[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 16 • https://inquiryintoinquiry.com/2023/12/05/differential-propositional-calcul… All, Note. The text below employs ‡A‡ for Fraktur or Gothic letter A and †A† for Calligraphic or Script letter A, but see the blog post linked above for the proper character formats. Differential Propositions • Qualitative Analogues of Differential Equations — The differential extension of a universe of discourse [†A†] is constructed by extending its initial alphabet ‡A‡ to include a set of symbols for “differential features”, or “basic changes” capable of occurring in [†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” d‡A‡ = {“da₁”, …, “daₙ”}, in principle just an arbitrary alphabet of symbols, disjoint from the initial alphabet ‡A‡ = {“a₁”, …, “aₙ”} and given the meanings just indicated. In practice the precise interpretation of the symbols in d‡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 ‡A‡ and d‡A‡. Resources — Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Differential Propositions • Qualitative Analogues of Differential Equations • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Regards, Jon cc: https://www.academia.edu/community/LY90rL