Negation

In <a href="/facts/Logic/8JnpJLtt">logic</a>, negation, also called the logical not or logical complement, is an <a href="/facts/Operation_(mathematics)/Yplv602Q">operation</a> that takes a <a href="/facts/Proposition_(mathematics)/f2Pe1FMD">proposition</a> 
 
 
 
 P
 
 
 {\displaystyle P}
 
 to another proposition "not 
 
 
 
 P
 
 
 {\displaystyle P}
 
", written 
 
 
 
 ¬
 P
 
 
 {\displaystyle \neg P}
 
, 
 
 
 
 
 
 ∼
 
 
 P
 
 
 {\displaystyle {\mathord {\sim }}P}
 
, 
 
 
 
 
 P
 
 ′
 
 
 
 
 {\displaystyle P^{\prime }}
 
 or 
 
 
 
 
 
 P
 ¯
 
 
 
 
 {\displaystyle {\overline {P}}}
 
. It is interpreted intuitively as being true when 
 
 
 
 P
 
 
 {\displaystyle P}
 
 is false, and false when 
 
 
 
 P
 
 
 {\displaystyle P}
 
 is true. For example, if 
 
 
 
 P
 
 
 {\displaystyle P}
 
 is "Spot runs", then "not 
 
 
 
 P
 
 
 {\displaystyle P}
 
" is "Spot does not run". An operand of a negation is called a negand or negatum.
Negation is a <a href="/facts/Unary_operation/kb6CkgsX">unary</a> <a href="/facts/Logical_connective/VkPhUs6M">logical connective</a>. It may furthermore be applied not only to propositions, but also to <a href="/facts/Notion_(philosophy)/6hPT1oFP">notions</a>, <a href="/facts/Truth_value/SY4e2w8l">truth values</a>, or <a href="/facts/Interpretation_(logic)/goPmjjQG">semantic values</a> more generally. In <a href="/facts/Classical_logic/ls62MAms">classical logic</a>, negation is normally identified with the <a href="/facts/Truth_function/aH5kBhQ7">truth function</a> that takes truth to falsity (and vice versa). In <a href="/facts/Intuitionistic_logic/zI7ulCnM">intuitionistic logic</a>, according to the <a href="/facts/Brouwer%25E2%2580%2593Heyting%25E2%2580%2593Kolmogorov_interpretation/Tm5t5LaF">Brouwer–Heyting–Kolmogorov interpretation</a>, the negation of a proposition 
 
 
 
 P
 
 
 {\displaystyle P}
 
 is the proposition whose proofs are the refutations of 
 
 
 
 P
 
 
 {\displaystyle P}
 
.

Negation open-in-new

Negation