Re: Cactus Rules
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CR. Note 22
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I'm puzzled by the blind-spot that prevented me
from seeing this very simple and natural family
of propositions, especially since I had already
counted a third of their number. At any rate,
here they be, and modulo the usual number of
corrections I think that these complete the
set of 256 propositions on three variables.
Table 18. Desultory Junctions and Their Complements
o---------o------------o-----------------o---------------------------o
| 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_224 | q_11100000 | 1 1 1 0 0 0 0 0 | p ((q)(r)) |
| | | | |
| q_200 | q_11001000 | 1 1 0 0 1 0 0 0 | q ((p)(r)) |
| | | | |
| q_168 | q_10101000 | 1 0 1 0 1 0 0 0 | r ((p)(q)) |
| | | | |
| q_14 | q_00001110 | 0 0 0 0 1 1 1 0 | (p) ((q)(r)) |
| | | | |
| q_50 | q_00110010 | 0 0 1 1 0 0 1 0 | (q) ((p)(r)) |
| | | | |
| q_84 | q_01010100 | 0 1 0 1 0 1 0 0 | (r) ((p)(q)) |
| | | | |
o---------o------------o-----------------o---------------------------o
| | | | |
| q_31 | q_00011111 | 0 0 0 1 1 1 1 1 | (p ((q)(r))) |
| | | | |
| q_55 | q_00110111 | 0 0 1 1 0 1 1 1 | (q ((p)(r))) |
| | | | |
| q_87 | q_01010111 | 0 1 0 1 0 1 1 1 | (r ((p)(q))) |
| | | | |
| q_241 | q_11110001 | 1 1 1 1 0 0 0 1 | ((p) ((q)(r))) |
| | | | |
| q_205 | q_11001101 | 1 1 0 0 1 1 0 1 | ((q) ((p)(r))) |
| | | | |
| q_171 | q_10101011 | 1 0 1 0 1 0 1 1 | ((r) ((p)(q))) |
| | | | |
o---------o------------o-----------------o---------------------------o
Jon Awbrey
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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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