Editing Material conditional (section)

{{short description|Logical connective}}
{{Redirect|Logical conditional|other related meanings|Conditional statement (disambiguation){{!}}Conditional statement}}
{{distinguish|Material inference|Material implication (rule of inference)}}
{{Infobox logical connective
| title        = Material conditional
| other titles = IMPLY
| Venn diagram = Venn1011.svg
| wikifunction = Z10329
| definition   = <math>x \to y</math>
| truth table  = <math>(1011)</math>
| logic gate   = IMPLY_ANSI.svg
| DNF          = <math>\overline{x} + y</math>
| CNF          = <math>\overline{x} + y</math>
| Zhegalkin    = <math>1 \oplus x \oplus xy</math>
| 0-preserving = no
| 1-preserving = yes
| monotone     = no
| affine       = no
| self-dual    = no
}}
{{Logical connectives sidebar}}
The '''material conditional''' (also known as '''material implication''') is a [[binary operation]] commonly used in [[mathematical logic|logic]]. When the conditional symbol <math>\to</math> is [[Interpretation (logic)|interpreted]] as material implication, a formula <math> P \to Q</math> is true unless <math>P</math> is true and <math>Q</math> is false.

Material implication is used in all the basic systems of [[classical logic]] as well as some [[nonclassical logic]]s. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many [[programming language]]s. However, many logics replace material implication with other operators such as the [[strict conditional]] and the [[variably strict conditional]]. Due to the [[paradoxes of material implication]] and related problems, material implication is not generally considered a viable analysis of [[conditional sentence]]s in [[natural language]].