[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 11 • https://inquiryintoinquiry.com/2024/12/10/differential-propositional-calcul… Special Classes of Propositions (cont.) Next we take up the family of positive propositions and follow the same plan as before, tracing the rule of their formation in the case of a 3‑dimensional universe of discourse. Positive Propositions — The positive propositions p : Bⁿ → B may be written as products: • https://inquiryintoinquiry.files.wordpress.com/2020/02/positive-proposition… In a universe of discourse based on three boolean variables, p, q, r, there are 2³ = 8 positive propositions, taking the shapes shown in Figure 9. Figure 9. Positive Propositions on Three Variables • https://inquiryintoinquiry.files.wordpress.com/2020/03/venn-diagrams-e280a2… At the top is the venn diagram for the positive proposition of rank 3, corresponding to the boolean product or logical conjunction pqr. Next are the venn diagrams for the three positive propositions of rank 2, corresponding to the three boolean products, pr, qr, pq, respectively. Next are the three positive propositions of rank 1, which are none other than the three basic propositions, p, q, r. At the bottom is the positive proposition of rank 0, the everywhere true proposition or the constant 1 function, which may be expressed by the form (( )) or by a simple 1. 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/VoqgZr cc: https://www.researchgate.net/post/Differential_Propositional_Calculus