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Logical Graphs • Formal Development 3
Logical Interpretation One way of assigning logical meaning to the initial equations is known as the entitative interpretation (En). Under En, the axioms read as follows. Another way of assigning...
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Logical Graphs • Formal Development 4
Equational Inference All the initials have the form of equations. This means the inference steps they license are reversible. The proof annotation scheme employed below makes use of double bars to...
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Logical Graphs • Formal Development 5
Frequently Used Theorems To familiarize ourselves with equational proofs in logical graphs let’s run though the proofs of a few basic theorems in the primary algebra. C1. Double Negation Theorem The...
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Logical Graphs • Formal Development 6
Frequently Used Theorems (cont.) C2. Generation Theorem One theorem of frequent use goes under the nickname of the weed and seed theorem (WAST). The proof is just an exercise in mathematical...
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Logical Graphs • Formal Development 7
Frequently Used Theorems (concl.) C3. Dominant Form Theorem The third of the frequently used theorems of service to this survey is one Spencer Brown annotates as Consequence 3 (C3) or Integration. A...
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Exemplary Proofs Using no more than the axioms and theorems recorded so far, it is possible to prove a multitude of much more complex theorems. A number of all‑time favorites are linked below....
View ArticleLogical Graphs • Discussion 10
Re: Logical Graphs • Formal Development Re: Laws of Form • Armahedi Mahzar AM: GSB took J1 : (a(a)) = as the first algebraic primitive and the second one is transposition so he only need only 2...
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Re: Logical Graphs • Formal Development Re: Laws of Form • Lyle Anderson LA: What does it mean to assign a label or name to a node of the Logical Graph? In LoF, the variables of the algebra represent...
View ArticleSurvey of Animated Logical Graphs • 8
This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual...
View ArticleSurvey of Theme One Program • 7
This is a Survey of resources relating to the Theme One Program I worked on all through the 1980s. The aim was to develop fundamental algorithms and data structures for integrating empirical learning...
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