Changes

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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}, $\operatorname{E}\mathfrak{A} = \mathfrak{A} \cup \operatorname{d}\mathfrak{A}.$

An initial universe of discourse, $A^\circ$, supplies the groundwork for any number of further extensions, beginning with the \textit{first order differential extension}, $\operatorname{E}A^\circ.$ This 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}, $\operatorname{E}\mathfrak{A},$ defined as follows:

 

$\operatorname{E}\mathfrak{A} = \mathfrak{A} \cup \operatorname{d}\mathfrak{A} = \{ ``a_1", \ldots, ``a_n", ``\operatorname{d}a_1", \ldots, ``\operatorname{d}a_n" \}.$

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