Category Archives: Propositional Equation Reasoning Systems

Logical Graphs • First Impressions 7

Posted on September 6, 2024 by Jon Awbrey

Computational Representation The parse graphs we’ve been looking at so far bring us one step closer to the pointer graphs it takes to make the above types of maps and trees live in computer memory but they are still a … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 6

Posted on September 5, 2024 by Jon Awbrey

Duality : Logical and Topological (concl.) We have now treated in some detail various forms of the axiom or initial equation which is formulated in string form as “( ( ) ) =    ”.  For the sake of comparison, let’s record the planar and dual … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 5

Posted on September 4, 2024 by Jon Awbrey

Duality : Logical and Topological (cont.) It is easy to see the relation between the parenthetical expressions of Peirce’s logical graphs, showing their contents in order of containment, and the corresponding dual graphs, forming a species of rooted trees to be … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 4

Posted on September 3, 2024 by Jon Awbrey

Duality : Logical and Topological (cont.) Last time we took up the axiom or initial equation shown below. (3) We noted it could be written inline as “( ( ) ) =    ” or set off in the following text display. ( ( ) ) =     When we turn … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 3

Posted on September 1, 2024 by Jon Awbrey

Duality : Logical and Topological In using logical graphs there are two types of duality to consider, logical duality and topological duality. Graphs of the order Peirce considered, those embedded in a continuous manifold like that represented by a plane sheet of … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 2

Posted on August 31, 2024 by Jon Awbrey

Abstract Point of View The bird’s eye view in question is more formally known as the perspective of formal equivalence, from which remove one overlooks many distinctions which appear momentous in more concrete settings.  Expressions inscribed in different formalisms whose … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 1

Posted on August 30, 2024 by Jon Awbrey

Moving Pictures of Thought A logical graph is a graph‑theoretic structure in one of the systems of graphical syntax Charles S. Peirce developed for logic. Introduction In numerous papers on qualitative logic, entitative graphs, and existential graphs, C.S. Peirce developed several versions of … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions

Posted on August 26, 2024 by Jon Awbrey

Moving Pictures of Thought A logical graph is a graph‑theoretic structure in one of the systems of graphical syntax Charles S. Peirce developed for logic. Introduction In numerous papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Theme One Program • Motivation 6

Posted on June 8, 2024 by Jon Awbrey

Comments I made in reply to a correspondent’s questions about delimiters and tokenizing in the Learner module may be worth sharing here. In one of the projects I submitted toward a Master’s in psychology I used the Theme One program to … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Motivation 5

Posted on June 7, 2024 by Jon Awbrey

Since I’m working from decades‑old memories of first inklings I thought I might peruse the web for current information about Zipf’s Law.  I see there is now something called the Zipf–Mandelbrot (and sometimes –Pareto) Law and that was interesting because … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments