Cf: Differential Propositional Calculus : 8
At:
http://inquiryintoinquiry.com/2020/03/07/differential-propositional-calculus-%e2%80%a2-8/
Differential Extensions
=======================
An initial universe of discourse, A+, supplies the groundwork for any number of further extensions, beginning with the
"first order differential extension", EA+. The construction of EA+ can be described in the following stages:
Note. Breaking here because the rest of this
post requires too much math formatting.
Please see the blog post linked above or
the wiki copy at the following location:
Differential Propositional Calculus : Part 2 : Differential_Extensions
https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2#Differential_Extensions
<...>
A proposition in a differential extension of a universe of discourse is called a "differential proposition" and forms
the analogue of a system of differential equations in ordinary calculus. With these constructions, the "first order
extended universe" EA+ and the "first order differential proposition" f : EA->B, we have arrived, in concept at least,
at the foothills of "differential logic".
Table 11 summarizes the notations needed to describe the first order differential extensions of propositional calculi in
a systematic manner.
Table 11. Differential Extension : Basic Notation
https://inquiryintoinquiry.files.wordpress.com/2020/03/differential-extension-basic-notation.png
Regards,
Jon
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
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