## Peirce’s 1870 “Logic Of Relatives” • Comment 10.7

Here is what I get when I analyze Peirce’s “giver of a horse to a lover of a woman” example along the same lines as the dyadic compositions.

We may begin with the mark-up shown in Figure 19.

 (19)

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a triadic giving relation $G \subseteq T \times U \times V$ with a dyadic loving relation $L \subseteq U \times W$ so as to obtain a specialized type of triadic relation $(G \circ L) \subseteq T \times V \times W.$ The applicable constraints on tuples are shown in Table 20.

$\text{Table 20.} ~~ \text{Composite of Triadic and Dyadic Relations}$
$\mathit{1}$ $\mathit{1}$ $\mathit{1}$ $\mathit{1}$
$G$ $T$ $U$ $V$
$L$   $U$   $W$
$G \circ L$ $T$   $V$ $W$

The hypergraph picture of the abstract composition is given in Figure 21.

 (21)
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