Tag Archives: Inquiry Driven Systems

Differential Propositional Calculus • Overview

Posted on November 27, 2024 by Jon Awbrey

The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time. W. Ross Ashby • An Introduction to Cybernetics Differential logic is the component of logic … Continue reading →

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, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic • Overview

Posted on November 25, 2024 by Jon Awbrey

A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions.  Indeed, one of the first lessons I learned when I … Continue reading →

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, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 18

Posted on November 23, 2024 by Jon Awbrey

Tangent and Remainder Maps If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition in the following way. The next venn diagram shows the differential … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 17

Posted on November 22, 2024 by Jon Awbrey

Enlargement and Difference Maps Continuing with the example the following venn diagram shows the enlargement or shift map in the same style of field picture we drew for the tacit extension A very important conceptual transition has just occurred here, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 16

Posted on November 19, 2024 by Jon Awbrey

Propositions and Tacit Extensions Now that we’ve introduced the field picture as an aid to visualizing propositions and their analytic series, a pleasing way to picture the relationship of a proposition to its enlargement or shift map and its difference … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 15

Posted on November 18, 2024 by Jon Awbrey

Differential Fields The structure of a differential field may be described as follows.  With each point of there is associated an object of the following type:  a proposition about changes in that is, a proposition   In that frame of … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 14

Posted on November 16, 2024 by Jon Awbrey

Field Picture Let us summarize the outlook on differential logic we’ve reached so far.  We’ve been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse to considering a larger … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 13

Posted on November 14, 2024 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables Two views of how the difference operator acts on the set of sixteen functions are shown below.  Table A5 shows the expansion of over the set of ordinary variables and Table A6 shows the expansion … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 12

Posted on November 12, 2024 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables A first view of how the shift operator acts on the set of sixteen functions was provided by Table A3 in the previous post, expanding the expressions of over the set of ordinary variables. … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 11

Posted on November 10, 2024 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables As promised last time, 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 and act on that … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments