Editing Truth value (section)

== Classical logic ==
{| class="floatright" cellpadding=0 style="text-align:center;"
 |-
 |
 | style="font-size:300%; font-weight:700;" | ⊤
 | rowspan=5 |
 | style="font-size:300%;"                  | ·'''∧'''·
 |-
 |
 | true
 | <small>[[logical conjunction|conjunction]]</small>
 |-
 | style="font-size:250%; font-weight:300;" | ¬
 | style="font-size:200%; font-weight:500;" | ↕
 | style="font-size:200%; font-weight:500;" | ↕
 |-
 |
 | style="font-size:300%; font-weight:700;" | ⊥
 | style="font-size:300%;"                  | ·'''∨'''·
 |-
 |
 | false
 | <small>[[logical disjunction|disjunction]]</small>
 |-
 | colspan=4 style="padding-left:24px; padding-top:8px; padding-bottom:14px; text-align:left;" | <small>Negation interchanges <br/>true with false and <br/>conjunction with disjunction.</small>
 |}
In [[classical logic]], with its intended semantics, the truth values are ''[[logical truth|true]]'' (denoted by ''1'' or the [[verum]] ⊤), and ''[[false (logic)|untrue]]'' or ''[[false (logic)|false]]'' (denoted by ''0'' or the [[falsum]] ⊥); that is, classical logic is a [[two-valued logic]]. This set of two values is also called the [[Boolean domain]]. Corresponding semantics of [[logical connective]]s are [[truth function]]s, whose values are expressed in the form of [[truth table]]s. [[Logical biconditional]] becomes the [[equality (mathematics)|equality]] binary relation, and [[negation]] becomes a [[bijection]] which [[permutation|permutes]] true and false. Conjunction and disjunction are [[Dual (mathematics)#Duality in logic and set theory|dual]] with respect to negation, which is expressed by [[De Morgan's laws]]:
: ¬({{math|{{mvar|p}} ∧ {{mvar|q}}) ⇔ ¬{{mvar|p}} ∨ ¬{{mvar|q}}}}
: ¬({{math|{{mvar|p}} ∨ {{mvar|q}}) ⇔ ¬{{mvar|p}} ∧ ¬{{mvar|q}}}}

[[Propositional variable]]s become [[Variable (computer science)|variables]] in the Boolean domain. Assigning values for propositional variables is referred to as [[valuation (logic)|valuation]].
<!-- Also something should be written about first-order logics -->