Double negation

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Elimination and introduction

Valid Rules of replacement Inferences Converse Formal proof

14 related topics

Proofs

Here Jan Łukasiewicz Hypothetical syllogism metatheorem

3 related topics

Overview

Propositional logic Classical logic Logically equivalent Intuitionistic logic Negation

10 related topics

Key facts & relationships

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Field: Propositional calculus · Classical logic
Statement: If a statement is true, then it is not the case that the statement is not true, and vice versa."
Symbolic statement: A ≡ ∼ ( ∼ A ) {\displaystyle A\equiv \ \sim (\sim A)}
Type: Theorem

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Bibliography

William Hamilton Sir William Hamilton, 9th Baronet
Christoph Sigwart
Stephen C. Kleene
ISBN ISBN (identifier)

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Map overview Semantic statistics

Nodes36

Edges35

Triples18

Avg. degree1.94

Density0.055556

Components1

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Double negation

Top relations

related to In classical propositional calculus system · 5

Double negation → Hilbert, In Hilbert-style, Jan, L1, We

related to Elimination and introduction · 4

Double negation → Double, It, The, They

Field · 2

Double negation → Classical logic, Propositional calculus

Statement · 1

Double negation → If a statement is true, then it is not the case that the statement is not true, and vice versa."

Symbolic statement · 1

Double negation → A ≡ ∼ ( ∼ A ) {\displaystyle A\equiv \ \sim (\sim A)}

Type · 1

Double negation → Theorem

related to Formal notation · 1

Double negation → The

Important terminology Word statistics

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Important terminology

logic negation double propositional classical theorem introduction statement true intuitionistic elimination displaystyle proof case calculus rule equivalence principle also russell

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Double negation	Field	Propositional calculus	1.00	infobox
Double negation	Field	Classical logic	1.00	infobox
Double negation	Statement	If a statement is true, then it is not the case that the statement is not true, and vice versa."	1.00	infobox
Double negation	Symbolic statement	A ≡ ∼ ( ∼ A ) {\displaystyle A\equiv \ \sim (\sim A)}	1.00	infobox
Double negation	Type	Theorem	1.00	infobox
intuitionistic logic	instance of	but not of weaker logics	0.80	text
minimal logic	instance of	but not of weaker logics	0.80	text
It's not the case that it's not raining is weaker than It's raining	instance of	a statement	0.80	text
Double negation	related to Elimination and introduction	Double	0.60	section
Double negation	related to Elimination and introduction	They	0.60	section
Double negation	related to Elimination and introduction	The	0.60	section
Double negation	related to Elimination and introduction	It	0.60	section

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Min side: 3