Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/

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 styles of syntax amenable to interpretation for logical applications.

Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.

Beginnings —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/

Elements —

Logic Syllabus
• https://oeis.org/wiki/Logic_Syllabus

Logical Graphs
• https://oeis.org/wiki/Logical_Graphs

Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator

Propositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems

Examples —

Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_law

Praeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theorema

Proof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations

Excursions —

Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview

Futures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_Graphs

Applications —

Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_Problems

Exploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data

Differential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview

Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata

Peirce's Law • 1
• https://inquiryintoinquiry.com/2023/10/19/peirces-law-1/

A Curious Truth of Classical Logic —

Peirce's law is a propositional calculus formula which states a non‑obvious truth of classical logic and affords a novel way of defining classical propositional calculus.

Introduction —

Peirce's law is commonly expressed in the following form.

• ((p ⇒ q) ⇒ p) ⇒ p

Peirce's law holds in classical propositional calculus, but not in intuitionistic propositional calculus. The precise axiom system one chooses for classical propositional calculus determines whether Peirce's law is taken as an axiom or proven as a theorem.

History —

Here is Peirce's own statement and proof of the law:

❝A “fifth icon” is required for the principle of excluded middle and other propositions connected with it. One of the simplest formulae of this kind is:

• {(x ‒< y) ‒< x} ‒< x.

❝This is hardly axiomatical. That it is true appears as follows. It can only be false by the final consequent x being false while its antecedent (x ‒< y) ‒< x is true. If this is true, either its consequent, x, is true, when the whole formula would be true, or its antecedent x ‒< y is false. But in the last case the antecedent of x ‒< y, that is x, must be true.❞ (Peirce, CP 3.384).

Peirce goes on to point out an immediate application of the law:

❝From the formula just given, we at once get:

• {(x ‒< y) ‒< α} ‒< x,

❝where the α is used in such a sense that (x ‒< y) ‒< α means that from (x ‒< y) every proposition follows. With that understanding, the formula states the principle of excluded middle, that from the falsity of the denial of x follows the truth of x.❞ (Peirce, CP 3.384).

#Peirce #Logic #LogicalGraphs #PeircesLaw