Differential Propositional Calculus • 16

Posted on December 5, 2023 by Jon Awbrey

Differential Propositions • Qualitative Analogues of Differential Equations

The differential extension of a universe of discourse [\mathcal{A}] is constructed by extending its initial alphabet \mathfrak{A} to include a set of symbols for differential features, or basic changes capable of occurring in [\mathcal{A}].  The added symbols are taken to denote primitive features of change, qualitative attributes of motion, or propositions about how items in the universe of discourse may change or move in relation to features noted in the original alphabet.

With that in mind we define the corresponding differential alphabet or tangent alphabet \mathrm{d}\mathfrak{A} = \{``\mathrm{d}a_1", \ldots, ``\mathrm{d}a_n"\}, in principle just an arbitrary alphabet of symbols, disjoint from the initial alphabet \mathfrak{A} = \{``a_1", \ldots, ``a_n"\} and given the meanings just indicated.

In practice the precise interpretation of the symbols in \mathrm{d}\mathfrak{A} is conceived to be changeable from point to point of the underlying space A.  Indeed, for all we know, the state space A might well be the state space of a language interpreter, one concerned with the idiomatic meanings of the dialect generated by \mathfrak{A} and \mathrm{d}\mathfrak{A}.

Resources

cc: FB | Differential Logic • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs (1) (2) • Cybernetics • Structural Modeling • Systems 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 • 16

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