Tag Archives: Dynamical Systems

Differential Propositional Calculus • Discussion 2

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 The times are rife with distraction, so … Continue reading

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Differential Propositional Calculus • Discussion 1

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 Re: Cybernetics Communications • Klaus Krippendorff KK: … Continue reading

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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Differential Propositional Calculus • 8

Differential Extensions An initial universe of discourse, supplies the groundwork for any number of further extensions, beginning with the first order differential extension,   The construction of can be described in the following stages: The initial alphabet, is extended by … Continue reading

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Differential Propositional Calculus • 7

Special Classes of Propositions (concl.) Last and literally least in extent, we examine the family of singular propositions in a 3-dimensional universe of discourse. In our model of propositions as mappings of a universe of discourse to a set of … Continue reading

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Differential Propositional Calculus • 6

Special Classes of Propositions (cont.) Next we take up the family of positive propositions and follow the same plan as before, tracing the rule of their formation in the case of a 3-dimensional universe of discourse. Positive Propositions In a … Continue reading

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Differential Propositional Calculus • 5

Special Classes of Propositions (cont.) Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual … Continue reading

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Differential Propositional Calculus • 4

Special Classes of Propositions Before moving on, let’s unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above. A universe of discourse based on the logical features is a set plus the … Continue reading

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Differential Propositional Calculus • 3

Formal Development The preceding discussion outlined the ideas leading to the differential extension of propositional logic.  The next task is to lay out the concepts and terminology needed to describe various orders of differential propositional calculi. Elementary Notions Logical description … Continue reading

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Differential Propositional Calculus • 2

Cactus Calculus Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable -ary scope. A bracketed list of propositional expressions in the form indicates exactly one of the propositions is false. A … Continue reading

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Differential Propositional Calculus • 1

A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target … Continue reading

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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment