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Theme One Program • Exposition 7

$\text{Logical Interpretations of Cactus Structures}$

$\text{Logical Interpretations of Cactus Structures}$

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$\text{Logical Interpretations of Cactus Structures}$
$\text{Expression}$	$\begin{matrix} \text{Existential} \\ \text{Interpretation} \end{matrix}$	$\begin{matrix} \text{Entitative} \\ \text{Interpretation} \end{matrix}$
$~$	$\mathrm{true}$	$\mathrm{false}$
$\texttt{(} ~ \texttt{)}$	$\mathrm{false}$	$\mathrm{true}$
$C_1 \ldots C_k$	$C_1 \land \ldots \land C_k$	$C_1 \lor \ldots \lor C_k$
$\texttt{(} C_1 \texttt{,} \ldots \texttt{,} C_k \texttt{)}$	$\begin{matrix} \text{just one of} \\[6px] C_1, \ldots, C_k \\[6px] \text{is false} \end{matrix}$	$\begin{matrix} \text{not just one of} \\[6px] C_1, \ldots, C_k \\[6px] \text{is true} \end{matrix}$