Changes

We have been using the lower case letters <math>p, q, r\!</math> for the basic propositions of abstract type <math>\mathbb{B}^3 \to \mathbb{B}</math> and the upper case letters <math>P, Q, R\!</math> for the basic regions of the universe of discourse where <math>p, q, r,\!</math> respectively, hold true.

We have been using the lower case letters <math>p, q, r\!</math> for the basic propositions of abstract type <math>\mathbb{B}^3 \to \mathbb{B}</math> and the upper case letters <math>P, Q, R\!</math> for the basic regions of the universe of discourse where <math>p, q, r,\!</math> respectively, hold true.

The set of signs <font face=calligrapher>X</font> = {"''p''", "''q''", "''r''"} is the ''alphabet'' for the universe of discourse that is notated as ''X''^&nbsp;&bull; = [<font face=calligrapher>X</font>] = [''p'', ''q'', ''r''], already getting sloppy about quotation marks to single out the signs.

The set of signs <math>\mathcal{X} = \{ {}^{\backprime\backprime} p {}^{\prime\prime}, {}^{\backprime\backprime} q {}^{\prime\prime}, {}^{\backprime\backprime} r {}^{\prime\prime} \}</math> is the ''alphabet'' for the universe of discourse that is notated as <math>X^\circ = [\mathcal{X}] = [p, q, r],</math> already getting sloppy about quotation marks to single out the signs.

The universe ''X''^&nbsp;&bull; is composed of two different spaces of objects.  The first is the space of positions ''X'' = <font face=symbol>á</font>''p'', ''q'', ''r''<font face=symbol>ñ</font> = {<''p'', ''q'', ''r''>}.  The second is the space of propositions ''X''&uarr; = (''X'' &rarr; '''B''').

The universe <math>X^\circ</math> is composed of two different spaces of objects.  The first is the space of positions <math>X = \langle p, q, r \rangle = \{ (p, q, r) \}.</math> The second is the space of propositions <math>X^\uparrow = (X \to \mathbb{B}).</math>

Let us make the following definitions:

Let us make the following definitions: