Re: Ontolog Forum • Joseph Simpson

JS:

Today I found an interesting publication that might relate to the current discussion of Animated Logical Graphs (ALG).  Please see:

• Mathematician Solves Computer Science Conjecture in Two Pages

The “sensitivity” conjecture may be a topic that could be explored using ALG.  There appear to be many interesting connections between ALG and the sensitivity conjecture.  I am looking for an area where ALG application examples may be created and discussed.  My first attempt at an example, using the Augmented Model-Exchange Isomorphism (AMEI), raised a number of conceptual and structural application issues.  Which can be addressed as we move forward.  My plan is to continue the search for specific application areas.  I believe that finding domain specific applications will help me better understand the ALG material.

Take care, be good to yourself and have fun,

Joe

Dear Joe,

Boolean functions and different ways of contemplating their complexity are definitely the right ballpark, or at least the right planet, for field-testing logical graphs.

I don’t know much about the Boolean Sensitivity Conjecture but I happened to run across an enlightening article about it just yesterday and I did a while ago begin an exploration into what appears to be a related question, Péter Frankl’s “Union-Closed Sets Conjecture”.  See the resource pages linked below.

At any rate, now that we’ve entered the ballpark, or standard orbit, of boolean functions, I can skip a bit of dancing around and jump to the next blog post I have on deck.

Resources

• R.J. Lipton ∧∨ K.W. Regan
• The Easiest Impossible Problem
• Enriching the Frankl Conjecture
• Discrepancy Games and Sensitivity
• Scott Aaronson • Sensitivity Conjecture Resolved
• Frankl Conjecture • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8) • (9) • (10) • (11) • (12)

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