[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 37

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Here is what I get when I try to analyze Peirce's
"giver of a horse to a lover of a woman" example
along the same lines as the 2-adic compositions.

We may begin with the mark-up shown in Figure 6.

o-------------------------------------------------o
|                                                 |
|                                                 |
|         `g`__$__%    $'l'__*   *w   %h          |
|              o  o    o     o   o    o           |
|               \  \  /       \ /    /            |
|                \  \/         @    /             |
|                 \ /\______ ______/              |
|                  @        @                     |
|                                                 |
|                                                 |
o-------------------------------------------------o
Figure 6.  Giver of a Horse to a Lover of a Woman

If we analyze this in accord with the "spreadsheet" model
of relational composition, the core of it is a particular
way of composing a 3-adic "giving" relation G c T x U x V
with a 2-adic "loving" relation L c U x W so as to obtain
a specialized sort of 3-adic relation (G o L) c T x W x V.
The applicable constraints on tuples are shown in Table 9.

Table 9.  Composite of Triadic and Dyadic Relations
o---------o---------o---------o---------o---------o
|         #   !1!   |   !1!   |   !1!   |   !1!   |
o=========o=========o=========o=========o=========o
|    G    #    T    |    U    |         |    V    |
o---------o---------o---------o---------o---------o
|    L    #         |    U    |    W    |         |
o---------o---------o---------o---------o---------o
|  G o L  #    T    |         |    W    |    V    |
o---------o---------o---------o---------o---------o

The hypergraph picture of the abstract composition is given in Figure 10.

o---------------------------------------------------------------------o
|                                                                     |
|                                G o L                                |
|                       ___________ at ___________                       |
|                      /                  \    \                      |
|                     /  G              L  \    \                     |
|                    /   @              @   \    \                    |
|                   /   /|\            / \   \    \                   |
|                  /   / | \          /   \   \    \                  |
|                 /   /  |  \        /     \   \    \                 |
|                /   /   |   \      /       \   \    \                |
|               o   o    o    o    o         o   o    o               |
|               T   T    U    V    U         W   W    V               |
|            1,_#   #`g`_$____%    $'l'______*   *1   %1              |
|               o   o    o    o    o         o   o    o               |
|                \ /      \    \  /           \ /    /                |
|                 @        \    \/             @    /                 |
|                !1!        \   /\            !1!  /                  |
|                            \ /  \_______ _______/                   |
|                             @           @                           |
|                            !1!         !1!                          |
|                                                                     |
o---------------------------------------------------------------------o
Figure 10.  Anything that is a Giver of Anything to a Lover of Anything

Jon Awbrey

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