[Inquiry] Re: Differential Logic

[Jon Awbrey]

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DLOG.  Note D33

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Thematization:  Truth Tables (concl.)

In order to show what all of the thematic extensions from two dimensions
to three dimensions look like in terms of coordinates, Tables 28 and 29
present ordinary truth tables for the functions f_i : B^2 -> B and for
the corresponding thematizations theta(f_i) = !f!_i : B^3 -> B.

Table 28.  Propositions on Two Variables
o-------o-----o----------------------------------------------------------------o
| u   v |     | f   f   f   f   f   f   f   f   f   f   f   f   f   f   f   f  |
|       |     | 00  01  02  03  04  05  06  07  08  09  10  11  12  13  14  15 |
o-------o-----o----------------------------------------------------------------o
|       |     |                                                                |
| 0   0 |     | 0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1  |
|       |     |                                                                |
| 0   1 |     | 0   0   1   1   0   0   1   1   0   0   1   1   0   0   1   1  |
|       |     |                                                                |
| 1   0 |     | 0   0   0   0   1   1   1   1   0   0   0   0   1   1   1   1  |
|       |     |                                                                |
| 1   1 |     | 0   0   0   0   0   0   0   0   1   1   1   1   1   1   1   1  |
|       |     |                                                                |
o-------o-----o----------------------------------------------------------------o

Table 29.  Thematic Extensions of Bivariate Propositions
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| u   v | f^¢ |!f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! !f! |
|       |     | 00  01  02  03  04  05  06  07  08  09  10  11  12  13  14  15 |
o-------o-----o----------------------------------------------------------------o
|       |     |                                                                |
| 0  0  |  0  | 1   0   1   0   1   0   1   0   1   0   1   0   1   0   1   0  |
|       |     |                                                                |
| 0  0  |  1  | 0   1   0   1   0   1   0   1   0   1   0   1   0   1   0   1  |
|       |     |                                                                |
| 0  1  |  0  | 1   1   0   0   1   1   0   0   1   1   0   0   1   1   0   0  |
|       |     |                                                                |
| 0  1  |  1  | 0   0   1   1   0   0   1   1   0   0   1   1   0   0   1   1  |
|       |     |                                                                |
| 1  0  |  0  | 1   1   1   1   0   0   0   0   1   1   1   1   0   0   0   0  |
|       |     |                                                                |
| 1  0  |  1  | 0   0   0   0   1   1   1   1   0   0   0   0   1   1   1   1  |
|       |     |                                                                |
| 1  1  |  0  | 1   1   1   1   1   1   1   1   0   0   0   0   0   0   0   0  |
|       |     |                                                                |
| 1  1  |  1  | 0   0   0   0   0   0   0   0   1   1   1   1   1   1   1   1  |
|       |     |                                                                |
o-------o-----o----------------------------------------------------------------o

Jon Awbrey

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