For negation in linguistics, see Affirmation and negation.
For other uses, see Negation (disambiguation).
No agreement exists as to the possibility of defining negation, as to its logical status, function and meaning, as to its field of applicability, and as to the interpretation of the negative judgment (F.H.
These algebras provide a semantics for classical and intuitionistic logic, respectively.
The notation Np is Łukasiewicz notation.
Another way to express this is that each variable always makes a difference in the truth-value of the operation, or it never makes a difference.
Negation is a linear logical operator.
In Boolean algebra, a self dual function is a function such that:
Negations of quantifiers
Rules of inference
See also: double negation
Programming language and ordinary language
As in mathematics, negation is used in computer science to construct logical statements.
The exclamation mark "!"
Some languages (C++, Perl, etc.) provide more than one operator for negation.
Some modern computers and operating systems will display ¬ as !
on files encoded in ASCII.
Most modern languages allow the above statement to be shortened from if (!
(r == t)) to if (r != t), which allows sometimes, when the compiler/interpreter is not able to optimize it, faster programs.
In computer science there is also bitwise negation.
This takes the value given and switches all the binary 1s to 0s and 0s to 1s.
See bitwise operation.
This is often used to create ones' complement or "~" in C or C++ and two's complement (just simplified to "-" or the negative sign since this is equivalent to taking the arithmetic negative value of the number) as it basically creates the opposite (negative value equivalent) or mathematical complement of the value (where both values are added together they create a whole).
To get the absolute (positive equivalent) value of a given integer the following would work as the "-" changes it from negative to positive (it is negative because "x < 0" yields true)
To demonstrate logical negation:
Inverting the condition and reversing the outcomes produces code that is logically equivalent to the original code, i.e. will have identical results for any input (note that depending on the compiler used, the actual instructions performed by the computer may differ).
This convention occasionally surfaces in ordinary written speech, as computer-related slang for not.
For example, the phrase !voting means "not voting".
Another example is the phrase !clue which is used as a synonym for "no-clue" or "clueless".
Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/Negation.