Re: Cactus Rules
Jon Awbrey <[email protected]> Sun, 21 Mar 2004 00:00:04 -0500
| Newsgroups | gmane.comp.inquiry,gmane.comp.misc.ontology.general |
|---|---|
| Message-ID | <[email protected]> |
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o CR. Note 14 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o 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] 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_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 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o