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Rationalizing the usage of boolean variables to represent propositional features and functions in this manner, I can now discuss these concepts in greater detail, introducing additional notation along the way.

Rationalizing the usage of boolean variables to represent propositional features and functions in this manner, I can now discuss these concepts in greater detail, introducing additional notation along the way.

<pre>

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1. The sign "xi", appearing in the contextual frame "_ : Bn >B", whether explicitly or implicitly, can be interpreted as denoting the ith coordinate function xi : Bn >B.  The entire collection of coordinate maps in X = {xi} contributes to the definition of the "coordinate space" or "vector space" X : Bn, notated as follows:

 

<p>The sign <math>{}^{\backprime\backprime} x_i {}^{\prime\prime},\!</math> appearing in the contextual frame <math>{}^{\backprime\backprime} \underline{~~~} : \mathbb{B}^n \to \mathbb{B} {}^{\prime\prime},\!</math> or interpreted as belonging to that frame, denotes the <math>i^\text{th}\!</math> coordinate function <math>\underline{\underline{x_i}} : \mathbb{B}^n \to \mathbb{B}.</math> The entire collection of coordinate maps in <math>\underline{\underline{X}} = \{ \underline{\underline{x_i}} \}\!</math> contributes to the definition of the ''coordinate space'' or ''vector space'' <math>\underline{X} : \mathbb{B}^n,\!</math> notated as follows:</p>

 

X  =  <X> = <x1, ..., xn> = {<x1, ..., xn>} : Bn.

<p>Associated with the coordinate space <math>\underline{X}\!</math> are various families of boolean-valued functions <math>f : \underline{X} \to \mathbb{B}.\!</math></p></li>

Associated with the coordinate space X are various families of boolean valued functions f : X >B.

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a. The set of all functions f : X >B has a cardinality of 22^n and is denoted as follows:

a. The set of all functions f : X >B has a cardinality of 22^n and is denoted as follows: