[FOM] Animated Proofs : Praeclarum Theorema
Jon Awbrey
jawbrey at att.net
Mon Mar 22 13:46:59 EDT 2010
More fun with proof animations ...
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 the propositions in their argument lists.
This generalizes the corresponding syntactical 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 provides us with 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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