In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols together with their name, pronunciation, and the related field of mathematics. Additionally, the third column contains an informal definition, the fourth column gives a short example, the fifth and sixth give the unicode location and name for use in HTML documents. The last column provides the LaTeX symbol.
Outside logic, different symbols have the same meaning, and the same symbol can have different meanings, depending on the context.
Advanced and rarely used logical symbols
These symbols are sorted by their Unicode value:
U+00B7 · MIDDLE DOT, an outdated way for denoting AND, still in use in electronics; for example "A · B" is the same as "A & B"
· : Center dot with a line above it; Outdated way for denoting NAND, for example "A·B" is the same as "A NAND B" or "A | B" or "¬ (A & B)". See also Unicode U+22C5 ⋅ dot operator.
U+0305 ̅ COMBINING OVERLINE, used as abbreviation for standard numerals (Typographical Number Theory). For example, using HTML style "4̅" is a shorthand for the standard numeral "SSSS0".
Overline is also a rarely used format for denoting Gödel numbers: for example, "A V B" says the Gödel number of "(A V B)".
Overline is also an outdated way for denoting negation, still in use in electronics: for example, "A V B" is the same as "¬(A V B)".
U+2191 ↑ UPWARDS ARROW or U+007C | VERTICAL LINE: Sheffer stroke, the sign for the NAND operator.
U+2201 ∁ Complement
U+2204 ∄ THERE DOES NOT EXIST: strike out existential quantifier same as "¬∃"
U+2234 ∴ Therefore: Therefore
U+2235 ∵ Because: because
U+22A7 ⊧ Models: is a model of
U+22A8 ⊨ True: is true of
U+22AC ⊬ DOES NOT PROVE: negated ⊢, the sign for "does not prove", for example T ⊬ P says "P is not a theorem of T"
U+22AD ⊭ Not true: is not true of
U+22BC ⊼ NAND: NAND operator. In HTML, it can also be produced by <span style="text-decoration: overline">∧</span>: ∧
U+22BD ⊽ Nor: NOR operator. In HTML, it can also be produced by <span style="text-decoration: overline">∨</span>: ∨
U+25C7 ◇ WHITE DIAMOND: modal operator for "it is possible that", "it is not necessarily not" or rarely "it is not provable not" (in most modal logics it is defined as "¬◻¬")
U+22C6 ⋆ STAR OPERATOR: usually used for ad-hoc operators
U+22A5 ⊥ UP TACK or U+2193 ↓ DOWNWARDS ARROW: Webb-operator or Peirce arrow, the sign for NOR. Confusingly, "⊥" is also the sign for contradiction or absurdity.
U+2310 ⌐ REVERSED NOT SIGN
U+231C ⌜ TOP LEFT CORNER and U+231D ⌝ 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. And 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+25FB ◻ WHITE MEDIUM SQUARE or U+25A1 □ WHITE SQUARE: modal operator for "it is necessary that" (in modal logic), or "it is provable that" (in provability logic), or "it is obligatory that" (in deontic logic), or "it is believed that" (in doxastic logic); also as empty clause (alternatives:
∅
and ⊥).
Note that the following operators are rarely supported by natively installed fonts. If you wish to use these in a web page, you should always embed the necessary fonts so the page viewer can see the web page without having the necessary fonts installed in their computer.
U+27E1 ⟡ WHITE CONCAVE-SIDED DIAMOND
U+27E2 ⟢ WHITE CONCAVE-SIDED DIAMOND WITH LEFTWARDS TICK: modal operator for was never
U+27E3 ⟣ WHITE CONCAVE-SIDED DIAMOND WITH RIGHTWARDS TICK: modal operator for will never be
U+27E4 ⟤ WHITE SQUARE WITH LEFTWARDS TICK: modal operator for was always
U+27E5 ⟥ WHITE SQUARE WITH RIGHTWARDS TICK: modal operator for will always be
U+297D ⥽ 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 hook is also used as strict implication by C.I.Lewis
p
⥽
q
≡
◻
(
p
→
q
)
, the corresponding LaTeX macro is strictif. See here for an image of glyph. Added to Unicode 3.2.0.
U+2A07 ⨇ TWO LOGICAL AND OPERATOR
Poland and Germany
As of 2014 in Poland, the universal quantifier is sometimes written
∧
and the existential quantifier as
∨
. The same applies for Germany.
