Tag Archives: Venn Diagrams

Minimal Negation Operators • 4

Posted on September 1, 2017 by Jon Awbrey

Note.  I’m including a more detailed definition of minimal negation operators in terms of conventional logical operations largely because readers of particular tastes have asked for it in the past.  But it can easily be skipped until one has a … Continue reading →

Posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 10 Comments

Minimal Negation Operators • 3

Posted on August 30, 2017 by Jon Awbrey

It will take a few more rounds of stage-setting before we are able to entertain concrete examples of applications but the following may indicate the direction of generalization embodied in minimal negation operators. To begin, let’s observe two ways of … Continue reading →

Posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 11 Comments

Minimal Negation Operators • 2

Posted on August 30, 2017 by Jon Awbrey

Re: Minimal Negation Operators • 1 The brief description of minimal negation operators given in the previous post is enough to convey the rule of their construction.  For future reference, a more formal definition is given below. Initial Definition The … Continue reading →

Posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 11 Comments

Minimal Negation Operators • 1

Posted on August 27, 2017 by Jon Awbrey

To accommodate moderate levels of complexity in the application of logical graphs to practical problems our Organon requires a class of organules called “minimal negation operators”.  I outlined the history of their early development from Peirce’s alpha graphs for propositional … Continue reading →

Posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 13 Comments

Indicator Functions • 1

Posted on March 13, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? One of the things it helps to understand about 19th Century mathematicians, and those who built the bridge to the 20th, is that they were capable of high abstraction … Continue reading →

Posted in Abstraction, Boole, Boolean Functions, C.S. Peirce, Category Theory, Characteristic Functions, Euler, Indicator Functions, John Venn, Logic, Mathematics, Peirce, Propositional Calculus, Set Theory, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , | Leave a comment