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# Negation

In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true. 

77 relations: Ada (programming language), Affirmation and negation, Algebraic semantics (mathematical logic), ALGOL 60, Apophasis, ASCII, B (programming language), BASIC, Binary number, Binary opposition, Bitwise operation, Boolean algebra, Boolean algebra (structure), Brouwer–Heyting–Kolmogorov interpretation, C (programming language), C++, Classical logic, Complement (set theory), Computer science, Conditional proof, Contradiction, Cyclic negation, De Morgan's laws, Distributive property, Double negation, Double-negation translation, Dov Gabbay, Eiffel (programming language), Exclusive or, False (logic), Georg Henrik von Wright, Heyting algebra, Interpretation (logic), Intuitionistic logic, Inverter (logic gate), Involution (mathematics), Java (programming language), JavaScript, Kripke semantics, Lattice (order), Laurence R. Horn, List of logic symbols, Logic, Logical conjunction, Logical connective, Logical consequence, Logical disjunction, Logical equivalence, Logical NOR, MathWorld, ... Expand index (27 more) »

Ada is a structured, statically typed, imperative, and object-oriented high-level computer programming language, extended from Pascal and other languages.

## Affirmation and negation

In linguistics and grammar, affirmation and negation (abbreviated respectively and) are the ways that grammar encode negative and positive polarity in verb phrases, clauses, or other utterances.

## Algebraic semantics (mathematical logic)

In mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic.

## ALGOL 60

ALGOL 60 (short for Algorithmic Language 1960) is a member of the ALGOL family of computer programming languages.

## Apophasis

Apophasis (Greek: ἀπόφασις from ἀπόφημι apophemi, "to say no") is a rhetorical device wherein the speaker or writer brings up a subject by either denying it, or denying that it should be brought up.

## ASCII

ASCII, abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication.

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## B (programming language)

B is a programming language developed at Bell Labs circa 1969.

## BASIC

BASIC (an acronym for Beginner's All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages whose design philosophy emphasizes ease of use.

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## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## Binary opposition

A nebular opposition (also binary system) is a pair of related terms or concepts that are opposite in meaning.

## Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

## Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

## Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

## Brouwer–Heyting–Kolmogorov interpretation

In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L. E. J. Brouwer and Arend Heyting, and independently by Andrey Kolmogorov.

## C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

## C++

C++ ("see plus plus") is a general-purpose programming language.

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## Classical logic

Classical logic (or standard logic) is an intensively studied and widely used class of formal logics.

## Complement (set theory)

In set theory, the complement of a set refers to elements not in.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Conditional proof

A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.

In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.

## Cyclic negation

In many-valued logic with linearly ordered truth values, cyclic negation is a unary truth function that takes a truth value n and returns n &minus; 1 as value if n is not the lowest value; otherwise it returns the highest value.

## De Morgan's laws

In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

## Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

## Double negation

In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition A is logically equivalent to not (not-A), or by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.

## Double-negation translation

In proof theory, a discipline within mathematical logic, double-negation translation, sometimes called negative translation, is a general approach for embedding classical logic into intuitionistic logic, typically by translating formulas to formulas which are classically equivalent but intuitionistically inequivalent.

## Dov Gabbay

Dov M. Gabbay (born October 23, 1945) is a British logician.

## Eiffel (programming language)

Eiffel is an object-oriented programming language designed by Bertrand Meyer (an object-orientation proponent and author of Object-Oriented Software Construction) and Eiffel Software.

## Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

## False (logic)

In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective.

## Georg Henrik von Wright

Georg Henrik von Wright (14 June 1916 &ndash; 16 June 2003) was a Finnish philosopher, who succeeded Ludwig Wittgenstein as professor at the University of Cambridge.

## Heyting algebra

In mathematics, a Heyting algebra is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that c ∧ a ≤ b is equivalent to c ≤ a → b. From a logical standpoint, A → B is by this definition the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound.

## Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language.

## Intuitionistic logic

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof.

## Inverter (logic gate)

In digital logic, an inverter or NOT gate is a logic gate which implements logical negation.

## Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

## Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

## JavaScript

JavaScript, often abbreviated as JS, is a high-level, interpreted programming language.

## Kripke semantics

Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal.

## Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

## Laurence R. Horn

Laurence Robert Horn (born 1945) is an American linguist.

## List of logic symbols

In logic, a set of symbols is commonly used to express logical representation.

## Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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## Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

## Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.

## Logical consequence

Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.

## Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

## Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

## Logical NOR

In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or.

## MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

## Modus ponens

In propositional logic, modus ponens (MP; also modus ponendo ponens (Latin for "mode that affirms by affirming") or implication elimination) is a rule of inference.

## Natural deduction

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning.

## Negation as failure

Negation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive \mathrm~p (i.e. that ~p is assumed not to hold) from failure to derive ~p.

## Notion (philosophy)

A notion in philosophy is a reflection in the mind of real objects and phenomena in their essential features and relations.

## Operating system

An operating system (OS) is system software that manages computer hardware and software resources and provides common services for computer programs.

## Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

## Paraconsistent logic

A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way.

## Pascal (programming language)

Pascal is an imperative and procedural programming language, which Niklaus Wirth designed in 1968–69 and published in 1970, as a small, efficient language intended to encourage good programming practices using structured programming and data structuring. It is named in honor of the French mathematician, philosopher and physicist Blaise Pascal. Pascal was developed on the pattern of the ALGOL 60 language. Wirth had already developed several improvements to this language as part of the ALGOL X proposals, but these were not accepted and Pascal was developed separately and released in 1970. A derivative known as Object Pascal designed for object-oriented programming was developed in 1985; this was used by Apple Computer and Borland in the late 1980s and later developed into Delphi on the Microsoft Windows platform. Extensions to the Pascal concepts led to the Pascal-like languages Modula-2 and Oberon.

## Perl

Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages, Perl 5 and Perl 6.

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## PHP

PHP: Hypertext Preprocessor (or simply PHP) is a server-side scripting language designed for Web development, but also used as a general-purpose programming language.

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## PL/I

PL/I (Programming Language One, pronounced) is a procedural, imperative computer programming language designed for scientific, engineering, business and system programming uses.

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## Plato's beard

Plato's beard refers to a paradoxical argument dubbed by Willard Van Orman Quine in his 1948 paper On What There Is in which he stated that: This is the old Platonic riddle of nonbeing.

## Possible world

In philosophy and logic, the concept of a possible world is used to express modal claims.

## Proposition

The term proposition has a broad use in contemporary analytic philosophy.

## Ratfor

Ratfor (short for Rational Fortran) is a programming language implemented as a preprocessor for Fortran 66.

In logic, reductio ad absurdum ("reduction to absurdity"; also argumentum ad absurdum, "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.

## Seed7

Seed7 is an extensible general-purpose programming language designed by Thomas Mertes.

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## Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems.

## Slang

Slang is language (words, phrases, and usages) of an informal register that members of special groups like teenagers, musicians, or criminals favor (over a standard language) in order to establish group identity, exclude outsiders, or both.

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## Square of opposition

The square of opposition is a diagram representing the relations between the four basic categorical propositions.

## Truth function

In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values.

## Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

## Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

## Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.

## University of Chicago Press

The University of Chicago Press is the largest and one of the oldest university presses in the United States.

## Wiley-Blackwell

Wiley-Blackwell is the international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons.

## Wolters Kluwer

Wolters Kluwer N.V. is a global information services company.

## References

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