[Inquiry] Re: Differential Logic

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

DLOG.  Note B9

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Another way of looking at this situation is by letting the (first order)
differential features du, dv, dw be viewed as the features of another
universe of discourse, called the "tangent universe of X with respect
to the interpretation c" and notated as "dX.c".  In this setting,
Dq.c, the "difference proposition of q at the interpretation c",
where c = uvw, is marked by the shaded region in Figure 4.

o-------------------------------------------------o
| dX.uvw                                          |
|                                                 |
|                 o-------------o                 |
|                /               \                |
|               /                 \               |
|              /                   \              |
|             /                     \             |
|            o          dU           o            |
|            |                       |            |
|            |                       |            |
|            |                       |            |
|        o---o---------o   o---------o---o        |
|       /     \%%%%%%%%%\ /%%%%%%%%%/     \       |
|      /       \%%%%%%%%%o%%%%%%%%%/       \      |
|     /         \%%%%%%%/%\%%%%%%%/         \     |
|    /           \%%%%%/%%%\%%%%%/           \    |
|   o             o---o-----o---o             o   |
|   |                 |%%%%%|                 |   |
|   |       dV        |%%%%%|       dW        |   |
|   |                 |%%%%%|                 |   |
|   o                 o%%%%%o                 o   |
|    \                 \%%%/                 /    |
|     \                 \%/                 /     |
|      \                 o                 /      |
|       \               / \               /       |
|        o-------------o   o-------------o        |
|                                                 |
|                                                 |
o-------------------------------------------------o
Figure 4.  Tangent Venn Diagram for Dq.uvw

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o