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The actions of the \PMlinkname{difference operator}{FiniteDifference} $\operatorname{D}$ and the \PMlinkname{tangent operator}{TangentMap} $\operatorname{d}$ on each of the 16 propositional forms on two variables are shown in the Tables below.

The actions of the \PMlinkname{difference operator}{FiniteDifference} $\operatorname{D}$ and the \PMlinkname{tangent operator}{TangentMap} $\operatorname{d}$ on the 16 propositional forms in two variables are shown in the Tables below.

Table A7 expands the resulting differential forms over a so-called ``logical basis":

Table A7 expands the resulting differential forms over a \textit{logical basis}:

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This is a set of singular propositions indicating mutually exclusive and exhaustive ``cells" or coordinate points of the universe of discourse.  For this reason, it may also be referred to as a cell-basis, point-basis, or singular basis.  In this setting it is frequently convenient to use the following abbreviations:

This set consists of the singular propositions in the first order differential variables, indicating mutually exclusive and exhaustive \textit{cells} of the tangent universe of discourse.  Accordingly, this set of differential propositions may also be referred to as the cell-basis, point-basis, or singular differential basis.  In this setting it is frequently convenient to use the following abbreviations:

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Table A8 expands the resulting differential forms over a so-called ``algebraic basis":

Table A8 expands the resulting differential forms over an \textit{algebraic basis}:

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$\{ 1,\ \operatorname{d}x,\ \operatorname{d}y,\ \operatorname{d}x\,\operatorname{d}y \}.$

$\{ 1,\ \operatorname{d}x,\ \operatorname{d}y,\ \operatorname{d}x\,\operatorname{d}y \}.$

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