## Table of Contents

81 relations: Ada (programming language), Affirmation and negation, Algebraic semantics (mathematical logic), ALGOL 60, Apophasis, B (programming language), BASIC, Binary number, Binary opposition, Bitwise operation, Boolean algebra, Boolean algebra (structure), Brouwer–Heyting–Kolmogorov interpretation, C++, Classical logic, Complement (set theory), Computer science, Concept, Conditional proof, Contradiction, Contraposition, Cyclic negation, De Morgan's laws, Distributive property, Double-negation translation, Dov Gabbay, Eiffel (programming language), Eric S. Raymond, Exclamation mark, Exclusive or, False (logic), First-order 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, ... Expand index (31 more) »

- Logical connectives
- Unary operations

## Ada (programming language)

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

See Negation and Ada (programming language)

## Affirmation and negation

In linguistics and grammar, affirmation (abbreviated) and negation are ways in which grammar encodes positive and negative polarity into verb phrases, clauses, or other utterances. Negation and affirmation and negation are semantics.

See Negation and Affirmation and negation

## Algebraic semantics (mathematical logic)

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

See Negation and Algebraic semantics (mathematical logic)

## ALGOL 60

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

## Apophasis

Apophasis 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.

## B (programming language)

B is a programming language developed at Bell Labs circa 1969 by Ken Thompson and Dennis Ritchie.

See Negation and B (programming language)

## BASIC

BASIC (Beginners' All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages designed for ease of use.

## Binary number

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one).

See Negation and Binary number

## Binary opposition

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

See Negation and Binary opposition

## Bitwise operation

In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits.

See Negation and Bitwise operation

## Boolean algebra

In mathematics and mathematical logic, Boolean algebra is a branch of algebra.

See Negation and Boolean algebra

## Boolean algebra (structure)

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

See Negation and Boolean algebra (structure)

## 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.

See Negation and Brouwer–Heyting–Kolmogorov interpretation

## C++

C++ (pronounced "C plus plus" and sometimes abbreviated as CPP) is a high-level, general-purpose programming language created by Danish computer scientist Bjarne Stroustrup.

See Negation and C++

## Classical logic

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic.

See Negation and Classical logic

## Complement (set theory)

In set theory, the complement of a set, often denoted by A^\complement, is the set of elements not in.

See Negation and Complement (set theory)

## Computer science

Computer science is the study of computation, information, and automation.

See Negation and Computer science

## Concept

A concept is defined as an abstract idea. Negation and concept are semantics.

## 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.

See Negation and Conditional proof

## Contradiction

In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact.

See Negation and Contradiction

## Contraposition

In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as.

See Negation and Contraposition

## 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 − 1 as value if n is not the lowest value; otherwise it returns the highest value.

See Negation and Cyclic negation

## De Morgan's laws

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference.

See Negation and De Morgan's laws

## Distributive property

In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x \cdot (y + z).

See Negation and Distributive property

## 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.

See Negation and Double-negation translation

## Dov Gabbay

Dov M. Gabbay (born October 26, 1945) is an Israeli 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.

See Negation and Eiffel (programming language)

## Eric S. Raymond

Eric Steven Raymond (born December 4, 1957), often referred to as ESR, is an American software developer, open-source software advocate, and author of the 1997 essay and 1999 book The Cathedral and the Bazaar.

See Negation and Eric S. Raymond

## Exclamation mark

The exclamation mark (also known as exclamation point in American English) is a punctuation mark usually used after an interjection or exclamation to indicate strong feelings or to show emphasis.

See Negation and Exclamation mark

## Exclusive or

Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. Negation and exclusive or are logical connectives and semantics.

## False (logic)

In logic, false or untrue is the state of possessing negative truth value and is a nullary logical connective. Negation and false (logic) are logical connectives.

See Negation and False (logic)

## First-order logic

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

See Negation and First-order logic

## Georg Henrik von Wright

Georg Henrik von Wright (14 June 1916 – 16 June 2003) was a Finnish philosopher.

See Negation and Georg Henrik von Wright

## Heyting algebra

In mathematics, a Heyting algebra (also known as pseudo-Boolean 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).

See Negation and Heyting algebra

## Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language. Negation and interpretation (logic) are semantics.

See Negation and Interpretation (logic)

## 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.

See Negation and Intuitionistic logic

## Inverter (logic gate)

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

See Negation and Inverter (logic gate)

## Involution (mathematics)

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

See Negation and Involution (mathematics)

## Java (programming language)

Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible.

See Negation and Java (programming language)

## JavaScript

JavaScript, often abbreviated as JS, is a programming language and core technology of the Web, alongside HTML and CSS.

## 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.

See Negation and Kripke semantics

## Lattice (order)

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

See Negation and Lattice (order)

## Laurence R. Horn

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

See Negation and Laurence R. Horn

## List of logic symbols

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

See Negation and List of logic symbols

## Logic

Logic is the study of correct reasoning.

## Logical conjunction

In logic, mathematics and linguistics, and (\wedge) is the truth-functional operator of conjunction or logical conjunction. Negation and logical conjunction are logical connectives and semantics.

See Negation and Logical conjunction

## Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Negation and logical connective are logical connectives.

See Negation and Logical 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.

See Negation and Logical consequence

## Logical disjunction

In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as \lor and read aloud as "or". Negation and logical disjunction are formal semantics (natural language), logical connectives and semantics.

See Negation and Logical disjunction

## Logical equivalence

In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model.

See Negation and Logical equivalence

## Logical NOR

In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. Negation and logical NOR are logical connectives.

## 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 known as modus ponendo ponens, implication elimination, or affirming the antecedent, is a deductive argument form and 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.

See Negation and Natural deduction

## 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. Note that \mathrm ~p can be different from the statement \neg p of the logical negation of p, depending on the completeness of the inference algorithm and thus also on the formal logic system.

See Negation and Negation as failure

## Operation (mathematics)

In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value.

See Negation and Operation (mathematics)

## Order of operations

In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression.

See Negation and Order of operations

## Paraconsistent logic

Paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way.

See Negation and Paraconsistent logic

## Pascal (programming language)

Pascal is an imperative and procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using structured programming and data structuring.

See Negation and Pascal (programming language)

## Perl

Perl is a high-level, general-purpose, interpreted, dynamic programming language.

## PHP

PHP is a general-purpose scripting language geared towards web development.

See Negation and PHP

## PL/I

PL/I (Programming Language One, pronounced and sometimes written PL/1) is a procedural, imperative computer programming language initially developed by IBM.

## Plato's beard

In metaphysics, Plato's beard is a paradoxical argument dubbed by Willard Van Orman Quine in his 1948 paper "On What There Is".

See Negation and Plato's beard

## Possible world

A possible world is a complete and consistent way the world is or could have been. Negation and possible world are semantics.

See Negation and Possible world

## Proposition

A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Negation and proposition are semantics.

## Ratfor

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

## Reductio ad absurdum

In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.

See Negation and Reductio ad absurdum

## Seed7

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

## Signed number representations

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

See Negation and Signed number representations

## Slang

A slang is a vocabulary (words, phrases, and linguistic usages) of an informal register, common in everyday conversation but avoided in formal writing.

## Square of opposition

In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions.

See Negation and Square of opposition

## The C Programming Language

The C Programming Language (sometimes termed K&R, after its authors' initials) is a computer programming book written by Brian Kernighan and Dennis Ritchie, the latter of whom originally designed and implemented the C programming language, as well as co-designed the Unix operating system with which development of the language was closely intertwined.

See Negation and The C Programming Language

## Theorem

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.

## Truth function

In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output.

See Negation and Truth function

## 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. Negation and truth table are semantics.

## 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, which in classical logic has only two possible values (true or false).

## Two's complement

Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values.

See Negation and Two's complement

## Unary operation

In mathematics, a unary operation is an operation with only one operand, i.e. a single input. Negation and unary operation are unary operations.

See Negation and Unary operation

## University of Chicago Press

The University of Chicago Press is the university press of the University of Chicago, a private research university in Chicago, Illinois.

See Negation and University of Chicago Press

## Wiley-Blackwell

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

See Negation and Wiley-Blackwell

## Wolters Kluwer

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

See Negation and Wolters Kluwer

## See also

### Logical connectives

- Conditioned disjunction
- Conjunction/disjunction duality
- Converse (logic)
- Converse nonimplication
- Exclusive or
- False (logic)
- If and only if
- Indicative conditional
- Logical NOR
- Logical biconditional
- Logical conjunction
- Logical connective
- Logical disjunction
- Logical equality
- Logical truth
- Material conditional
- Material nonimplication
- Modal operator
- Negation
- Sheffer stroke
- Strict conditional

### Unary operations

- Barrel shifter
- Counter (digital)
- Cube (algebra)
- Cube root
- Eighth power
- Exponentiation
- Factorial
- Fifth power (algebra)
- Floor and ceiling functions
- Fourth power
- Fractional part
- Increment and decrement operators
- Indirection
- Inverse function
- Magnitude (mathematics)
- Multiplicative inverse
- Natural logarithm
- Negation
- Ones' complement
- Parity (mathematics)
- Seventh power
- Sign function
- Sixth power
- Sizeof
- Square (algebra)
- Square root
- Trigonometric functions
- Type conversion
- Unary function
- Unary operation

## References

Also known as !vote, ¬, Logical Complement, Logical NOT, Logical Negation, Logical opposite, Negate, Negated, Negation (algebra), Negation (logic), Negation (logical connective), Negation (logics), Negation elimination, Negation sign, Not (logic), Not operator, Not sign, Quantifier negation, U+00AC, , ¬.