Changes

In the customary fashion, the name <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> of the variable <math>x_i\!</math> is flexibly interpreted to serve two additional roles.  In algebraic and geometric contexts <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> is taken to name the <math>i^\text{th}\!</math> ''coordinate function'' <math>\underline{\underline{x_i}} : \mathbb{B}^n \to \mathbb{B}.\!</math>  In logical contexts <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> serves to name the <math>i^\text{th}\!</math> ''basic property'' or ''simple proposition'', also called <math>{}^{\backprime\backprime} \underline{\underline{x_i}} {}^{\prime\prime},\!</math> that goes into the construction of a propositional universe of discourse, in effect, becoming one of the ''sentence letters'' of a truth table and being used to label one of the ''simple enclosures'' of a venn diagram.

In the customary fashion, the name <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> of the variable <math>x_i\!</math> is flexibly interpreted to serve two additional roles.  In algebraic and geometric contexts <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> is taken to name the <math>i^\text{th}\!</math> ''coordinate function'' <math>\underline{\underline{x_i}} : \mathbb{B}^n \to \mathbb{B}.\!</math>  In logical contexts <math>{}^{\backprime\backprime} x_i {}^{\prime\prime}\!</math> serves to name the <math>i^\text{th}\!</math> ''basic property'' or ''simple proposition'', also called <math>{}^{\backprime\backprime} \underline{\underline{x_i}} {}^{\prime\prime},\!</math> that goes into the construction of a propositional universe of discourse, in effect, becoming one of the ''sentence letters'' of a truth table and being used to label one of the ''simple enclosures'' of a venn diagram.

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.

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:

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: