Changes

: A ''literal'' is one of the <math>2k\!</math> propositions <math>x_1, \ldots, x_k, (x_1), \ldots, (x_k),</math> in other words, either a ''posited'' basic proposition <math>x_j\!</math> or a ''negated'' basic proposition <math>(x_j),\!</math> for some <math>j = 1 ~\text{to}~ k.</math>

: A ''literal'' is one of the <math>2k\!</math> propositions <math>x_1, \ldots, x_k, (x_1), \ldots, (x_k),</math> in other words, either a ''posited'' basic proposition <math>x_j\!</math> or a ''negated'' basic proposition <math>(x_j),\!</math> for some <math>j = 1 ~\text{to}~ k.</math>

* In mathematics generally, the '''[[fiber (mathematics)|fiber]]''' of a point ''y'' under a function ''f''&nbsp;:&nbsp;''X''&nbsp;→&nbsp;''Y'' is defined as the inverse image <math>f^{-1}(y)</math>.

: In mathematics generally, the ''[[fiber (mathematics)|fiber]]'' of a point <math>y \in Y</math> under a function <math>f : X \to Y</math> is defined as the inverse image <math>f^{-1}(y) \subseteq X.</math>

* In the case of a boolean function ''f''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B''', there are just two fibers:

* In the case of a boolean function ''f''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B''', there are just two fibers:

** The fiber of 1 under ''f'', defined as <math>f^{-1}(1)</math>, is the set of points where ''f'' is 1.

** The fiber of 1 under ''f'', defined as <math>f^{-1}(1)</math>, is the set of points where ''f'' is 1.

* When 1 is interpreted as the logical value ''true'', then <math>f^{-1}(1)</math> is called the '''fiber&nbsp;of&nbsp;truth''' in the proposition ''f''.  Frequent mention of this fiber makes it useful to have a shorter way of referring to it.  This leads to the definition of the notation <math>[|f|] = f^{-1}(1)\!</math> for the fiber of truth in the proposition ''f''.

* When 1 is interpreted as the logical value ''true'', then <math>f^{-1}(1)\!</math> is called the '''fiber&nbsp;of&nbsp;truth''' in the proposition ''f''.  Frequent mention of this fiber makes it useful to have a shorter way of referring to it.  This leads to the definition of the notation <math>[|f|] = f^{-1}(1)\!</math> for the fiber of truth in the proposition ''f''.

* A '''singular boolean function''' ''s''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B''' is a boolean function whose fiber of 1 is a single point of '''B'''^''k''.

* A '''singular boolean function''' ''s''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B''' is a boolean function whose fiber of 1 is a single point of '''B'''^''k''.