ONT Re: Cactus Rules
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CR. Note 14
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I will explain my concept of "thematization"
or "thematic extension" after I copy out the
series of Tables that is formed on its basis.
In the meantime, here is a general exposition:
| Jon Awbrey, "Differential Logic and Dynamic Systems"
| DLOG D28. http://suo.ieee.org/ontology/msg04826.html
| DLOG D29. http://suo.ieee.org/ontology/msg04827.html
| DLOG D30. http://suo.ieee.org/ontology/msg04828.html
| DLOG D31. http://suo.ieee.org/ontology/msg04829.html
| DLOG D32. http://suo.ieee.org/ontology/msg04830.html
| DLOG D33. http://suo.ieee.org/ontology/msg04832.html
In order to make the pattern of their construction
more evident, I have left the expressions of the
thematic extensions in their unreduced forms.
Table 10. Thematic Extensions: [q, r] -> [p, q, r]
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| L_1 | L_2 | L_3 | L_4 |
| | | | |
| Decimal | Binary | Vector | Cactus |
o---------o------------o-----------------o---------------------o
| | p : 1 1 1 1 0 0 0 0 | |
| | q : 1 1 0 0 1 1 0 0 | |
| | r : 1 0 1 0 1 0 1 0 | |
o---------o------------o-----------------o---------------------o
| | | | |
| q_15 | q_00001111 | 0 0 0 0 1 1 1 1 | ((p , ( ) )) |
| | | | |
| q_30 | q_00011110 | 0 0 0 1 1 1 1 0 | ((p , (q) (r) )) |
| | | | |
| q_45 | q_00101101 | 0 0 1 0 1 1 0 1 | ((p , (q) r )) |
| | | | |
| q_60 | q_00111100 | 0 0 1 1 1 1 0 0 | ((p , (q) )) |
| | | | |
| q_75 | q_01001011 | 0 1 0 0 1 0 1 1 | ((p , q (r) )) |
| | | | |
| q_90 | q_01011010 | 0 1 0 1 1 0 1 0 | ((p , (r) )) |
| | | | |
| q_105 | q_01101001 | 0 1 1 0 1 0 0 1 | ((p , (q , r) )) |
| | | | |
| q_120 | q_01111000 | 0 1 1 1 1 0 0 0 | ((p , (q r) )) |
| | | | |
| q_135 | q_10000111 | 1 0 0 0 0 1 1 1 | ((p , q r )) |
| | | | |
| q_150 | q_10010110 | 1 0 0 1 0 1 1 0 | ((p , ((q , r)) )) |
| | | | |
| q_165 | q_10100101 | 1 0 1 0 0 1 0 1 | ((p , r )) |
| | | | |
| q_180 | q_10110100 | 1 0 1 1 0 1 0 0 | ((p , (q (r)) )) |
| | | | |
| q_195 | q_11000011 | 1 1 0 0 0 0 1 1 | ((p , q )) |
| | | | |
| q_210 | q_11010010 | 1 1 0 1 0 0 1 0 | ((p , ((q) r) )) |
| | | | |
| q_225 | q_11100001 | 1 1 1 0 0 0 0 1 | ((p , ((q) (r)) )) |
| | | | |
| q_240 | q_11110000 | 1 1 1 1 0 0 0 0 | ((p , )) |
| | | | |
o---------o------------o-----------------o---------------------o
Jon Awbrey
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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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