Encyclopedia

List of logic symbols

Wikipedia contributorsAdapted for Fathomly · View authors

6 min read
Source updated September 11, 2026

In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contain an informal explanation, a short example, the Unicode location, the name for use in HTML documents, and the LaTeX symbol.

01Propositional logic

Logical connectives
Logic Name	Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Read as	Explanation
Negation	¬	U+00AC	¬ ¬	$\neg$ \lnot or \neg	NOT	$\neg (\neg A)\Leftrightarrow A$
	~	U+007E	˜ &tilde;	$\sim$ \sim
	!	U+0021	&excl;	$\neg$ \lnot or \neg
	′	U+2032	′	$'$ '
Conjunction	∧	U+2227	∧ &and;	$\wedge$ \wedge or \land	AND	$A\land B\Leftrightarrow \neg (\neg A\lor \neg B)$
	·	U+00B7	· ·	$\cdot$ \cdot
	&	U+0026	& &	$\&$ \&
Inclusive disjunction	∨	U+2228	∨ &or;	$\lor$ \lor or \vee	OR	$A\lor B\Leftrightarrow \neg (\neg A\land \neg B)$
	+	U+002B	+ +
	∥	U+2225	∥ &parallel;	$\parallel$ \parallel
Exclusive disjunction	⊕	U+2295	⊕ &oplus;	$\oplus$ \oplus	XOR, either ... or ...	$A\veebar B\Leftrightarrow (A\lor B)\land \neg (A\land B)$
	⊻	U+22BB	⊻ &veebar;	$\veebar$ \veebar
	↮	U+21AE	↮	$\not \leftrightarrow$ \nleftrightarrow
	≢	U+2262	≢ &nequiv;	$\not \equiv$ \not\equiv
Non-conjunction (Sheffer stroke)	↑	U+2191		$\uparrow$ \uparrow	NAND, neither ... nor ...	$A\uparrow B\Leftrightarrow \neg (A\land B)$
	\|	U+007C		$\mid$ \vert, \mid
	⊼	U+22BC		$\barwedge$ \barwedge
Non-disjunction	↓	U+2193		$\downarrow$ \downarrow	NOR	$A\downarrow B\Leftrightarrow \neg (A\lor B)$
Non-disjunction	⊽	U+22BD		${\overline {\vee }}$ \overline{\vee}	NOR	$A\downarrow B\Leftrightarrow \neg (A\lor B)$
Conditional	⇒	U+21D2	⇒ ⇒	$\Rightarrow$ \Rightarrow $\implies$ \implies	Implies, then	$(A\Rightarrow B)\Leftrightarrow \neg (A\land \neg B)$
	→	U+2192	→ →	$\to$ \to or \rightarrow
	⊃	U+2283	⊃ ⊃	$\supset$ \supset
Biconditional	⇔	U+21D4	⇔ ⇔	$\Leftrightarrow$ \Leftrightarrow $\iff$ \iff	If and only if, iff, XNOR	$(A\Leftrightarrow B)\Leftrightarrow (\neg A\land \neg B)\lor (A\land B)$
	↔	U+2194	↔ ↔	$\leftrightarrow$ \leftrightarrow
	≡	U+2261	≡ &equiv;	$\equiv$ \equiv
	⊙	U+2299		$\odot$ \odot

Common propositional logic symbolsOther symbols
Logic Name	Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Read as	Category	Explanation	Examples
true (tautology)	⊤	U+22A4	⊤ &top;	$\top$ \top	top, truth, tautology, verum, full clause	propositional logic, Boolean algebra, first-order logic	$\top$ denotes a proposition that is always true.	The proposition $\top \lor P$ is always true since at least one of the two is unconditionally true.
	T
	1
false (contradiction)	⊥	U+22A5	⊥ &perp;	$\bot$ \bot	bottom, falsity, contradiction, falsum, empty clause	propositional logic, Boolean algebra, first-order logic	$\bot$ denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines.	The proposition $\bot \wedge P$ is always false since at least one of the two is unconditionally false.
	F
	0
precedence grouping	( )	U+0028 U+0029	( ) ( )	$(~)$ ( )	parentheses; brackets	almost all logic syntaxes, as well as metalanguage	Perform the operations inside the parentheses first.	(8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1, but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4.

Advanced or rarely used

Advanced or rarely used propositional symbols
Symbol	Unicode value (hexadecimal)	Logic Name
⌐	U+2310	reversed not sign
⨇	U+2A07	two logical AND operator

02First-order logic

Common first-order logic symbols
Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Logic Name	Read as	Category	Explanation	Examples
∀	U+2200	∀ ∀	$\forall$ \forall	universal quantification	given any, for all, for every, for each, for any	first-order logic	$\forall x$ $P(x)$ or $(x)$ $P(x)$ says "given any $x$ , $x$ has property $P$ ."	$\forall n\in \mathbb {N} :n^{2}\geq n.$
()				universal quantification	given any, for all, for every, for each, for any	first-order logic		$\forall n\in \mathbb {N} :n^{2}\geq n.$
∃	U+2203	∃ ∃	$\exists$ \exists	existential quantification	there exists, for some	first-order logic	$\exists x$ $P(x)$ says "there exists an $x$ (at least one) such that $x$ has property $P$ ."	$\exists n\in \mathbb {N} :$ n is even.
∃!	U+2203 U+0021	∃ ! ∃!	$\exists !$ \exists !	uniqueness quantification	there exists exactly one	first-order logic (abbreviation)	$\exists !x$ $P(x)$ says "there exists exactly one $x$ such that $x$ has property $P$ ." Only $\forall$ and $\exists$ are part of formal logic. $\exists !x$ $P(x)$ is an abbreviation for $\exists x\forall y(P(y)\leftrightarrow y=x)$	$\exists !n\in \mathbb {N} :n+5=2n.$

Advanced or rarely used first-order symbols

Advanced or rarely used first-order logic symbols
Symbol	Unicode value (hexadecimal)	HTML value (decimal)	HTML entity (named)	LaTeX symbol	Logic Name	Read as	Category	Explanation
∄	U+2204			\nexists	there does not exist			Strike out existential quantifier. "¬∃" is sometimes used instead.

03Metalanguage and metalogic

Common metalanguage and metalogic symbols
Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Logic Name	Read as	Category	Explanation	Examples
$\mathbb {D}$	U+1D53B	𝔻 &Dopf;	\mathbb{D	domain of discourse	domain of discourse	metalanguage (first-order logic semantics)		$\mathbb {D} \mathbb {:} \mathbb {R}$
⊢	U+22A2	⊢ &vdash;	$\vdash$ \vdash	syntactic consequence	proves, syntactically entails (single) turnstile	metalanguage (metalogic)	$A\vdash B$ says " $B$ is a theorem of $A$ ". In other words, $A$ proves $B$ via a deductive system.	$(A\rightarrow B)\vdash (\lnot B\rightarrow \lnot A)$ (eg. by using natural deduction)
⊨	U+22A8	⊨ &vDash;	$\vDash$ \vDash, \models	semantic consequence or satisfaction	(semantically) entails or satisfies, models double turnstile	metalanguage (metalogic)	$A\vDash B$ says "in every model, it is not the case that $A$ is true and $B$ is false". ${\mathcal {M}},\sigma \vDash B$ says a formula $B$ is true in a model ${\mathcal {M}}$ with variable assignment $\sigma$ .	$(A\rightarrow B)\vDash (\lnot B\rightarrow \lnot A)$ (eg. by using truth tables)
≡	U+2261	&equiv;	$\equiv$ \equiv	logical equivalence	is logically equivalent to	metalanguage (metalogic)	It's when $A\vDash B$ and $B\vDash A$ . Whether a symbol means a material biconditional or a logical equivalence, depends on the author's style.	$(A\rightarrow B)\equiv (\lnot A\lor B)$
⟚	U+27DA
⇔	U+21D4	⇔ ⇔	$\Leftrightarrow$ \Leftrightarrow
⊬	U+22AC		⊬ \nvdash		does not syntactically entail (does not prove)	metalanguage (metalogic)	$A\nvdash B$ says " $B$ is not a theorem of $A$ ". In other words, $B$ is not derivable from $A$ via a deductive system.	$A\lor B\nvdash A\wedge B$
⊭	U+22AD		⊭\nvDash		does not semantically entail	metalanguage (metalogic)	$A\nvDash B$ says " $A$ does not guarantee the truth of $B$ ". In other words, $A$ does not make $B$ true.	$A\lor B\nvDash A\wedge B$
∴	U+2234		∴\therefore	therefore	therefore	metalanguage	abbreviation for "therefore"
∵	U+2235		∵ \because	because	because	metalanguage	abbreviation for "because".
≔	U+2254	≔ &coloneq;	≔ \coloneqq $:=$ :=	definition	is defined as	metalanguage	$a:=b$ means "from now on, $a$ is defined to be another name for $b$ ." This is a statement in the metalanguage, not the object language. The notation $a\equiv b$ may occasionally be seen in physics, meaning the same as $a:=b$ .	$\cosh x:={\frac {e^{x}+e^{-x}}{2}}$
≜	U+225C		$\triangleq$ \triangleq
≝	U+225D		${\stackrel {\scriptscriptstyle \mathrm {def} }{=}}$ \stackrel{ \scriptscriptstyle \mathrm{def}}{=}

Advanced or rarely used metalogical symbols

Advanced or rarely used metalogical symbols
Symbol	Unicode value (hexadecimal)	LaTeX symbol	Logic Name	Explanation
̅	U+0305	\overline{x}	combining overline	Used format for denoting Gödel numbers. Using HTML style "4̅" is an abbreviation for the standard numeral "SSSS0". It may also denote a negation (used primarily in electronics).
⌜ ⌝	U+231C U+231D	\ulcorner \urcorner	top left corner top right corner	Corner quotes, also called "Quine quotes"; for quasi-quotation, i.e. quoting specific context of unspecified ("variable") expressions; also used for denoting Gödel number; for example "⌜G⌝" denotes the Gödel number of G. (Typographical note: although the quotes appears as a "pair" in unicode (231C and 231D), they are not symmetrical in some fonts. In some fonts (for example Arial) they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈ and ⌉ (U+2308 and U+2309) or by using a negation symbol and a reversed negation symbol ⌐ ¬ in superscript mode.)
⟛	U+27DB		left and right tack	"Proves and is proved by".
⊩	U+22A9	\Vdash	forces	One of this symbol's uses is to mean "truthmakes" in the truthmaker theory of truth. It is also used to mean "forces" in the set theory method of forcing.
⋆	U+22C6	\star	star operator	May sometimes be used for ad-hoc operators.

04Modal logic

Common modal logic symbols
Symbol	Unicode value (hexadecimal)	HTML codes	LaTeX symbol	Logic Name	Read as	Category	Explanation	Examples
□	U+25A1		$\Box$ \Box	necessity (in a model)	box; it is necessary that	modal logic	modal operator for "it is necessary that" in alethic logic, "it is provable that" in provability logic, "it is obligatory that" in deontic logic, "it is believed that" in doxastic logic, "it is known that" in autoepistemic logic.	$\Box \forall xP(x)$ says "it is necessary that everything has property $P$ "
◇	U+25C7		$\Diamond$ \Diamond	possibility (in a model)	diamond; it is possible that	modal logic	modal operator for "it is possible that", (in most modal logics it is defined as "¬□¬", "it is not necessarily not").	$\Diamond \exists xP(x)$ says "it is possible that something has property $P$ "

Advanced or rarely used modal symbols

Advanced or rarely used modal logic symbols
Symbol	Unicode value (hexadecimal)	LaTeX symbol	Logic Name	Read as	Category	Explanation
⥽	U+297D	\strictif	right fish tail			Sometimes used for "relation", also used for denoting various ad hoc relations (for example, for denoting "witnessing" in the context of Rosser's trick). The fish tail is also used as strict implication by C.I.Lewis $p$ ⥽ $q\equiv \Box (p\rightarrow q)$ .
⟡	U+27E1		white concave-sided diamond	never	modal operator
⟢	U+27E2		white concave-sided diamond with leftwards tick	was never	modal operator
⟣	U+27E3		white concave-sided diamond with rightwards tick	will never be	modal operator
⟤	U+25A4		white square with leftwards tick	was always	modal operator
⟥	U+25A5		white square with rightwards tick	will always be	modal operator

Watch videos about List of logic symbolsExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article “List of logic symbols”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

Images, from Wikimedia Commons:

Venn10.svg by Watchduck You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck"., Public domain
Venn0001.svg by Watchduck, Public domain
Venn0111.svg by Unknown author, Public domain
Venn0110.svg by Unknown author, Public domain
Venn1110.svg by Unknown author, Public domain
Venn1000.svg by Unknown author, Public domain
Venn1011.svg by Unknown author, Public domain
Venn1001.svg by Unknown author, Public domain

Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.

List of logic symbols

01Propositional logic

Advanced or rarely used

02First-order logic

Advanced or rarely used first-order symbols

03Metalanguage and metalogic

Advanced or rarely used metalogical symbols

Sources and credits

Related topics

Glossary of logic

Józef Maria Bocheński

Glossary of Principia Mathematica