Author Archives: Jon Awbrey

Sign Relations • Examples

Posted on December 18, 2025 by Jon Awbrey

Soon after I made my third foray into grad school, this time in Systems Engineering, I was trying to explain sign relations to my advisor and he, being the very model of a modern systems engineer, asked me to give … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 1 Comment

Sign Relations • Signs and Inquiry

Posted on December 16, 2025 by Jon Awbrey

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry.  In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 1 Comment

Sign Relations • Definition

Posted on December 14, 2025 by Jon Awbrey

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting. Logic will here be defined … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 1 Comment

Sign Relations • Anthesis

Posted on December 12, 2025 by Jon Awbrey

Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 1 Comment

Cactus Language • Semantics 8

Posted on November 1, 2025 by Jon Awbrey

The 16 boolean functions on two variables are shown in the following Table. As before, all boolean functions on proper subsets of the current variables are subsumed in the Table at hand.  In particular, we have the following inclusions. 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 7

Posted on October 30, 2025 by Jon Awbrey

A good way to illustrate the action of the conjunction and surjunction operators is to show how they can be used to construct the boolean functions on any finite number of variables.  Though it’s not much to look at let’s … 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 6

Posted on October 27, 2025 by Jon Awbrey

If one takes the view that PARCEs and PARCs amount to a pair of intertranslatable representations for the same domain of objects then denotation brackets of the form can be used to indicate the logical denotation of a sentence or … 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 5

Posted on October 14, 2025 by Jon Awbrey

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

Posted on October 12, 2025 by Jon Awbrey

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

Posted on October 10, 2025 by Jon Awbrey

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