AskDefine | Define negate

Dictionary Definition

negate

Verb

1 be in contradiction with [syn: contradict, belie]
2 deny the truth of [syn: contradict, contravene]
3 prove negative; show to be false [syn: contradict] [ant: confirm]
4 make ineffective by counterbalancing the effect of; "Her optimism neutralizes his gloom"; "This action will negate the effect of my efforts" [syn: neutralize, neutralise, nullify]

User Contributed Dictionary

English

Pronunciation

ne·gate/nɪˈgeɪt, ˈnɛgeɪt/

Verb

  1. To deny the existence, evidence, or truth of; to contradict: an investigation tending to negate any supernatural influences.
  2. To nullify or cause to be ineffective; to nullify: Progress on the study has been negated by the lack of funds.
  3. To be negative; bring or cause negative results: a pessimism that always negates.
  4. To perform the NOT operation on.

Related terms

Italian

Adjective

negate p

Verb

negate
  1. second-person plural present tense of negare
  2. second-person plural imperative of negare
  3. feminine plural past participle of negare

Extensive Definition

In logic and mathematics, negation or not is an operation on logical values, for example, the logical value of a proposition, that sends true to false and false to true. Intuitively, the negation of a proposition holds exactly when that proposition does not hold. In grammar, nor is an adverb which acts as a coordinating conjunction.

Definition

Logical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true when its operand is false and a value of false when its operand is true. So, if statement A is true, then ¬A (pronounced "not A") would therefore be false; and conversely, if ¬A is true, then A would be false.
The truth table of ¬p (also written as ~p or NOT p) is as follows:
The logical negation of a proposition p is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following:
No matter how it is notated or symbolized, the logical negation ¬p is read as "it is not the case that p", or usually more simply as "not p".
  • Within a system of classical logic, double negation, that is, the negation of the negation of a proposition p, is logically equivalent to the initial proposition p. Expressed in symbolic terms, ¬(¬p) ⇔ p.
  • Within a system of intuitionistic logic, however, ¬¬p is a weaker statement than p. On the other hand, the logical equivalence ¬¬¬p ⇔ ¬p remains valid.
Logical negation can be defined in terms of other logical operations. For example, ¬p can be defined as p → F, where "→" is logical implication and F is absolute falsehood. Conversely, one can define F as p & ¬p for any proposition p, where "&" is logical conjunction. The idea here is that any contradiction is false. While these ideas work in both classical and intuitionistic logic, they don't work in Brazilian logic, where contradictions are not necessarily false. But in classical logic, we get a further identity: p → q can be defined as ¬p ∨ q, where "∨" is logical disjunction.
Algebraically, logical negation corresponds to the complement in a Boolean algebra (for classical logic) or a Heyting algebra (for intuitionistic logic).

Properties

If there exists a0, a1, ... , an \in such that f(b1, ... , bn) = a0 ⊕ (a1 \land b1) ⊕ ... ⊕ (an \land bn), for all b1, ... , bn \in .
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.
If f(a1, ... , an) = ~f(~a1, ... , ~an) for all a1, ... , an \in . Negation is a self dual logical operator.

Computer science

As in mathematics, negation is used in computer science to construct logical statements.
if (!(r == t))
The "!" signifies logical NOT in B, C, and languages with a C-inspired syntax such as C++, Java, JavaScript, Perl, and PHP. "NOT" is the operator used in ALGOL 60, BASIC, and languages with an ALGOL-inspired syntax such as Pascal, Ada, and Eiffel. Some languages (C++, Perl, etc.) provide more than one operator for negation. Few languages, like Ratfor, use ¬ for negation. Some modern computers and operating systems will display ¬ as ! on files encoded ASCII.
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).
Take the following for example:
Say we wanted to get the absolute (positive equivalent) value of a given integer to following would work as the "-" changes it from negative to positive (we know it is negative because it is true that "x unsigned int abs(int x)

Synonyms, Antonyms and Related Words

abate, abnegate, abolish, abrogate, agree to disagree, annihilate, annul, be at cross-purposes, be contrary to, be unmoved, be unwilling, beg off, belie, blow sky-high, blow up, break, break off, bring to naught, bring to nothing, buffer, call into question, cancel, cancel out, challenge, clash, collide, come to nothing, conflict, contest, contradict, contravene, controvert, counter, counteract, counterbalance, countercheck, cross, decline, decline to accept, deflate, deny, differ, disaccord, disaffirm, disagree, disallow, disbelieve, disclaim, disconfirm, discredit, disprove, dissent, explode, expose, frustrate, gag on, gainsay, hold out against, impugn, invalidate, jangle, jar, jostle, misbelieve, mismatch, mismate, negativate, negative, neutralize, not admit, not believe, not buy, not consent, not hear of, not swallow, not think of, nullify, object, offset, oppugn, prove the contrary, puncture, quash, rebut, redress, refuse, refuse consent, refuse to admit, refuse to credit, reject, repeal, repudiate, resist entreaty, resist persuasion, revoke, say nay, say no, shake the head, show up, stand aloof, stultify, thwart, traverse, turn down, unbelieve, undercut, undo, vary, vitiate, void, vote nay, vote negatively
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