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==Glossary of basic terms==

==Glossary of basic terms==

* A '''[[boolean domain]]''' <math>\mathbb{B}</math> is a generic 2-element [[set]], for example, <math>\mathbb{B} = \{ 0, 1 \},</math> whose elements are interpreted as [[logical value]]s, usually but not invariably with <math>0 = \operatorname{false}</math> and <math>1 = \operatorname{true}.</math>

: A ''[[boolean domain]]'' <math>\mathbb{B}</math> is a generic 2-element set, for example, <math>\mathbb{B} = \{ 0, 1 \},</math> whose elements are interpreted as logical values, usually but not invariably with <math>0 = \operatorname{false}</math> and <math>1 = \operatorname{true}.</math>

* A '''[[boolean variable]]''' <math>x\!</math> is a [[variable]] that takes its value from a boolean domain, as <math>x \in \mathbb{B}.</math>

: A ''boolean variable'' <math>x\!</math> is a variable that takes its value from a boolean domain, as <math>x \in \mathbb{B}.</math>

* In situations where [[boolean value]]s are interpreted as [[logical value]]s, a [[boolean-valued function]] ''f''&nbsp;:&nbsp;''X''&nbsp;→&nbsp;'''B''' or a [[boolean function]] ''g''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B''' is frequently called a '''[[proposition]]'''.

: In situations where boolean values are interpreted as logical values, a [[boolean-valued function]] <math>f : X \to \mathbb{B}</math> or a [[boolean function]] <math>g : \mathbb{B}^k \to \mathbb{B}</math> is frequently called a ''[[proposition]]''.

* Given a sequence of ''k'' boolean variables, ''x''₁,&nbsp;…,&nbsp;''x''_''k'', each variable ''x''_''j'' may be treated either as a [[basis element]] of the space '''B'''^''k'' or as a [[coordinate projection]] ''x''_''j''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B'''.

: Given a sequence of <math>k\!</math> boolean variables, <math>x_1, \ldots, x_k,</math> each variable <math>x_j\!</math> may be treated either as a ''basis element'' of the space <math>\mathbb{B}^k</math> or as a ''coordinate projection'' <math>x_j : \mathbb{B}^k \to \mathbb{B}.</math>

* This means that the ''k'' objects ''x''_''j'' for ''j'' = 1 to ''k'' are just so many boolean functions ''x''_''j''&nbsp;:&nbsp;'''B'''^''k''&nbsp;→&nbsp;'''B''' , subject to logical interpretation as a set of ''basic propositions'' that generate the complete set of <math>2^{2^k}</math> propositions over '''B'''^''k''.

: This means that the set of objects <math>\{ x_j : 1 \le j \le k \}</math> is a set of boolean functions <math>\{ x_j : \mathbb{B}^k \to \mathbb{B} \}</math> subject to logical interpretation as a set of ''basic propositions'' that collectively generate the complete set of <math>2^{2^k}</math> propositions over <math>\mathbb{B}^k.</math>

* A '''literal''' is one of the 2''k'' propositions ''x''₁,&nbsp;…,&nbsp;''x''_''k'', (''x''₁),&nbsp;…,&nbsp;(''x''_''k''), in other words, either a ''posited'' basic proposition ''x''_''j'' or a ''negated'' basic proposition (''x''_''j''), for some ''j'' = 1 to ''k''.

* A '''literal''' is one of the 2''k'' propositions ''x''₁,&nbsp;…,&nbsp;''x''_''k'', (''x''₁),&nbsp;…,&nbsp;(''x''_''k''), in other words, either a ''posited'' basic proposition ''x''_''j'' or a ''negated'' basic proposition (''x''_''j''), for some ''j'' = 1 to ''k''.