Logical Graphs • Formal Development 1
Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Formal Development Logical Graphs • First...
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Logical Graphs • Formal Development 2
Axioms The formal system of logical graphs is defined by a foursome of formal equations, called initials when regarded purely formally, in abstraction from potential interpretations, and called axioms...
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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....
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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...
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