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ONT Re: Differential Logic

To: Inquiry <inquiry@stderr.org>, Ontology <ontology@ieee.org>, SemioCom <gdsemiocom@univ-perp.fr>
Subject: ONT Re: Differential Logic
From: Jon Awbrey <jawbrey@oakland.edu>
Date: Sat, 31 May 2003 23:00:01 -0400
References: <3E982563.F67459A5@oakland.edu> <3EB73352.259E602@oakland.edu> <3ED7BACC.9E14FC98@oakland.edu> <3ED7C655.E94D97BB@oakland.edu>
Sender: owner-ontology@majordomo.ieee.org

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

DLOG.  Note D69

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

Operator Maps:  Box Views

o-----------------------o
|                       |
|                       |
|                       |
|      o--o   o--o      |
|     /    \ /    \     |
|    /      o      \    |
|   /  du  / \  dv  \   |
|  o      /   \      o  |
|  |     o     o     |  |
|  |     |     |     |  |
|  |     o     o     |  |
|  o      \   /      o  |
|   \      \ /      /   |
|    \      o      /    |
|     \    / \    /     |
|      o--o   o--o      |
|                       |
|                       |
|                       |
o-----------------------@
                         \
o-----------------------o \
|                       |  \
|                       |   \
|                       |    \
|      o--o   o--o      |     \
|     /    \ /    \     |      \
|    /      o      \    |       \
|   /  du  / \  dv  \   |        \
|  o      /   \      o  |         \
|  |     o     o     |  @          \
|  |     |     |     |  |\          \
|  |     o     o     |  | \          \
|  o      \   /      o  |  \          \
|   \      \ /      /   |   \          \
|    \      o      /    |    \          \
|     \    / \    /     |     \          \
|      o--o   o--o      |      \          \
|                       |       \          \
|                       |        \          \
|                       |         \          \
o-----------------------o          \          \
                                    \          \
o-----------------------@   o--------\----------\---o   o-----------------------o
|                       |\  |         \          \  |   |```````````````````````|
|                       | \ |          \          @ |   |```````````````````````|
|                       |  \|           \           |   |```````````````````````|
|      o--o   o--o      |   \      o--o  \o--o      |   |``````o--o```o--o``````|
|     /    \ /    \     |   |\    /    \ /\   \     |   |`````/````\`/````\`````|
|    /      o      \    |   | \  /      o  @   \    |   |````/``````o``````\````|
|   /  du  / \  dv  \   |   |  \/  du  /`\  dv  \   |   |```/``du``/`\``dv``\```|
|  o      /   \      o  |   |  o\     /```\      o  |   |``o``````/```\``````o``|
|  |     o     o     |  |   |  | \   o`````o     |  |   |``|`````o`````o`````|``|
|  |     |     |     |  |   |  |  @  |``@--|-----|------@``|`````|`````|`````|``|
|  |     o     o     |  |   |  |     o`````o     |  |   |``|`````o`````o`````|``|
|  o      \   /      o  |   |  o      \```/      o  |   |``o``````\```/``````o``|
|   \      \ /      /   |   |   \      \`/      /   |   |```\``````\`/``````/```|
|    \      o      /    |   |    \      o      /    |   |````\``````o``````/````|
|     \    / \    /     |   |     \    / \    /     |   |`````\````/`\````/`````|
|      o--o   o--o      |   |      o--o   o--o      |   |``````o--o```o--o``````|
|                       |   |                       |   |```````````````````````|
|                       |   |                       |   |```````````````````````|
|                       |   |                       |   |```````````````````````|
o-----------------------o   o-----------------------o   o-----------------------o
 \                     /     \                     /     \                     /
  \       !h!J        /        \        J        /        \       !h!J        /
   \                 /           \             /           \                 /
    \               /   o----------\---------/----------o   \               /
     \             /    |            \     /            |    \             /
      \           /     |              \ /              |     \           /
       \         /      |         o-----o-----o         |      \         /
        \       /       |        /`````````````\        |       \       /
         \     /        |       /```````````````\       |        \     /
   o------\---/------o  |      /`````````````````\      |  o------\---/------o
   |       \ /       |  |     /```````````````````\     |  |       \ /       |
   |     o--o--o     |  |    /`````````````````````\    |  |     o--o--o     |
   |    /```````\    |  |   o```````````````````````o   |  |    /```````\    |
   |   /`````````\   |  |   |```````````````````````|   |  |   /`````````\   |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |  |````dx`````|  @----@ |```````````x`````@-----|------@  |``` dx ````|  |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |   \`````````/   |  |   |```````````````````````|   |  |   \`````````/   |
   |    \```````/    |  |   o```````````````````````o   |  |    \```````/    |
   |     o-----o     |  |    \`````````````````````/    |  |     o-----o     |
   |                 |  |     \```````````````````/     |  |                 |
   o-----------------o  |      \`````````````````/      |  o-----------------o
                        |       \```````````````/       |
                        |        \`````````````/        |
                        |         o-----------o         |
                        |                               |
                        |                               |
                        o-------------------------------o
Figure 56-b1.  Radius Map of the Conjunction J = uv

o-----------------------o
|                       |
|                       |
|                       |
|      o--o   o--o      |
|     /    \ /    \     |
|    /      o      \    |
|   /  du  /`\  dv  \   |
|  o      /```\      o  |
|  |     o`````o     |  |
|  |     |`````|     |  |
|  |     o`````o     |  |
|  o      \```/      o  |
|   \      \`/      /   |
|    \      o      /    |
|     \    / \    /     |
|      o--o   o--o      |
|                       |
|                       |
|                       |
o-----------------------@
                         \
o-----------------------o \
|                       |  \
|                       |   \
|                       |    \
|      o--o   o--o      |     \
|     /````\ /    \     |      \
|    /``````o      \    |       \
|   /``du``/ \  dv  \   |        \
|  o``````/   \      o  |         \
|  |`````o     o     |  @          \
|  |`````|     |     |  |\          \
|  |`````o     o     |  | \          \
|  o``````\   /      o  |  \          \
|   \``````\ /      /   |   \          \
|    \``````o      /    |    \          \
|     \````/ \    /     |     \          \
|      o--o   o--o      |      \          \
|                       |       \          \
|                       |        \          \
|                       |         \          \
o-----------------------o          \          \
                                    \          \
o-----------------------@   o--------\----------\---o   o-----------------------o
|                       |\  |         \          \  |   |```````````````````````|
|                       | \ |          \          @ |   |```````````````````````|
|                       |  \|           \           |   |```````````````````````|
|      o--o   o--o      |   \      o--o  \o--o      |   |``````o--o```o--o``````|
|     /    \ /````\     |   |\    /    \ /\   \     |   |`````/    \`/    \`````|
|    /      o``````\    |   | \  /      o  @   \    |   |````/      o      \````|
|   /  du  / \``dv``\   |   |  \/  du  /`\  dv  \   |   |```/  du  / \  dv  \```|
|  o      /   \``````o  |   |  o\     /```\      o  |   |``o      /   \      o``|
|  |     o     o`````|  |   |  | \   o`````o     |  |   |``|     o     o     |``|
|  |     |     |`````|  |   |  |  @  |``@--|-----|------@``|     |     |     |``|
|  |     o     o`````|  |   |  |     o`````o     |  |   |``|     o     o     |``|
|  o      \   /``````o  |   |  o      \```/      o  |   |``o      \   /      o``|
|   \      \ /``````/   |   |   \      \`/      /   |   |```\      \ /      /```|
|    \      o``````/    |   |    \      o      /    |   |````\      o      /````|
|     \    / \````/     |   |     \    / \    /     |   |`````\    /`\    /`````|
|      o--o   o--o      |   |      o--o   o--o      |   |``````o--o```o--o``````|
|                       |   |                       |   |```````````````````````|
|                       |   |                       |   |```````````````````````|
|                       |   |                       |   |```````````````````````|
o-----------------------o   o-----------------------o   o-----------------------o
 \                     /     \                     /     \                     /
  \        EJ         /        \        J        /        \        EJ         /
   \                 /           \             /           \                 /
    \               /   o----------\---------/----------o   \               /
     \             /    |            \     /            |    \             /
      \           /     |              \ /              |     \           /
       \         /      |         o-----o-----o         |      \         /
        \       /       |        /`````````````\        |       \       /
         \     /        |       /```````````````\       |        \     /
   o------\---/------o  |      /`````````````````\      |  o------\---/------o
   |       \ /       |  |     /```````````````````\     |  |       \ /       |
   |     o--o--o     |  |    /`````````````````````\    |  |     o--o--o     |
   |    /```````\    |  |   o```````````````````````o   |  |    /```````\    |
   |   /`````````\   |  |   |```````````````````````|   |  |   /`````````\   |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |  |````dx`````|  @----@ |```````````x`````@-----|------@  |``` dx ````|  |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |   \`````````/   |  |   |```````````````````````|   |  |   \`````````/   |
   |    \```````/    |  |   o```````````````````````o   |  |    \```````/    |
   |     o-----o     |  |    \`````````````````````/    |  |     o-----o     |
   |                 |  |     \```````````````````/     |  |                 |
   o-----------------o  |      \`````````````````/      |  o-----------------o
                        |       \```````````````/       |
                        |        \`````````````/        |
                        |         o-----------o         |
                        |                               |
                        |                               |
                        o-------------------------------o
Figure 56-b2.  Secant Map of the Conjunction J = uv

o-----------------------o
|                       |
|                       |
|                       |
|      o--o   o--o      |
|     /    \ /    \     |
|    /      o      \    |
|   /  du  /`\  dv  \   |
|  o      /```\      o  |
|  |     o`````o     |  |
|  |     |`````|     |  |
|  |     o`````o     |  |
|  o      \```/      o  |
|   \      \`/      /   |
|    \      o      /    |
|     \    / \    /     |
|      o--o   o--o      |
|                       |
|                       |
|                       |
o-----------------------@
                         \
o-----------------------o \
|                       |  \
|                       |   \
|                       |    \
|      o--o   o--o      |     \
|     /````\ /    \     |      \
|    /``````o      \    |       \
|   /``du``/ \  dv  \   |        \
|  o``````/   \      o  |         \
|  |`````o     o     |  @          \
|  |`````|     |     |  |\          \
|  |`````o     o     |  | \          \
|  o``````\   /      o  |  \          \
|   \``````\ /      /   |   \          \
|    \``````o      /    |    \          \
|     \````/ \    /     |     \          \
|      o--o   o--o      |      \          \
|                       |       \          \
|                       |        \          \
|                       |         \          \
o-----------------------o          \          \
                                    \          \
o-----------------------@   o--------\----------\---o   o-----------------------o
|                       |\  |         \          \  |   |                       |
|                       | \ |          \          @ |   |                       |
|                       |  \|           \           |   |                       |
|      o--o   o--o      |   \      o--o  \o--o      |   |      o--o   o--o      |
|     /    \ /````\     |   |\    /    \ /\   \     |   |     /````\ /````\     |
|    /      o``````\    |   | \  /      o  @   \    |   |    /``````o``````\    |
|   /  du  / \``dv``\   |   |  \/  du  /`\  dv  \   |   |   /``du``/`\``dv``\   |
|  o      /   \``````o  |   |  o\     /```\      o  |   |  o``````/```\``````o  |
|  |     o     o`````|  |   |  | \   o`````o     |  |   |  |`````o`````o`````|  |
|  |     |     |`````|  |   |  |  @  |``@--|-----|------@  |`````|`````|`````|  |
|  |     o     o`````|  |   |  |     o`````o     |  |   |  |`````o`````o`````|  |
|  o      \   /``````o  |   |  o      \```/      o  |   |  o``````\```/``````o  |
|   \      \ /``````/   |   |   \      \`/      /   |   |   \``````\`/``````/   |
|    \      o``````/    |   |    \      o      /    |   |    \``````o``````/    |
|     \    / \````/     |   |     \    / \    /     |   |     \````/ \````/     |
|      o--o   o--o      |   |      o--o   o--o      |   |      o--o   o--o      |
|                       |   |                       |   |                       |
|                       |   |                       |   |                       |
|                       |   |                       |   |                       |
o-----------------------o   o-----------------------o   o-----------------------o
 \                     /     \                     /     \                     /
  \        DJ         /        \        J        /        \        DJ         /
   \                 /           \             /           \                 /
    \               /   o----------\---------/----------o   \               /
     \             /    |            \     /            |    \             /
      \           /     |              \ /              |     \           /
       \         /      |         o-----o-----o         |      \         /
        \       /       |        /`````````````\        |       \       /
         \     /        |       /```````````````\       |        \     /
   o------\---/------o  |      /`````````````````\      |  o------\---/------o
   |       \ /       |  |     /```````````````````\     |  |       \ /       |
   |     o--o--o     |  |    /`````````````````````\    |  |     o--o--o     |
   |    /```````\    |  |   o```````````````````````o   |  |    /```````\    |
   |   /`````````\   |  |   |```````````````````````|   |  |   /`````````\   |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |  |````dx`````|  @----@ |```````````x`````@-----|------@  |``` dx ````|  |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |   \`````````/   |  |   |```````````````````````|   |  |   \`````````/   |
   |    \```````/    |  |   o```````````````````````o   |  |    \```````/    |
   |     o-----o     |  |    \`````````````````````/    |  |     o-----o     |
   |                 |  |     \```````````````````/     |  |                 |
   o-----------------o  |      \`````````````````/      |  o-----------------o
                        |       \```````````````/       |
                        |        \`````````````/        |
                        |         o-----------o         |
                        |                               |
                        |                               |
                        o-------------------------------o
Figure 56-b3.  Chord Map of the Conjunction J = uv

o-----------------------o
|                       |
|                       |
|                       |
|      o--o   o--o      |
|     /    \ /    \     |
|    /      o      \    |
|   /  du  / \  dv  \   |
|  o      /   \      o  |
|  |     o     o     |  |
|  |     |     |     |  |
|  |     o     o     |  |
|  o      \   /      o  |
|   \      \ /      /   |
|    \      o      /    |
|     \    / \    /     |
|      o--o   o--o      |
|                       |
|                       |
|                       |
o-----------------------@
                         \
o-----------------------o \
|                       |  \
|                       |   \
|                       |    \
|      o--o   o--o      |     \
|     /````\ /    \     |      \
|    /``````o      \    |       \
|   /``du``/`\  dv  \   |        \
|  o``````/```\      o  |         \
|  |`````o`````o     |  @          \
|  |`````|`````|     |  |\          \
|  |`````o`````o     |  | \          \
|  o``````\```/      o  |  \          \
|   \``````\`/      /   |   \          \
|    \``````o      /    |    \          \
|     \````/ \    /     |     \          \
|      o--o   o--o      |      \          \
|                       |       \          \
|                       |        \          \
|                       |         \          \
o-----------------------o          \          \
                                    \          \
o-----------------------@   o--------\----------\---o   o-----------------------o
|                       |\  |         \          \  |   |                       |
|                       | \ |          \          @ |   |                       |
|                       |  \|           \           |   |                       |
|      o--o   o--o      |   \      o--o  \o--o      |   |      o--o   o--o      |
|     /    \ /````\     |   |\    /    \ /\   \     |   |     /````\ /````\     |
|    /      o``````\    |   | \  /      o  @   \    |   |    /``````o``````\    |
|   /  du  /`\``dv``\   |   |  \/  du  /`\  dv  \   |   |   /``du``/ \``dv``\   |
|  o      /```\``````o  |   |  o\     /```\      o  |   |  o``````/   \``````o  |
|  |     o`````o`````|  |   |  | \   o`````o     |  |   |  |`````o     o`````|  |
|  |     |`````|`````|  |   |  |  @  |``@--|-----|------@  |`````|     |`````|  |
|  |     o`````o`````|  |   |  |     o`````o     |  |   |  |`````o     o`````|  |
|  o      \```/``````o  |   |  o      \```/      o  |   |  o``````\   /``````o  |
|   \      \`/``````/   |   |   \      \`/      /   |   |   \``````\ /``````/   |
|    \      o``````/    |   |    \      o      /    |   |    \``````o``````/    |
|     \    / \````/     |   |     \    / \    /     |   |     \````/ \````/     |
|      o--o   o--o      |   |      o--o   o--o      |   |      o--o   o--o      |
|                       |   |                       |   |                       |
|                       |   |                       |   |                       |
|                       |   |                       |   |                       |
o-----------------------o   o-----------------------o   o-----------------------o
 \                     /     \                     /     \                     /
  \        dJ         /        \        J        /        \        dJ         /
   \                 /           \             /           \                 /
    \               /   o----------\---------/----------o   \               /
     \             /    |            \     /            |    \             /
      \           /     |              \ /              |     \           /
       \         /      |         o-----o-----o         |      \         /
        \       /       |        /`````````````\        |       \       /
         \     /        |       /```````````````\       |        \     /
   o------\---/------o  |      /`````````````````\      |  o------\---/------o
   |       \ /       |  |     /```````````````````\     |  |       \ /       |
   |     o--o--o     |  |    /`````````````````````\    |  |     o--o--o     |
   |    /```````\    |  |   o```````````````````````o   |  |    /```````\    |
   |   /`````````\   |  |   |```````````````````````|   |  |   /`````````\   |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |  |````dx`````|  @----@ |```````````x`````@-----|------@  |``` dx ````|  |
   |  o```````````o  |  |   |```````````````````````|   |  |  o```````````o  |
   |   \`````````/   |  |   |```````````````````````|   |  |   \`````````/   |
   |    \```````/    |  |   o```````````````````````o   |  |    \```````/    |
   |     o-----o     |  |    \`````````````````````/    |  |     o-----o     |
   |                 |  |     \```````````````````/     |  |                 |
   o-----------------o  |      \`````````````````/      |  o-----------------o
                        |       \```````````````/       |
                        |        \`````````````/        |
                        |         o-----------o         |
                        |                               |
                        |                               |
                        o-------------------------------o
Figure 56-b4.  Tangent Map of the Conjunction J = uv

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Follow-Ups:
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  - From: Jon Awbrey <jawbrey@oakland.edu>
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  - From: Jon Awbrey <jawbrey@oakland.edu>
- ONT Re: Differential Logic
  - From: Jon Awbrey <jawbrey@oakland.edu>
- ONT Re: Differential Logic
  - From: Jon Awbrey <jawbrey@oakland.edu>
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