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bertanimauro / cellularAutomata

3 variables - 256 different concepts - logic implication as a bitwise operator - addition translate in logical form
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where was born #1

Open bertanimauro opened 3 years ago

bertanimauro commented 3 years ago

I'm not sure if I understood but ((a&b=a) - >(a->b)) where & is a bitwise operator

Ref:https://inquiryintoinquiry.com/2021/08/26/animated-logical-graphs-81/

bertanimauro commented 3 years ago

Scanning the Table we observe the 16 points of X fall into 10 orbits total, divided into 4 orbits of 1 point each and 6 orbits of 2 points each. The points in singleton orbits are called fixed points of the transformation group since they are not moved but mapped into themselves by all group actions. The bottom row of the Table tabulates the total number of fixed points for the group operations 1 and t respectively. The group identity 1 always fixes all points, so its total is 16. The group action t fixes only the four points in singleton orbits, giving a total of 4

f_7 => f_1 !(a && b) => (!a || !b) https://www.wolframalpha.com/input/?i=%21%28a+%26%26+b%29+%3D%3E+%28%21a+%7C%7C+%21b%29

f_2 => f_11 (!x && y) => (x=>y) https://www.wolframalpha.com/input/?i=%28%21a+%26%26+b%29+%3D%3E+%28a+%3D%3E+b%29

REF: https://inquiryintoinquiry.com/2021/02/28/animated-logical-graphs-62/

bertanimauro commented 3 years ago

A sign relation L = O x S x I, as a set L embedded in a cartesian product O x S x I, tells how the signs in S and the interpretant signs in I correlate with the objects or objective situations in O.

The 256 concepts are the object O (the word of 8 bit), the way in which express these concepts with 3 variables and different operators are the Sign

REF: https://inquiryintoinquiry.com/2021/03/09/animated-logical-graphs-66/ https://inquiryintoinquiry.com/2021/03/30/animated-logical-graphs-69/

bertanimauro commented 3 years ago

Points in singleton orbits are called fixed points of the transformation group T : X \to X since they are left unchanged, or changed into themselves, by all group actions. Viewed in the frame of the sign relation L \subseteq O \times X \times X, where the transformations in T are literally translations in the linguistic sense, these T-invariant graphs have the same denotations in O for both Existential Interpreters and Entitative Interpreters.

tThey are not translations but concepts included in other concepts. a-> b = aCb. The truth of b is much broader but if a is true then b is also true

REF: https://inquiryintoinquiry.com/2021/04/22/animated-logical-graphs-72/

bertanimauro commented 3 years ago

REF: https://inquiryintoinquiry.com/2021/05/01/survey-of-animated-logical-graphs-4/

bertanimauro commented 3 years ago
00000001 1 00000001 1
00000001 1 00000011 3
00000001 1 00000101 5
00000001 1 00000111 7
00000001 1 00001001 9
00000001 1 00001011 11
00000001 1 00001101 13
00000001 1 00001111 15
00000010 2 00000010 2
00000010 2 00000011 3
00000010 2 00000110 6
00000010 2 00000111 7
00000010 2 00001010 10
00000010 2 00001011 11
00000010 2 00001110 14
00000010 2 00001111 15
00000011 3 00000011 3
00000011 3 00000111 7
00000011 3 00001011 11
00000011 3 00001111 15
00000100 4 00000100 4
00000100 4 00000101 5
00000100 4 00000110 6
00000100 4 00000111 7
00000100 4 00001100 12
00000100 4 00001101 13
00000100 4 00001110 14
00000100 4 00001111 15
00000101 5 00000101 5
00000101 5 00000111 7
00000101 5 00001101 13
00000101 5 00001111 15
00000110 6 00000110 6
00000110 6 00000111 7
00000110 6 00001110 14
00000110 6 00001111 15
00000111 7 00000111 7
00000111 7 00001111 15
00001000 8 00001000 8
00001000 8 00001001 9
00001000 8 00001010 10
00001000 8 00001011 11
00001000 8 00001100 12
00001000 8 00001101 13
00001000 8 00001110 14
00001000 8 00001111 15
00001001 9 00001001 9
00001001 9 00001011 11
00001001 9 00001101 13
00001001 9 00001111 15
00001010 10 00001010 10
00001010 10 00001011 11
00001010 10 00001110 14
00001010 10 00001111 15
00001011 11 00001011 11
00001011 11 00001111 15
00001100 12 00001100 12
00001100 12 00001101 13
00001100 12 00001110 14
00001100 12 00001111 15
00001101 13 00001101 13
00001101 13 00001111 15
00001110 14 00001110 14
00001110 14 00001111 15
00001111 15 00001111 15

ref: https://inquiryintoinquiry.com/2021/02/26/animated-logical-graphs-61/ https://inquiryintoinquiry.com/2021/02/28/animated-logical-graphs-62/

bertanimauro commented 3 years ago

https://groups.io/g/lawsofform/message/914

bertanimauro commented 3 years ago

https://list.iupui.edu/sympa/arc/peirce-l/2020-06/thrd5.html#00092 https://rjlipton.wordpress.com/2020/06/13/proof-checking-not-line-by-line/ https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems#Analysis_of_contingent_propositions

https://inquiryintoinquiry.com/2021/08/26/animated-logical-graphs-81/ Fouth note a Pierce-list. I didn't know. It was a coincidence. There was no malice.