List of logic symbols
Updated: 5/20/2026, 7:02:30 PM Wikipedia source
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 contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, and the LaTeX symbol.
Tables
· Basic logic symbols
material conditional (material implication)
material conditional (material implication)
Symbol
⇒
→
⊃
Unicode
value
(hexadecimal)
U+21D2
U+2192
U+2283
HTML
codes
& ;
& ;
& ;
⇒
→
⊃
LaTeX
symbol
⇒
{\displaystyle \Rightarrow }
\Rightarrow
⟹
{\displaystyle \implies }
\implies
→
{\displaystyle \to }
\to or \rightarrow
⊃
{\displaystyle \supset }
\supset
Logic Name
material conditional (material implication)
Read as
implies,
if P then Q,
it is not the case that P and not Q
Category
propositional logic, Boolean algebra, Heyting algebra
Explanation
A
⇒
B
{\displaystyle A\Rightarrow B}
is false when A is true and B is false but true otherwise.
In other mathematical contexts, see glossary of mathematical symbols,
→
{\displaystyle \rightarrow }
may indicate the domain and codomain of a function and
Examples
x
=
2
⇒
x
2
=
4
{\displaystyle x=2\Rightarrow x^{2}=4}
is true, but
x
2
=
4
⇒
x
=
2
{\
material biconditional (material equivalence)
material biconditional (material equivalence)
Symbol
⇔
↔
≡
Unicode
value
(hexadecimal)
U+21D4
U+2194
U+2261
HTML
codes
& ;
& ;
& ;
⇔
↔
≡
LaTeX
symbol
⇔
{\displaystyle \Leftrightarrow }
\Leftrightarrow
⟺
{\displaystyle \iff }
\iff
↔
{\displaystyle \leftrightarrow }
\leftrightarrow
≡
{\displaystyle \equiv }
\equiv
Logic Name
material biconditional (material equivalence)
Read as
if and only if, iff, xnor
Category
propositional logic, Boolean algebra
Explanation
A
⇔
B
{\displaystyle A\Leftrightarrow B}
is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.
Examples
x
+
5
=
y
+
2
⇔
x
+
3
=
y
{\displaystyle x+5=y+2\Leftrightarrow x+3=y}
negation
negation
Symbol
¬
~
!
′
Unicode
value
(hexadecimal)
U+00AC
U+007E
U+0021
U+2032
HTML
codes
& ;
& ;
& ;
& ;
¬
˜
!
′
LaTeX
symbol
¬
{\displaystyle \neg }
\lnot or \neg
∼
{\displaystyle \sim }
\sim
′
{\displaystyle '}
'
Logic Name
negation
Read as
not
Category
propositional logic, Boolean algebra
Explanation
The statement
¬
A
{\displaystyle \lnot A}
is true if and only if A is false.
A slash placed through another operator is the same as
¬
{\displaystyle \neg }
placed in front.
The prime symbol is placed after the negated thing, e .
Examples
¬
(
¬
A
)
⇔
A
{\displaystyle \neg (\neg A)\Leftrightarrow A}
x
≠
y
⇔
¬
(
x
=
y
)
{\displaystyle x\neq y\Leftrightarrow \neg (x=y)}
logical conjunction
logical conjunction
Symbol
∧
·
&
Unicode
value
(hexadecimal)
U+2227
U+00B7
U+0026
HTML
codes
& ;
& ;
& ;
∧
·
&
LaTeX
symbol
∧
{\displaystyle \wedge }
\wedge or \land
⋅
{\displaystyle \cdot }
\cdot
&
{\displaystyle \&}
\&
Logic Name
logical conjunction
Read as
and
Category
propositional logic, Boolean algebra
Explanation
The statement A ∧ B is true if A and B are both true; otherwise, it is false.
Examples
n < 4 ∧ n >2 ⇔ n = 3 when n is a natural number.
logical (inclusive) disjunction
logical (inclusive) disjunction
Symbol
∨
+
∥
Unicode
value
(hexadecimal)
U+2228
U+002B
U+2225
HTML
codes
& ;
& ;
& ;
∨
+
∥
LaTeX
symbol
∨
{\displaystyle \lor }
\lor or \vee
∥
{\displaystyle \parallel }
\parallel
Logic Name
logical (inclusive) disjunction
Read as
or
Category
propositional logic, Boolean algebra
Explanation
The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false.
Examples
n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number.
exclusive disjunction
exclusive disjunction
Symbol
⊕
⊻
↮
≢
Unicode
value
(hexadecimal)
U+2295
U+22BB
U+21AE
U+2262
HTML
codes
& ;
& ;
& ;
& ;
⊕
⊻
—
≢
LaTeX
symbol
⊕
{\displaystyle \oplus }
\oplus
⊻
{\displaystyle \veebar }
\veebar
↮
{\displaystyle \not \leftrightarrow }
\nleftrightarrow
≢
{\displaystyle \not \equiv }
\not\equiv
Logic Name
exclusive disjunction
Read as
xor,
either ... or ... (but not both)
Category
propositional logic, Boolean algebra
Explanation
The statement
A
⊕
B
{\displaystyle A\oplus B}
is true when either A or B, but not both, are true. This is equivalent to
¬(A ↔ B), hence the symbols
↮
{\displaystyle \nleftrightarrow }
and
≢
{\displaystyle
Examples
¬
A
⊕
A
{\displaystyle \lnot A\oplus A}
is always true and
A
⊕
A
{\displaystyle A\oplus A}
is always false (if vacuous truth is excluded).
true (tautology)
true (tautology)
Symbol
⊤
T
1
Unicode
value
(hexadecimal)
U+22A4
HTML
codes
& ;
⊤
LaTeX
symbol
⊤
{\displaystyle \top }
\top
Logic Name
true (tautology)
Read as
top, truth, tautology, verum, full clause
Category
propositional logic, Boolean algebra, first-order logic
Explanation
⊤
{\displaystyle \top }
denotes a proposition that is always true.
Examples
The proposition
⊤
∨
P
{\displaystyle \top \lor P}
is always true since at least one of the two is unconditionally true.
false (contradiction)
false (contradiction)
Symbol
⊥
F
0
Unicode
value
(hexadecimal)
U+22A5
HTML
codes
& ;
⊥
LaTeX
symbol
⊥
{\displaystyle \bot }
\bot
Logic Name
false (contradiction)
Read as
bottom, falsity, contradiction, falsum, empty clause
Category
propositional logic, Boolean algebra, first-order logic
Explanation
⊥
{\displaystyle \bot }
denotes a proposition that is always false.
The symbol ⊥ may also refer to perpendicular lines.
Examples
The proposition
⊥
∧
P
{\displaystyle \bot \wedge P}
is always false since at least one of the two is unconditionally false.
universal quantification
universal quantification
Symbol
∀
()
Unicode
value
(hexadecimal)
U+2200
HTML
codes
& ;
∀
LaTeX
symbol
∀
{\displaystyle \forall }
\forall
Logic Name
universal quantification
Read as
given any, for all, for every, for each, for any
Category
first-order logic
Explanation
∀
x
{\displaystyle \forall x}
P
(
x
)
{\displaystyle P(x)}
or
(
x
)
{\displaystyle (x)}
P
(
x
)
{\displaystyle P(x)}
says “gi
Examples
∀
n
∈
N
:
n
2
≥
n
.
{\displaystyle \forall n\in \mathbb {N} :n^{2}\geq n.}
existential quantification
existential quantification
Symbol
∃
Unicode
value
(hexadecimal)
U+2203
HTML
codes
& ;
∃
LaTeX
symbol
∃
{\displaystyle \exists }
\exists
Logic Name
existential quantification
Read as
there exists, for some
Category
first-order logic
Explanation
∃
x
{\displaystyle \exists x}
P
(
x
)
{\displaystyle P(x)}
says “there exists an
x
{\displaystyle x}
(at least one) such that
x
{\displaystyle x}
has property
Examples
∃
n
∈
N
:
{\displaystyle \exists n\in \mathbb {N} :}
n is even.
uniqueness quantification
uniqueness quantification
Symbol
∃!
Unicode
value
(hexadecimal)
U+2203 U+0021
HTML
codes
& ; & ;
∃!
LaTeX
symbol
∃
!
{\displaystyle \exists !}
\exists !
Logic Name
uniqueness quantification
Read as
there exists exactly one
Category
first-order logic (abbreviation)
Explanation
∃
!
x
{\displaystyle \exists !x}
P
(
x
)
{\displaystyle P(x)}
says “there exists exactly one
x
{\displaystyle x}
such that
x
{\displaystyle x}
has property
Examples
∃
!
n
∈
N
:
n
+
5
=
2
n
.
{\displaystyle \exists !n\in \mathbb {N} :n+5=2n.}
precedence grouping
precedence grouping
Symbol
( )
Unicode
value
(hexadecimal)
U+0028 U+0029
HTML
codes
& ; & ;
(
)
LaTeX
symbol
(
)
{\displaystyle (~)}
( )
Logic Name
precedence grouping
Read as
parentheses; brackets
Category
almost all logic syntaxes, as well as metalanguage
Explanation
Perform the operations inside the parentheses first.
Examples
(8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1, but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4.
domain of discourse
domain of discourse
Symbol
D
{\displaystyle \mathbb {D} }
Unicode
value
(hexadecimal)
U+1D53B
HTML
codes
& ;
𝔻
LaTeX
symbol
\mathbb{D}
Logic Name
domain of discourse
Read as
domain of discourse
Category
metalanguage (first-order logic semantics)
Examples
D
:
R
{\displaystyle \mathbb {D} \mathbb {:} \mathbb {R} }
syntactic consequence
syntactic consequence
Symbol
⊢
Unicode
value
(hexadecimal)
U+22A2
HTML
codes
& ;
⊢
LaTeX
symbol
⊢
{\displaystyle \vdash }
\vdash
Logic Name
syntactic consequence
Read as
proves, syntactically entails
(single) turnstile
Category
metalanguage (metalogic)
Explanation
A
⊢
B
{\displaystyle A\vdash B}
says “
B
{\displaystyle B}
is
a theorem of
A
{\displaystyle A}
”.
In other words,
A
{\displaystyle A}
proves
B
Examples
(
A
→
B
)
⊢
(
¬
B
→
¬
A
)
{\displaystyle (A\rightarrow B)\vdash (\lnot B\rightarrow \lnot A)}
(eg. by using natural deduction)
semantic consequence
or satisfaction
semantic consequence
or satisfaction
Symbol
⊨
Unicode
value
(hexadecimal)
U+22A8
HTML
codes
& ;
⊨
LaTeX
symbol
⊨
{\displaystyle \vDash }
\vDash, \models
Logic Name
semantic consequence
or satisfaction
Read as
(semantically) entails
or satisfies, models
double turnstile
Category
metalanguage (metalogic)
Explanation
A
⊨
B
{\displaystyle A\vDash B}
says
“in every model,
it is not the case that
A
{\displaystyle A}
is true and
B
{\displaystyle B}
is false”.
M
,
Examples
(
A
→
B
)
⊨
(
¬
B
→
¬
A
)
{\displaystyle (A\rightarrow B)\vDash (\lnot B\rightarrow \lnot A)}
(eg. by using truth tables)
logical equivalence
logical equivalence
Symbol
≡
⟚
⇔
Unicode
value
(hexadecimal)
U+2261
U+27DA
U+21D4
HTML
codes
& ;
—
& ;
≡
—
⇔
LaTeX
symbol
≡
{\displaystyle \equiv }
\equiv
⇔
{\displaystyle \Leftrightarrow }
\Leftrightarrow
Logic Name
logical equivalence
Read as
is logically equivalent to
Category
metalanguage (metalogic)
Explanation
It’s when
A
⊨
B
{\displaystyle A\vDash B}
and
B
⊨
A
{\displaystyle B\vDash A}
. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.
Examples
(
A
→
B
)
≡
(
¬
A
∨
B
)
{\displaystyle (A\rightarrow B)\equiv (\lnot A\lor B)}
necessity (in a model)
necessity (in a model)
Symbol
□
Unicode
value
(hexadecimal)
U+25A1
LaTeX
symbol
◻
{\displaystyle \Box }
\Box
Logic Name
necessity (in a model)
Read as
box; it is necessary that
Category
modal logic
Explanation
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.
Examples
◻
∀
x
P
(
x
)
{\displaystyle \Box \forall xP(x)}
says “it is necessary that everything has property
P
{\displaystyle P}
”
possibility (in a model)
possibility (in a model)
Symbol
◇
Unicode
value
(hexadecimal)
U+25C7
LaTeX
symbol
◊
{\displaystyle \Diamond }
\Diamond
Logic Name
possibility (in a model)
Read as
diamond;
it is possible that
Category
modal logic
Explanation
modal operator for “it is possible that”, (in most modal logics it is defined as “¬□¬”, “it is not necessarily not”).
Examples
◊
∃
x
P
(
x
)
{\displaystyle \Diamond \exists xP(x)}
says “it is possible that something has property
P
{\displaystyle P}
”
therefore
therefore
Symbol
∴
Unicode
value
(hexadecimal)
U+2234
LaTeX
symbol
∴\therefore
Logic Name
therefore
Read as
therefore
Category
metalanguage
Explanation
abbreviation for “therefore”.
because
because
Symbol
∵
Unicode
value
(hexadecimal)
U+2235
LaTeX
symbol
∵\because
Logic Name
because
Read as
because
Category
metalanguage
Explanation
abbreviation for “because”.
definition
definition
Symbol
≔
≜
≝
Unicode
value
(hexadecimal)
U+2254
U+225C
U+225D
HTML
codes
& ;
≔
LaTeX
symbol
≔ \coloneqq
:=
{\displaystyle :=}
:=
≜
{\displaystyle \triangleq }
\triangleq
=
d
Logic Name
definition
Read as
is defined as
Category
metalanguage
Explanation
a
:=
b
{\displaystyle a:=b}
means "from now on,
a
{\displaystyle a}
is defined to be another name for
b
{\displaystyle b}
." This is a statement in the metalanguage, not the object language. The notation
Examples
cosh
x
:=
e
x
+
e
−
x
2
Sheffer stroke, NAND
Sheffer stroke, NAND
Symbol
↑
|
⊼
Unicode
value
(hexadecimal)
U+2191
U+007C
U+22BC
LaTeX
symbol
↑
{\displaystyle \uparrow }
\uparrow
∣
{\displaystyle \mid }
\vert, \mid
⊼
{\displaystyle \barwedge }
\barwedge
Logic Name
Sheffer stroke, NAND
Read as
NAND, not both
up arrow
Category
Propositional logic
Explanation
NAND is the negation of conjunction so
A
↑
B
{\displaystyle A\uparrow B}
is true if and only if it's not the case that both A and B are true.
See also NAND gate
Peirce Arrow,
NOR
Peirce Arrow,
NOR
Symbol
↓
⊽
Unicode
value
(hexadecimal)
U+2193
U+22BD
LaTeX
symbol
↓
{\displaystyle \downarrow }
\downarrow
∨
¯
{\displaystyle {\overline {\vee }}}
\overline{\vee}
Logic Name
Peirce Arrow,
NOR
Read as
nor
down arrow
Category
Propositional logic
Explanation
NOR is the negation of disjunction so
A
↓
B
{\displaystyle A\downarrow B}
is true if and only if both A and B are false.
See also NOR gate
| Symbol | Unicode value (hexadecimal) | HTML codes | LaTeX symbol | Logic Name | Read as | Category | Explanation | Examples |
| ⇒ → ⊃ | U+21D2 U+2192 U+2283 | & ; & ; & ; ⇒ → ⊃ | ⇒ {\displaystyle ightarrow } ightarrow ⟹ {\displaystyle \implies } \implies → {\displaystyle \to } \to or ightarrow ⊃ {\displaystyle \supset } \supset | material conditional (material implication) | implies, if P then Q, it is not the case that P and not Q | propositional logic, Boolean algebra, Heyting algebra | A ⇒ is false when A is true and B is false but true otherwise. In other mathematical contexts, see glossary of mathematical symbols, → {\displaystyle ightarrow } may indicate the domain and codomain of a function and | x = 2 ⇒ x 2 = 4 {\displaystyle x=2 ightarrow x^{2}=4} is true, but x 2 = 4 ⇒ x = 2 {\ |
| ⇔ ↔ ≡ | U+21D4 U+2194 U+2261 | & ; & ; & ; ⇔ ↔ ≡ | ⇔ {\displaystyle \Leftrightarrow } \Leftrightarrow ⟺ {\displaystyle \iff } \iff ↔ {\displaystyle \leftrightarrow } \leftrightarrow ≡ {\displaystyle \equiv } \equiv | material biconditional (material equivalence) | if and only if, iff, xnor | propositional logic, Boolean algebra | A ⇔ is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style. | x + 5 = y + 2 ⇔ x + 3 = |
| ¬ ~ ! ′ | U+00AC U+007E U+0021 U+2032 | & ; & ; & ; & ; ¬ ˜ ! ′ | ¬ {\displaystyle eg } \lnot or eg ∼ {\displaystyle \sim } \sim ′ {\displaystyle '} ' | negation | not | propositional logic, Boolean algebra | The statement ¬ is true if and only if A is false. A slash placed through another operator is the same as ¬ {\displaystyle eg } placed in front. The prime symbol is placed after the negated thing, e . | ¬ ( ¬ A ) ⇔ x ≠ y ⇔ ¬ ( x = y ) {\displaystyle x eq y\Leftrightarrow eg (x=y)} |
| ∧ · & | U+2227 U+00B7 U+0026 | & ; & ; & ; ∧ · & | ∧ {\displaystyle \wedge } \wedge or \land ⋅ {\displaystyle \cdot } \cdot & {\displaystyle \&} \& | logical conjunction | and | propositional logic, Boolean algebra | The statement A ∧ B is true if A and B are both true; otherwise, it is false. | n < 4 ∧ n >2 ⇔ n = 3 when n is a natural number. |
| ∨ + ∥ | U+2228 U+002B U+2225 | & ; & ; & ; ∨ + ∥ | ∨ {\displaystyle \lor } \lor or \vee ∥ {\displaystyle \parallel } \parallel | logical (inclusive) disjunction | or | propositional logic, Boolean algebra | The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false. | n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number. |
| ⊕ ⊻ ↮ ≢ | U+2295 U+22BB U+21AE U+2262 | & ; & ; & ; & ; ⊕ ⊻ — ≢ | ⊕ {\displaystyle \oplus } \oplus ⊻ {\displaystyle \veebar } \veebar ↮ {\displaystyle ot \leftrightarrow } leftrightarrow ≢ {\displaystyle ot \equiv } ot\equiv | exclusive disjunction | xor, either ... or ... (but not both) | propositional logic, Boolean algebra | The statement A ⊕ is true when either A or B, but not both, are true. This is equivalent to ¬(A ↔ B), hence the symbols ↮ {\displaystyle leftrightarrow } and ≢ {\displaystyle | ¬ A ⊕ is always true and A ⊕ is always false (if vacuous truth is excluded). |
| ⊤ T 1 | U+22A4 | & ; ⊤ | ⊤ {\displaystyle \top } \top | true (tautology) | top, truth, tautology, verum, full clause | propositional logic, Boolean algebra, first-order logic | ⊤ {\displaystyle \top } denotes a proposition that is always true. | The proposition ⊤ ∨ is always true since at least one of the two is unconditionally true. |
| ⊥ F 0 | U+22A5 | & ; ⊥ | ⊥ {\displaystyle \bot } \bot | false (contradiction) | bottom, falsity, contradiction, falsum, empty clause | propositional logic, Boolean algebra, first-order logic | ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. | The proposition ⊥ ∧ is always false since at least one of the two is unconditionally false. |
| ∀ () | U+2200 | & ; ∀ | ∀ {\displaystyle \forall } \forall | universal quantification | given any, for all, for every, for each, for any | first-order logic | ∀ P ( x ) {\displaystyle P(x)} or ( x ) {\displaystyle (x)} P ( x ) {\displaystyle P(x)} says “gi | ∀ n ∈ N : n 2 ≥ :n^{2}\geq n.} |
| ∃ | U+2203 | & ; ∃ | ∃ {\displaystyle \exists } \exists | existential quantification | there exists, for some | first-order logic | ∃ P ( x ) {\displaystyle P(x)} says “there (at least one) has property | ∃ n ∈ :} n is even. |
| ∃! | U+2203 U+0021 | & ; & ; ∃! | ∃ ! {\displaystyle \exists !} \exists ! | uniqueness quantification | there exists exactly one | first-order logic (abbreviation) | ∃ ! P ( x ) {\displaystyle P(x)} says “there such has property | ∃ ! n ∈ N : n + 5 = 2 :n+5=2n.} |
| ( ) | U+0028 U+0029 | & ; & ; ( ) | ( ) {\displaystyle (~)} ( ) | precedence grouping | 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. |
| } | U+1D53B | & ; 𝔻 | \mathbb{D} | domain of discourse | domain of discourse | metalanguage (first-order logic semantics) | \mathbb {:} \mathbb {R} } | |
| ⊢ | U+22A2 | & ; ⊢ | ⊢ {\displaystyle \vdash } \vdash | syntactic consequence | proves, syntactically entails (single) turnstile | metalanguage (metalogic) | A ⊢ says “ is ”. proves B | ( A → B ) ⊢ ( ¬ B → ¬ A ) {\displaystyle (A ightarrow B)\vdash (\lnot B ightarrow \lnot A)} (eg. by using natural deduction) |
| ⊨ | U+22A8 | & ; ⊨ | ⊨ {\displaystyle \vDash } \vDash, \models | semantic consequence or satisfaction | (semantically) entails or satisfies, models double turnstile | metalanguage (metalogic) | A ⊨ says “in is is false”. M , | ( A → B ) ⊨ ( ¬ B → ¬ A ) {\displaystyle (A ightarrow B)\vDash (\lnot B ightarrow \lnot A)} (eg. by using truth tables) |
| ≡ ⟚ ⇔ | U+2261 U+27DA U+21D4 | & ; — & ; ≡ — ⇔ | ≡ {\displaystyle \equiv } \equiv ⇔ {\displaystyle \Leftrightarrow } \Leftrightarrow | logical equivalence | is logically equivalent to | metalanguage (metalogic) | It’s when A ⊨ and B ⊨ . Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style. | ( A → B ) ≡ ( ¬ A ∨ B ) {\displaystyle (A ightarrow B)\equiv (\lnot A\lor B)} |
| ⊬ | U+22AC | ⊬ vdash | does not syntactically entail (does not prove) | metalanguage (metalogic) | A ⊬ says “ is ”. is not derivable from | A ∨ B ⊬ A ∧ | ||
| ⊭ | U+22AD | ⊭ vDash | does not semantically entail | metalanguage (metalogic) | A ⊭ says “ does ”. does not make | A ∨ B ⊭ A ∧ | ||
| □ | U+25A1 | ◻ {\displaystyle \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. | ◻ ∀ x P ( x ) {\displaystyle \Box \forall xP(x)} says “it ” | |
| ◇ | U+25C7 | ◊ {\displaystyle \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”). | ◊ ∃ x P ( x ) {\displaystyle \Diamond \exists xP(x)} says “it ” | |
| ∴ | U+2234 | ∴\therefore | therefore | therefore | metalanguage | abbreviation for “therefore”. | ||
| ∵ | U+2235 | ∵\because | because | because | metalanguage | abbreviation for “because”. | ||
| ≔ ≜ ≝ | U+2254 U+225C U+225D | & ; ≔ | ≔ \coloneqq := {\displaystyle :=} := ≜ {\displaystyle \triangleq } \triangleq = d | definition | is defined as | metalanguage | a := means "from is ." This is a statement in the metalanguage, not the object language. The notation | cosh x := e x + e − x 2 |
| ↑ | ⊼ | U+2191 U+007C U+22BC | ↑ {\displaystyle \uparrow } \uparrow ∣ {\displaystyle \mid } \vert, \mid ⊼ {\displaystyle \barwedge } \barwedge | Sheffer stroke, NAND | NAND, not both up arrow | Propositional logic | NAND is the negation of conjunction so A ↑ is true if and only if it's not the case that both A and B are true. See also NAND gate | ||
| ↓ ⊽ | U+2193 U+22BD | ↓ {\displaystyle \downarrow } \downarrow ∨ ¯ {\displaystyle {\overline {\vee }}} \overline{\vee} | Peirce Arrow, NOR | nor down arrow | Propositional logic | NOR is the negation of disjunction so A ↓ is true if and only if both A and B are false. See also NOR gate |
· Advanced or rarely used logical symbols
| Symbol | Unicode value (hexadecimal) | HTML value (decimal) | HTML entity (named) | 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). ⥽ q ≡ ◻ ( p | ||||
| ̅ | 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 . 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. | ||||
| ∄ | U+2204 | exists | there does not exist | Strike out existential quantifier. “¬∃” used some times instead. | ||||
| ⊙ | U+2299 | \odot | circled dot operator | A sign for the XNOR operator (material biconditional and XNOR are the same operation). | ||||
| ⟛ | 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+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 | ||||
| ⋆ | U+22C6 | \star | star operator | May sometimes be used for ad-hoc operators. | ||||
| ⌐ | U+2310 | reversed not sign | ||||||
| ⨇ | U+2A07 | two logical AND operator |
References
- HTML 5 Nightlyhttps://www.w3.org/html/wg/drafts/html/master/syntax.html#named-character-references
- Virtually all Turkish high school math textbooks use p' for negation due to the books handed out by the Ministry of Nati
- Although this character is available in LaTeX, the MediaWiki TeX system does not support it.
- Quine, W . (1981): Mathematical Logic, §6
- The Principles of Mathematics Revisitedhttps://books.google.com/books?id=JHBnE0EQ6VgC&pg=PA113