Category Archives: Visualization

Cactus Language • Semantics 1

Alas, and yet what are you, my written and painted thoughts!  It is not long ago that you were still so many‑coloured, young and malicious, so full of thorns and hidden spices you made me sneeze and laugh — and … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Mechanics 5

Re: Cactus Language • Mechanics 4 The following Table summaries the mechanics of the parsing rules given in the previous post. A substructure of a painted and rooted cactus is defined recursively as follows.  Starting from the root node of … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Mechanics 4

To develop a parser for cactus languages in a functional programming style takes a way to express the description of a PARC in terms of its nodes, by recursion from the root up.  That requires each node to be specified … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Cactus Language • Mechanics 3

Although the definition of a cactus graph lobe in terms of its intrinsic structural components is logically sufficient it is also useful to characterize the structure of a lobe in extrinsic relational terms, that is, to view the structure that … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Mechanics 2

The structure of a painted cactus, insofar as it presents itself to the visual imagination, can be described as follows.  The overall structure, as given by its underlying graph, falls within the species of graph commonly known as a rooted … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Discussion 3

Re: Cactus Language • Stylistics 1 Re: Cybernetics • Shann Turnbull ST: How does your posting meet the test of being relevant to the Wiener definition of Cybernetic? Cybernetics can explain how all living things are self‑regulating, self‑governing and to … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Cactus Language • Mechanics 1

We are only now beginning to see how this works.  Clearly one of the mechanisms for picking a reality is the sociohistorical sense of what is important — which research program, with all its particularity of knowledge, seems most fundamental, … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Cactus Language • Pragmatics 16

Stricture, Strait, Constraint, Information, Complexity The ways in which strictures and straits at different levels of complexity relate to one another can be given systematic treatment by introducing the following pair of definitions. Excerpt of a Stricture The excerpt of … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Pragmatics 15

Stricture, Strait, Constraint, Information, Complexity From here it is easy to see how the concatenation of languages is related to the intersection of sets and thus to the conjunction of logical propositions.  In the upshot a cartesian product is described … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Cactus Language • Pragmatics 14

Stricture, Strait, Constraint, Information, Complexity To give a concrete example of strictures and straits in action, let us institute a frame of discussion where the number of places in a relation is bounded at two and the variety of sets … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments