Re: Animated Proofs : Praeclarum Theorema

Froggers,

There's an extension of Peirce's logical graphs for propositional
calculus that uses "minimal negation operators" -- the family of
connectives that assert "just one false" of their argument lists.
This generalizes trees to what graph theorists call "cacti" and
represents a minimal negation operator of k arguments by means
of a "cactus lobe" of k+1 nodes.

For instance, XOR(x, y) is graphed as follows, where * is the root node:

x   y
o---o
  \ /
   *

This all gives us a nice way of representing boolean expansions
and using them as disjunctive normal forms to establish results.

For example, here's a graphical DNF way of proving Leibniz's
Praeclarum Theorema -- with a proof animation at the end:

http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems#Praeclarum_theorema_:_Proof_by_CAST

Cheers,

Jon Awbrey

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