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Table 5 summarizes the basic notations that are needed to describe the (first order) differential extensions of propositional calculi in a corresponding manner.
The \textit{first order differential extension} of $A^\circ$ extends the initial alphabet, $\mathfrak{A} = \{ ``a_1", \ldots, ``a_n" \},$ by a \textit{first order differential alphabet} $\operatorname{d}\mathfrak{A} = \{ ``\operatorname{d}a_1", \ldots, ``\operatorname{d}a_n" \},$ resulting in the \textit{first order extended alphabet}, $\operatorname{E}\mathfrak{A} = \mathfrak{A} \cup \operatorname{d}\mathfrak{A}.$
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Table 5 summarizes the notations that are needed to describe the first order differential extensions of propositional calculi in a corresponding manner.
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