Re: Cactus Rules
Jon Awbrey <[email protected]> Thu, 18 Mar 2004 15:14:59 -0500
| Newsgroups | gmane.comp.inquiry,gmane.comp.misc.ontology.general |
|---|---|
| Message-ID | <[email protected]> |
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o CR. Note 8 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o In any k-dimensional universe of discourse X% = [x_1, ..., x_k] there are two other (2^k)-clans of propositions that ordinarily merit special attention. These are the "positive" propositions and the "singular" propositions, tabulated for the present case k = 3 in Tables 3 and 4, respectively, as usual throwing in the logical complements just for good measure. Table 3. Positive Propositions 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_255 | q_11111111 | 1 1 1 1 1 1 1 1 | (( )) | | | | | | | q_240 | q_11110000 | 1 1 1 1 0 0 0 0 | p | | | | | | | q_204 | q_11001100 | 1 1 0 0 1 1 0 0 | q | | | | | | | q_170 | q_10101010 | 1 0 1 0 1 0 1 0 | r | | | | | | | q_192 | q_11000000 | 1 1 0 0 0 0 0 0 | p q | | | | | | | q_160 | q_10100000 | 1 0 1 0 0 0 0 0 | p r | | | | | | | q_136 | q_10001000 | 1 0 0 0 1 0 0 0 | q r | | | | | | | q_128 | q_10000000 | 1 0 0 0 0 0 0 0 | p q r | | | | | | o---------o------------o-----------------o-------------------o | | | | | | q_1 | q_00000000 | 0 0 0 0 0 0 0 0 | ( ) | | | | | | | q_15 | q_00001111 | 0 0 0 0 1 1 1 1 | (p) | | | | | | | q_51 | q_00110011 | 0 0 1 1 0 0 1 1 | (q) | | | | | | | q_85 | q_01010101 | 0 1 0 1 0 1 0 1 | (r) | | | | | | | q_63 | q_00111111 | 0 0 1 1 1 1 1 1 | (p q) | | | | | | | q_95 | q_01011111 | 0 1 0 1 1 1 1 1 | (p r) | | | | | | | q_119 | q_01110111 | 0 1 1 1 0 1 1 1 | (q r) | | | | | | | q_127 | q_01111111 | 0 1 1 1 1 1 1 1 | (p q r) | | | | | | o---------o------------o-----------------o-------------------o Table 4. Singular Propositions 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_1 | q_00000001 | 0 0 0 0 0 0 0 1 | (p) (q) (r) | | | | | | | q_2 | q_00000010 | 0 0 0 0 0 0 1 0 | (p) (q) r | | | | | | | q_4 | q_00000100 | 0 0 0 0 0 1 0 0 | (p) q (r) | | | | | | | q_8 | q_00001000 | 0 0 0 0 1 0 0 0 | (p) q r | | | | | | | q_16 | q_00010000 | 0 0 0 1 0 0 0 0 | p (q) (r) | | | | | | | q_32 | q_00100000 | 0 0 1 0 0 0 0 0 | p (q) r | | | | | | | q_64 | q_01000000 | 0 1 0 0 0 0 0 0 | p q (r) | | | | | | | q_128 | q_10000000 | 1 0 0 0 0 0 0 0 | p q r | | | | | | o---------o------------o-----------------o-------------------o | | | | | | q_254 | q_11111110 | 1 1 1 1 1 1 1 0 | ((p) (q) r)) | | | | | | | q_253 | q_11111101 | 1 1 1 1 1 1 0 1 | ((p) (q) r ) | | | | | | | q_251 | q_11111011 | 1 1 1 1 1 0 1 1 | ((p) q (r)) | | | | | | | q_247 | q_11110111 | 1 1 1 1 0 1 1 1 | ((p) q r ) | | | | | | | q_239 | q_11101111 | 1 1 1 0 1 1 1 1 | ( p (q) (r)) | | | | | | | q_223 | q_11011111 | 1 1 0 1 1 1 1 1 | ( p (q) r ) | | | | | | | q_191 | q_10111111 | 1 0 1 1 1 1 1 1 | ( p q (r)) | | | | | | | q_127 | q_01111111 | 0 1 1 1 1 1 1 1 | ( p q r ) | | | | | | o---------o------------o-----------------o-------------------o Jon Awbrey o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o