[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 34 • https://inquiryintoinquiry.com/2024/12/29/differential-propositional-calcul… Example 2. Drives and Their Vicissitudes (cont.) With a little thought it is possible to devise a canonical indexing scheme for the states in differential logical systems. A scheme of that order allows for comparing changes of state in universes of discourse that weigh in on different scales of observation. To that purpose, let us index the states q in E^m X with the dyadic rationals (or the binary fractions) in the half‑open interval [0, 2). Formally and canonically, a state q_r is indexed by a fraction r = s/t whose denominator is the power of two t = 2^m and whose numerator is a binary numeral formed from the coefficients of state in a manner to be described next. The “differential coefficients” of the state q are the values d^k (q) for k = 0 to m, where d⁰A is defined as identical to A. To form the binary index d₀.d₁ … d_m of the state q the coefficient d^k A(q) is read off as the binary digit d_k associated with the place value 2^{-k}. Expressed in algebraic terms, the rational index r of the state q is given by the following equivalent formulations. Differential Coefficients • State Coordinates • https://inquiryintoinquiry.files.wordpress.com/2023/12/differential-logic-e… Resources — Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Differential Logic • Drives and Their Vicissitudes • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Regards, Jon cc: https://www.academia.edu/community/lJAaKx cc: https://www.researchgate.net/post/Differential_Propositional_Calculus