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Peirce’s 1870 “Logic of Relatives” • Comment 12.4

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\text{Equation 1a.}~ (a^b)^c = a^{bc}

(a^b)^c = a^(bc)

\text{Equation 1b.}~ (a^b)^c = a^{bc}.

(a^b)^c = a^(bc)

\text{Equation 2a.}~ (\mathit{s}^\mathit{l})^\mathrm{w} = \mathit{s}^{(\mathit{l}\mathrm{w})}

(s^ℓ)^w = s^(ℓw)

\text{Equation 2b.}~ (\mathit{s}^\mathit{l})^\mathrm{w} = \mathit{s}^{(\mathit{l}\mathrm{w})}.

(s^ℓ)^w = s^(ℓw)

Equation 3

Denotation Equation s^(ℓw)

\text{Bigraph Involution}~ \mathsf{S}^\mathsf{L}

Bigraph Involution S^L
\text{Bigraph Involution}~ \mathsf{S}^\mathsf{L}

Equation 4

Matrix Computation S^L

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Equation 1a

(a^b)^c ~=~ a^{bc}

Equation 1b

(a^b)^c ~=~ a^{bc}.

Equation 2a

(\mathit{s}^\mathit{l})^\mathrm{w} ~=~ \mathit{s}^{(\mathit{l}\mathrm{w})}

Equation 2b

(\mathit{s}^\mathit{l})^\mathrm{w} ~=~ \mathit{s}^{(\mathit{l}\mathrm{w})}.

Equation 3

\displaystyle \mathit{s}^{(\mathit{l}\mathrm{w})} ~=~ \bigcap_{x \in LW} \mathrm{proj}_1 (S \star x) ~=~ \bigcap_{x \in LW} S \cdot x

\text{Bigraph Involution}~ \mathsf{S}^\mathsf{L}

LOR 1870 Figure 56 (56)

Equation 4

\displaystyle (\mathsf{S}^\mathsf{L})_{xy} ~=~ \prod_{p \in X} \mathsf{S}_{xp}^{\mathsf{L}_{py}}