Cf: Differential Propositional Calculus : 3
At:
http://inquiryintoinquiry.com/2020/02/24/differential-propositional-calculus-%e2%80%a2-3/
I am working my way toward one of the places where Peirce's logic and semiotics,
Spencer Brown's Laws of Form, and Ashby's cybernetics meet, but there are a few
more courses of conceptual and notational bricks to lay down before we have the
proper foundation.
Formal Development
==================
The preceding discussion outlined the ideas leading to the differential
extension
of propositional logic. The next task is to lay out the concepts and
terminology
needed to describe various orders of differential propositional calculi.
Elementary Notions
==================
Logical description of a universe of discourse begins with a collection of
logical signs.
For simplicity in a first approach, we may assume these logical signs are
collected in
the form of a finite alphabet, \mathfrak{A} = {"a_1", ..., "a_n"}. Each of
these signs
is interpreted as denoting a logical feature, for example, a property that
objects of
the universe of discourse may have or a proposition about objects in the
universe of
discourse. There is then corresponding to the alphabet \mathfrak{A} a set of
logical
features, \mathcal{A} = {a_1, ..., a_n}.
Note. Breaking here because the rest of this post requires too much math
formatting.
Please see the blog post linked above or the wiki version at the following
location:
Differential Propositional Calculus : Part 2
https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2
<...>
Table 7 summarizes the notations needed to describe ordinary propositional
calculi in a systematic fashion.
Table 7. Propositional Calculus : Basic Notation
https://inquiryintoinquiry.files.wordpress.com/2020/02/propositional-calculus-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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