Differential Logic • 10

It’s been a while, so let’s review …

Tables A1 and A2 showed two ways of organizing the sixteen boolean functions or propositional forms on two variables, as expressed in several notations.  For ease of reference, here are fresh copies of those tables.

Table A1.  Propositional Forms on Two Variables

Table A1. Propositional Forms on Two Variables

Table A2.  Propositional Forms on Two Variables

Table A2. Propositional Forms on Two Variables

We took as our first example the boolean function f_{8}(p, q) = pq corresponding to the logical conjunction p \land q and examined how the differential operators \mathrm{E} and \mathrm{D} act on f_{8}.  Each differential operator takes a boolean function of two variables f_{8}(p, q) and gives back a boolean function of four variables, \mathrm{E}f_{8}(p, q, \mathrm{d}p, \mathrm{d}q) or \mathrm{D}f_{8}(p, q, \mathrm{d}p, \mathrm{d}q), respectively.

In the next several posts we’ll extend our scope to the full set of boolean functions on two variables and examine how the differential operators \mathrm{E} and \mathrm{D} act on that set.  There being some advantage to singling out the enlargement or shift operator \mathrm{E} in its own right, we’ll begin by computing \mathrm{E}f for each function f in the above tables.

cc: CyberneticsOntolog • Peirce List (1) (2)Structural ModelingSystems Science

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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.