Cf: Animated Logical Graphs ??? 36
http://inquiryintoinquiry.com/2020/08/21/animated-logical-graphs-36/
Re: Richard J. Lipton
https://rjlipton.wordpress.com/about-me/
::: Logical Complexity Of Proofs
https://rjlipton.wordpress.com/2020/08/19/logical-complexity-of-proofs/
Dear Dick,
You asked, "Is this measure, the logical flow of a proof, of any interest?"
I wasn't quite clear how you define the measure of flow in a proof --
it seemed to have something to do with the number of implication arrows
in the argument structure?
But this does bring up interesting issues of "proof style" ...
Propositional calculus as a formal language and boolean functions
as an object domain form an instructive microcosm for many issues
of logic writ large. The relation between proof theory and model
theory is one of those issues, despite, or maybe in virtue of,
propositional logic's status as a special case.
Folks who pursue the CSP-GSB line of development
in graphical syntax for propositional calculus are
especially likely to notice the following dimensions
of proof style.
Formal Duality
==============
This goes back to Peirce's discovery of the "amphecks"
( https://oeis.org/wiki/Ampheck ) and the duality between
Not Both (nand ( https://oeis.org/wiki/Logical_NAND ) ) and
Both Not (nnor ( https://oeis.org/wiki/Logical_NNOR ) ).
The same duality is present in Peirce's graphical systems
for propositional calculus. It is analogous to the duality
in projective geometry and it means we are always proving
two theorems for the price of one. That's a reduction in
complexity -- it raises the question of how many such
group-theoretic reductions we can find.
To be continued ...
Resources
=========
* Cactus Language
https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Applications
============
* Applications of a Propositional Calculator ??? Constraint Satisfaction
Problems
https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_Problems
* Exploratory Qualitative Analysis of Sequential Observation Data
http://web.archive.org/web/20180828161616/http://intersci.ss.uci.edu/wiki/index.php/Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data
Regards,
Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] .
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected]
with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of
the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and
co-managed by him and Ben Udell.
