Re: Richard J. Lipton • Logical Complexity Of Proofs
Re: Animated Logical Graphs • (35) (36) (37) (38) (39) (40) (41)

Now that our propositional formula is cast in the form of a graph its evaluation proceeds as a sequence of graphical transformations where each graph in turn belongs to the same formal equivalence class as its predecessor and thus of the first.  The sequence terminates in a canonical graph making it manifest whether the initial formula is identically true by virtue of its form or not.

To be continued …

Reference

• Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz : Logical Papers, Oxford University Press, London, UK.

Praeclarum Theorema

• This Blog
• OEIS Wiki • (1) • (2) • (3)
• PlanetMath • Praeclarum Theorema
• Metamath Proof Explorer • Praeclarum Theorema
• Frithjof Dau • Computer Animated Proof of Leibniz’s Praeclarum Theorema

Resources

• Logic Syllabus
• Logical Graphs
• Cactus Language
• Futures Of Logical Graphs
• Minimal Negation Operators
• Survey of Theme One Program
• Survey of Animated Logical Graphs
• Propositional Equation Reasoning Systems
• How To Succeed In Proof Business Without Really Trying

Applications

• Applications of a Propositional Calculator • Constraint Satisfaction Problems
• Exploratory Qualitative Analysis of Sequential Observation Data

cc: Cybernetics • Ontolog • Peirce (1) (2) (3) (4) (5) (6) (7) • Structural Modeling • Systems