Re: Cactus Rules
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CR. Note 18
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Table 14 shows the propositions q_i : B^3 -> B whose "fibers of truth",
that is, whose pre-images of 1, have the form of a single point in B^3
together with the three points that make up its immediate neighborhood.
Here I use the alternative syntax "x + y" for the exclusive-or (x , y).
Table 14. Proximal Propositions
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| L_1 | L_2 | L_3 | L_4 |
| | | | |
| Decimal | Binary | Vector | Cactus |
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| | 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 | |
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| | | | |
| q_23 | q_00010111 | 0 0 0 1 0 1 1 1 | (p)(q)(r) + ((p),(q),(r)) |
| | | | |
| q_43 | q_00101011 | 0 0 1 0 1 0 1 1 | (p)(q) r + ((p),(q), r ) |
| | | | |
| q_77 | q_01001101 | 0 1 0 0 1 1 0 1 | (p) q (r) + ((p), q ,(r)) |
| | | | |
| q_142 | q_10001110 | 1 0 0 0 1 1 1 0 | (p) q r + ((p), q , r ) |
| | | | |
| q_113 | q_01110001 | 0 1 1 1 0 0 0 1 | p (q)(r) + ( p ,(q),(r)) |
| | | | |
| q_178 | q_10110010 | 1 0 1 1 0 0 1 0 | p (q) r + ( p ,(q), r ) |
| | | | |
| q_212 | q_11010100 | 1 1 0 1 0 1 0 0 | p q (r) + ( p , q ,(r)) |
| | | | |
| q_232 | q_11101000 | 1 1 1 0 1 0 0 0 | p q r + ( p , q , r ) |
| | | | |
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Jon Awbrey
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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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