Differential Propositional Calculus • 16

Posted on December 14, 2024 by Jon Awbrey

Differential Propositions • Qualitative Analogues of Differential Equations

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

To give the new symbols a name, we define the differential alphabet or tangent alphabet \mathrm{d}\mathfrak{A} = \{``\mathrm{d}a_1", \ldots, ``\mathrm{d}a_n"\}, in principle just an arbitrary set 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: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

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, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Differential Propositional Calculus • 16

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