[CG] Re: Differential Logic

Differential Logic • 10 • https://inquiryintoinquiry.com/2024/11/09/differential-logic-10-a/ Propositional Forms on Two Variables — Tables A1 and A2 showed two ways of organizing the sixteen boolean functions or propositional forms on two variables, as expressed in several notations. In future discussions the two Tables will be described as the “Index Order” and the “Orbit Order” of propositions, respectively, “orbits” being the usual term in mathematics for similarity classes under a group action. For ease of comparison, here are fresh copies of both Tables on the same page. Table A1. Propositional Forms on Two Variables (Index Order) • https://inquiryintoinquiry.files.wordpress.com/2020/04/table-a1.-propositio… Table A2. Propositional Forms on Two Variables (Orbit Order) • https://inquiryintoinquiry.files.wordpress.com/2020/04/table-a2.-propositio… Recalling the discussion up to this point, we took as our first example the boolean function f₈(p, q) = pq corresponding to the logical conjunction p∧q and examined how the differential operators E and D act on f₈. Each operator takes the boolean function of two variables f₈(p, q) and gives back a boolean function of four variables, Ef₈(p, q, dp, dq) and Df₈(p, q, dp, dq), respectively. In the next several posts we'll extend our scope to the full set of boolean functions on two variables and examine how the differential operators E and D act on that set. There being some advantage to singling out the enlargement or shift operator E in its own right, we'll begin by computing Ef for each function f in the above Tables. Resources — Logic Syllabus • https://inquiryintoinquiry.com/logic-syllabus/ Survey of Differential Logic • https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/ Regards, Jon cc: https://www.academia.edu/community/LGvvRw cc: https://www.researchgate.net/post/Differential_Logic_The_Logic_of_Change_an…