The actions of the difference operator <math>\operatorname{D}</math> and the tangent operator <math>\operatorname{d}</math> on each of the 16 propositional forms on two variables are shown in the Tables below.
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Table A7 expands the resulting differential forms over a so-called "logical basis":
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:
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<math>\partial x = \operatorname{d}x\,(\operatorname{d}y)</math> and <math>\partial y = (\operatorname{d}x)\,\operatorname{d}y.</math>
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Table A8 expands the resulting differential forms over a so-called "algebraic basis":