Animated Logical Graphs • 39

Re: Richard J. LiptonLogical Complexity Of Proofs

Happy Peirce’s Birthday, Everyone ❢

We’ve been discussing aspects of proof style arising in connection with the complexity of proofs.  In previous posts we took up (1) the aspect of formal duality, reflecting in passing on the prospect of higher symmetries, and (2) the spectrum ranging from information-reducing to information-preserving inference rules.  Here’s a quick recap —

A third aspect of proof style arising in this connection is the degree of insight demanded and demonstrated in the performance of a proof.  Generally speaking, the same endpoint can be reached in many different ways from given starting points, by paths ranging from those exhibiting appreciable insight to those exercising little more than persistence in sticking to a set routine.

A modicum of insight suffices to suggest the quality of “insight” resists pinning down in a succinct definition but we do tend to recognize it when we see it, so let me inch forward by highlighting its salient features in a graded series of examples.

To be continued …

Resources

Applications

cc: CyberneticsOntolog • Peirce (1) (2) (3) (4) (5) (6)Structural ModelingSystems

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.