Tag Archives: Logical Graphs

Cactus Language • Semantics 5

Last time we reached the threshold of a potential codomain or target space for the kind of semantic function we need at this point, one able to supply logical meanings for the syntactic strings and graphs of a given cactus … 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 • Semantics 4

Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche);  written words are the signs of words spoken.  As writing, so also is speech not the same for all races of men.  But the … 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 • Semantics 3

The task before us is to specify a semantic function for the cactus language in other words, to define a mapping from the space of syntactic expressions to a space of logical statements which “interprets” each expression of as an … 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 • Semantics 2

It is common in formal settings to speak of interpretation as if it created a direct connection from the signs of a formal language to the objects of the intended domain, in effect, as if it determined the denotative component … 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 • 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