Differential Propositional Calculus • Discussion 6

Re: Oeis | Differential Propositional CalculusPart 1Part 2Appendices
Re: Blog | Differential Propositional Calculus • Discussion • (3)(4)(5)

HR:
  1. I think I like very much your Cactus Graphs.  Meaning that I am in the process of understanding them, and finding it much better not to have to draw circles, but lines.
  2. Less easy for me is the differential calculus.  Where is the consistency between \texttt{(} x \texttt{,} y \texttt{)} and \texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}?  \texttt{(} x \texttt{,} y \texttt{)} means that x and y are not equal and \texttt{(} x \texttt{,} y \texttt{,} z \texttt{)} means that one of them is false.  Unequality and truth/falsity for me are two concepts so different I cannot think them together or see a consistency between them.
  3. What about \texttt{(} w \texttt{,} x \texttt{,} y \texttt{,} z \texttt{)}?

Dear Helmut,

Table 1 shows the cactus graphs, the corresponding cactus expressions in “traversal string” or plain text form, their logical meanings under the “existential interpretation”, and their translations into conventional notations for a number of common propositional forms.  I’ll change variables to \{ x, a, b, c \} instead of \{ w, x, y, z \} at this point simply because I’ve already got a Table like that on hand.

As far as the consistency between \texttt{(} a \texttt{,} b \texttt{)} and \texttt{(} a \texttt{,} b \texttt{,} c \texttt{)} goes, that’s easy enough to see — if exactly one of two boolean variables is false then the two must have different values.

Out of time for today, so I’ll get to the rest of your questions next time.

Table 1.  Syntax and Semantics of a Calculus for Propositional Logic

Syntax and Semantics of a Calculus for Propositional Logic

cc: CyberneticsLaws of FormOntolog Forum • Peirce List (1) (2) (3)
cc: FB | Differential LogicStructural ModelingSystems Science

This entry was posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Differential Propositional Calculus • Discussion 6

  1. Pingback: Animated Logical Graphs • 67 | Inquiry Into Inquiry

  2. Pingback: Survey of Differential Logic • 3 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.