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.
: negated ⊢, the sign for "does not prove", for example T ⊬ P says "P is not a theorem of T"
: is not true of
: Affirmation operator
: NAND operator.
: NOR operator.
: modal operator for "it is possible that", "it is not necessarily not" or rarely "it is not provable not"
: usually used for ad-hoc operators
or : Webb-operator or Peirce arrow, the sign for NOR. Confusingly, "⊥" is also the sign for contradiction or absurdity.
and : corner quotes, also called "Quine quotes"; for quasi-quotation, i.e. quoting specific context of unspecified expressions; also used for denoting Gödel number; for example "⌜G⌝" denotes the Gödel number of G. , they are not symmetrical in some fonts. And in some fonts they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈ and ⌉
or : modal operator for "it is necessary that", or "it is provable that", or "it is obligatory that", or "it is believed that" ; also as empty clause.
: semantic equivalent
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 seethe web page without having the necessary fonts installed in their computer.
: modal operator for was never
: modal operator for will never be
: modal operator for was always
: modal operator for will always be
: sometimes used for "relation", also used for denoting various ad hoc relations The fish hook is also used as strict implication by C.I.Lewis ⥽, the corresponding LaTeX macro is \strictif. for an image of glyph. Added to Unicode 3.2.0.
in Poland, the universal quantifier is sometimes written and the existential quantifier as. The same applies for Germany.
Japan
The ⇒ symbol is often used in text to mean "result" or "conclusion", as in "We examined whether to sell the product ⇒ We will not sell it". Also, the → symbol is often used to denote "changed to" as in the sentence "The interest rate changed. March 20% → April 21%".
