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We have been studying the action of the difference operator <math>\operatorname{D},</math> also known as the ''localization operator'', on the proposition <math>f : X \times Y \to \mathbb{B}</math> that is commonly known as the conjunction <math>x \cdot y.</math>  We described <math>\operatorname{D}f</math> as a (first order) differential proposition, that is, a proposition of the type <math>\operatorname{D}f : X \times Y \times \operatorname{d}X \times \operatorname{d}Y \to \mathbb{B}.</math>  Abstracting from the augmented venn diagram that illustrates how the ''models'' or ''satisfying interpretations'' of <math>\operatorname{D}f</math> distribute within the extended universe <math>\operatorname{E}U = X \times Y \times \operatorname{d}X \times \operatorname{d}Y,</math> we can depict <math>\operatorname{D}f</math> in the form of a ''digraph'' or ''directed graph'', one whose points are labeled with the elements of <math>U =  X \times Y</math> and whose arrows are labeled with the elements of <math>\operatorname{d}U = \operatorname{d}X \times \operatorname{d}Y.</math>

We have been studying the action of the difference operator <math>\operatorname{D},</math> also known as the ''localization operator'', on the proposition <math>f : X \times Y \to \mathbb{B}</math> that is commonly known as the conjunction <math>x \cdot y.</math>  We described <math>\operatorname{D}f</math> as a (first order) differential proposition, that is, a proposition of the type <math>\operatorname{D}f : X \times Y \times \operatorname{d}X \times \operatorname{d}Y \to \mathbb{B}.</math>  Abstracting from the augmented venn diagram that illustrates how the ''models'' or ''satisfying interpretations'' of <math>\operatorname{D}f</math> distribute within the extended universe <math>\operatorname{E}U = X \times Y \times \operatorname{d}X \times \operatorname{d}Y,</math> we can depict <math>\operatorname{D}f</math> in the form of a ''digraph'' or ''directed graph'', one whose points are labeled with the elements of <math>U =  X \times Y</math> and whose arrows are labeled with the elements of <math>\operatorname{d}U = \operatorname{d}X \times \operatorname{d}Y.</math>

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