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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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