Logical negation

☞ This page belongs to resource collections on Logic and Inquiry.

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.

The truth table of \(\operatorname{NOT}~ p,\) also written \(\lnot p,\!\) appears below:

\(\text{Logical Negation}\!\)

\(p\!\)	\(\lnot p\!\)
\(\operatorname{F}\)	\(\operatorname{T}\)
\(\operatorname{T}\)	\(\operatorname{F}\)

The negation of a proposition \(p\!\) may be found notated in various ways in various contexts of application, often merely for typographical convenience. Among these variants are the following:

\(\text{Variant Notations}\!\)

\(\text{Notation}\!\)	\(\text{Vocalization}\!\)
\(\bar{p}\!\)	\(p\!\) bar
\(\tilde{p}\!\)	\(p\!\) tilde
\(p'\!\)	\(p\!\) prime \(p\!\) complement
\(!p\!\)	bang \(p\!\)

Syllabus

Focal nodes

• Inquiry Live
• Logic Live

Peer nodes

• Logical Negation @ InterSciWiki
• Logical Negation @ MyWikiBiz
• Logical Negation @ Subject Wikis
• Logical Negation @ Wikiversity
• Logical Negation @ Wikiversity Beta

Logical operators

Template:Col-break

• Exclusive disjunction
• Logical conjunction
• Logical disjunction
• Logical equality

Template:Col-break

• Logical implication
• Logical NAND
• Logical NNOR
• Negation

Template:Col-end

Related topics

Template:Col-break

• Ampheck
• Boolean domain
• Boolean function
• Boolean-valued function
• Differential logic

Template:Col-break

• Logical graph
• Minimal negation operator
• Multigrade operator
• Parametric operator
• Peirce's law

Template:Col-break

• Propositional calculus
• Sole sufficient operator
• Truth table
• Universe of discourse
• Zeroth order logic

Template:Col-end

Relational concepts

Template:Col-break

• Continuous predicate
• Hypostatic abstraction
• Logic of relatives
• Logical matrix

Template:Col-break

• Relation
• Relation composition
• Relation construction
• Relation reduction

Template:Col-break

• Relation theory
• Relative term
• Sign relation
• Triadic relation

Template:Col-end

Information, Inquiry

Template:Col-break

• Inquiry
• Dynamics of inquiry

Template:Col-break

• Semeiotic
• Logic of information

Template:Col-break

• Descriptive science
• Normative science

Template:Col-break

• Pragmatic maxim
• Truth theory

Template:Col-end

Related articles

Template:Col-break

• Cactus Language
• Futures Of Logical Graphs
• Propositional Equation Reasoning Systems

Template:Col-break

• Differential Logic : Introduction
• Differential Propositional Calculus
• Differential Logic and Dynamic Systems

Template:Col-break

• Prospects for Inquiry Driven Systems
• Introduction to Inquiry Driven Systems
• Inquiry Driven Systems : Inquiry Into Inquiry

Template:Col-end

Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

• Logical Negation, InterSciWiki
• Logical Negation, MyWikiBiz
• Logical Negation, Wikinfo
• Logical Negation, Wikiversity
• Logical Negation, Wikiversity Beta
• Logical Negation, Wikipedia