http://inquiryintoinquiry.com/surveys/ )
of previous blog and wiki posts on Differential Logic, material I plan to
develop toward a more compact and systematic account.

Elements
========

* Differential Propositional Calculus
( https://oeis.org/wiki/Differential_Propositional_Calculus )

* Differential Logic
( https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview )

Architectonics
==============

* Minimal Negation Operator
( https://oeis.org/wiki/Minimal_negation_operator )

* Cactus Language
( https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview )

Applications
============

* Differential Logic and Dynamic Systems

( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview )

* Differential Analytic Turing Automata
( https://oeis.org/wiki/Differential_Analytic_Turing_Automata )

Blog Dialogs
============

* Differential Logic
( https://inquiryintoinquiry.com/2008/07/29/differential-logic/ )

* Differential Logic and Dynamic Systems : Overview

( https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-%e2%80%a2-overview/ )

* The Present Is Big With The Future
( https://inquiryintoinquiry.com/?s=The+Present+Is+Big+With+The+Future )

* All Process, No Paradox
( https://inquiryintoinquiry.com/?s=All+Process+No+Paradox )

* Time, Topology, Differential Logic
( https://inquiryintoinquiry.com/?s=Time+Topology+Differential+Logic )

* Differential Logic, Dynamic Systems, Tangent Functors
( https://inquiryintoinquiry.com/?s=Differential+Logic+Dynamic+Systems+Tangent+Functors )

Explorations
============

* Frankl Conjecture
( http://inquiryintoinquiry.com/category/frankl-conjecture/ )

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache

[joseph simpson]

Jon:

Good luck, hope things return to a more normal state soon.

Take care, be good to yourself and have fun,

Joe

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Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

Git Hub link:

https://github.com/jjs0sbw

Research Gate link:

https://www.researchgate.net/profile/Joseph_Simpson3

YouTube Channel

https://www.youtube.com/user/jjs0sbw

Web Site:

https://systemsconcept.org/

[Jon Awbrey]

Cf: Differential Logic • Comment 5
https://inquiryintoinquiry.com/2021/05/14/differential-logic-comment-5/

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-05/thrd2.html#00055
::: John Sowa : “Modal Logic Is An Immense Swamp”
https://pilot.list.iupui.edu/sympa/arc/peirce-l/2021-05/msg00057.html

Dear John,

Best title I’ve read in a long time!
But the really immense swamp critter
here is the Naturally Evolved Organon
known as ornery natural language which
resists any augmentation by mathematics
and keeps trying to get by with a motley
assortment of evolution’s legacy software.

Re: Dana Scott:
"Tense operators (otherwise how can
you formulate principles of change?)"

The way physics adapted to quantitative change was not by
adding tense operators to Descartes’ analytic geometry but
by Leibniz and Newton developing the differential calculus.
The way logic will handle qualitative change is by finding
the appropriate logical analogue of differential calculus.
I took a few steps in that direction with the work linked
on the following page.

• Survey of Differential Logic
https://inquiryintoinquiry.com/2020/02/08/survey-of-differential-logic-2/

Regards,

Jon

[Jon Awbrey]

Cf: Survey of Differential Logic • 3
http://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

All,

I am finding one effect of the pandemic has been been to
blot out my memory of much work I blogged over the year and
many group discussions I have in mind as being “recent” and
“I’ll get back to it” actually occurred several months ago.
Thinking it will serve memory to recycle the more eddifying
currents of water under the bridge, here’s an update of my
Survey page on Differential Logic.

There's a lot of links, so I'll leave Readers on their own
recognizance to follow what they will from the link above.

Regards,

Jon

[Jon Awbrey]

Cf: Survey of Differential Logic • 3

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

All,

Linked above is a Survey of blog and wiki posts on Differential Logic,

material I plan to develop toward a more compact and systematic account.

Note. One effect of the pandemic has been been to blot out my memory

of much work I blogged over the year and many group discussions I have

in mind as “recent” and “I’ll get back to it” actually occurred several

months ago. Thinking it will serve memory to recycle the more eddifying
currents of water under the bridge, here’s an update of my Survey page on
Differential Logic.

Regards,

Jon

[Jon Awbrey]

Cf: Differential Logic • Discussion 16
http://inquiryintoinquiry.com/2022/05/11/differential-logic-discussion-16/

Re: Survey of Differential Logic • 3
https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/
Re: Laws of Form
https://groups.io/g/lawsofform/topic/differential_logic/91011396
::: Lyle Anderson ( https://groups.io/g/lawsofform/message/1872 )

<QUOTE LA:>
Thanks for posting this. Particularly the Differential Logic and Dynamic Systems
( https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview ).

It appears this is part of the trail to connecting Forms with Tensors.
Heim has already connected Tensors to Intelligence (artificial or “natural”)
and there is a current body of work making the same connection.
☞ Smart Tensors ( https://tensors.lanl.gov/ )
</QUOTE>

Thanks, Lyle, that's more or less the right ballpark. From my perspective
I view it as the qualitative substrate of differential geometry and the
“intelligence” part would come into play when we make the extension to
information geometries. But that's another inning, if not another season.

It is common in practice to find two different ways of approaching the field,
the way of tensors and the way of differential forms, a division I suspect goes
back to the divergent methods of Newton's fluxions and Leibniz's differentials.
We do have to integrate the two approaches over the long haul but it makes for
a smoother start to begin with differential forms, in large part because they
bear more of the relevant information “on their sleeves”, as the saying goes.

Regards,

Jon