Tag Archives: Graph Theory

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 • Jets and Sharks 3

Posted on June 23, 2024 by Jon Awbrey

Re: Theme One Program • Jets and Sharks • (1) • (2) Example 5. Jets and Sharks (cont.) Given a representation of the Jets and Sharks universe in computer memory, we naturally want to see if the memory serves to … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Jets and Sharks 2

Posted on June 22, 2024 by Jon Awbrey

Example 5. Jets and Sharks (cont.) As we saw last time, Theme One reads the text file shown below and constructs a cactus graph data structure in computer memory.  The cactus graph represents a single logical formula in propositional calculus and … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Theme One Program • Jets and Sharks 1

Posted on June 20, 2024 by Jon Awbrey

It is easy to spend a long time on the rudiments of learning and logic before getting down to practical applications — but I think we’ve circled square one long enough to expand our scope and see what the category … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments