Jon, List,
does the comma mean having something in common, so "y XOR x" = "(y,x)" , meaning that something that is x cannot be y, so that it its not so, that "x" and "y" have anything in common?
I was thinking about possibility and probability. Is it so, that possibility means "x OR NOT x", written ""x(x)" in entitative Graph, which would be written in EG and DPC like ((x)x): "NOT(NOT x AND x)". It implies that from x follows x (tautology).
Probability is possibility with values (is that so?), and maybe with a time range for this possibility, so I was thinking how can you write probability in a calculus. Maybe like e.g. "dx" has the probability of one third to happen in one hour, one may write it like "d/h((1/3x) 2/3x) = d/3h((x)2x). Maybe this is completely wrong, I am not good with mathematics, but maybe something like that?
Best,
Helmut
24. Februar 2020 um 20:08 Uhr
"Jon Awbrey" <[email protected]>wrote:
An: "Cybernetic Communications" <[email protected]>, "Ontolog Forum" <[email protected]>, "Structural Modeling" <[email protected]>, SysSciWG <[email protected]>, "Peirce List" <[email protected]>
Betreff: [PEIRCE-L] Re: Differential Propositional Calculus
"Jon Awbrey" <[email protected]>wrote:
An: "Cybernetic Communications" <[email protected]>, "Ontolog Forum" <[email protected]>, "Structural Modeling" <[email protected]>, SysSciWG <[email protected]>, "Peirce List" <[email protected]>
Betreff: [PEIRCE-L] Re: Differential Propositional Calculus
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
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
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
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
