====== Logical symbols ======

Overview of the most important logical symbols with references to the corresponding articles.

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**Note:** Over the history of logic, a number of different and sometimes contradictory symbol systems have been developed, many of which are still in use today. The attempt has been made to also list various alternative symbols that may be found in other publications. Among these, there are also symbols that may have confusing meanings. Those are marked with an <u questionable>underline</u> to indicate that their use is discouraged.
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===== Junctors =====

^ Symbol ^ Alternatives ^ Short name ^ Description ^ Article ^
^  <var>A</var> ''⟶'' <var>B</var>  | ''→'', ''⇒'', ''⟹'', <u questionable "not recommended, since also used as “is superset of”.">''⊃''</u>, <u questionable "not recommended since it is ambiguous">''⊨''</u>, <u questionable "not recommended, since it can be confused with “is greater than”.">''≻''</u> |  ''if''  | “If <var>A</var>, then <var>B</var>“ | [[glossary:conditional|Conditional]] |
^  <var>A</var> ''⟷'' <var>B</var>  | ''↔'', ''⇔'', ''⟺'', <u questionable "is also used for “logical equivalence”, although this often means the same thing">''≡''</u>, <u questionable "not recommended, as also used in the sense of “follows the distribution of” (and also sometimes as a negation).">''~''</u>, <u questionable "not recommended, since it is ambiguous.">''≻≺''</u> |  ''iff''  | „<var>B</var> exactly when <var>A</var>“ | [[glossary:biconditional|Biconditional]] |
^  <var>A</var> ''∧'' <var>B</var>  | ''&'', <u questionable "not recommended, as also used in the sense of “is intersection of”.">''∩''</u>, <u questionable "not recommended, as it is also used as multiplication sign and as generic placeholder">''·''</u> |  ''and''  | „<var>A</var> and <var>B</var>“ | [[glossary:conjunction|Conjunction]] |
^  <var>A</var> ''∨'' <var>B</var>  | ''∥'', <u questionable "not recommended, as also used as addition sign">''+''</u> |  ''or''  | „<var>A</var> or <var>B</var> [//or both//]“ | [[glossary:adjunction|Adjunction]] |
^  <var>A</var> ''⊻'' <var>B</var>  | ''⩒'', ''⊕'', <u questionable "not recommended since ambiguous">''≢''</u>, <u questionable "not recommended since ambiguous">''↮''</u>, <u questionable "not recommended, as it can be misunderstood as ≷ (greater than or less than)">''%%><%%''</u> |  ''xor''  | „<var>A</var> or <var>B</var> [//but not both//]“ | [[glossary:contravalence|Contravalence]] |
^  ''¬'' <var>A</var>  | ''!'', <u questionable "Overline: not recommended, as it has numerous other meanings in mathematics">''‾‾''</u>, <u questionable "not recommended, as also used in the sense of “follows the distribution of” (and also sometimes as symbol for the biconditional).">''∼''</u>  |  ''not''  | „not <var>B</var>“ | Negation |

See also <span maniculus "For more information on this topic, see:">⁠[[glossary:junctor|Junctor]]</span>

===== Quantors =====

^ Symbol ^ Alternatives ^ Description ^ Article ^
^  ''∀'' <var>A</var>: <var>B</var>  | <u questionable "not recommended, as it can also be misunderstood as a conjunction symbol">''͓∧''</u>| „For all <var>A</var> it is true, that <var>B</var>“ | [[glossary:universal_quantification|Universal quantification]] |
^  ''∃'' <var>A</var>: <var>B</var>  | <u questionable "Not recommended, as it can also be misunderstood as a contravalence symbol.">''͓∨''</u> | „There exist [at least one] <var>A</var>, for which <var>B</var> is true“ | [[glossary:existential_quantification|Existential quantification]] |
^  ''∄'' <var>A</var>: <var>B</var>  | | „There exists __no__ <var>A</var>, for which <var>B</var> is true“ | [[glossary:universal_quantification#negation|Universal quantification§Negation]] |

See also <span maniculus "For more information on this topic, see:">⁠[[glossary:quantor|Quantor]]</span>

===== Comparisons =====

^ Symbol ^ Alternatives ^ Description  ^ Article ^
^  <var>A</var> ''≡'' <var>B</var>  | <u questionable "not recommended, as also often used as symbols for the biconditional, although in many situations they signify the same thing">''↔'', ''⟷'', ''⇔'', ''⟺''</u>| „<var>A</var> is logically equivalent to <var>B</var>“ | [[glossary:logical_equivalence|Logical equivalence]] \\ (see also [[glossary:biconditional|Biconditional]] and [[glossary:contravalence|Contravalence]]) |
^  <var>A</var> ''≢'' <var>B</var>  | <u questionable "not recommended, as it can also be understood as a negation of the biconditional, although in many situations they say the same thing; Also: poor readability!">''↮'', ''⇎''</u> | „<var>A</var> is __not__ logically equivalent to <var>B</var>“ | ::: |

===== Mathematical symbols =====

Only those symbols which are used in articles on this site are listed here:

^ Symbol ^ Alternatives ^ Description ^ Article ^
^  ''∅''  | ''{}'', ''⦰'', ''<u questionable "O with slash: not recommended, as ambiguous">Ø</u>'', ''<u questionable "Phi: not recommended, since ambiguous">𝛷</u>'', ''<u questionable "Zero: not recommended, as ambiguous">0</u>'' , ''<u questionable "Epsilon: not recommended, since ambiguous">ε</u>'', ''<u questionable "Lambda: not recommended, since ambiguous">Λ</u>'' | Empty set | [[glossary:empty_set|Empty set]] |

===== More information =====

  * [[wp>List of logic symbols|List of logic symbols]] on //Wikipedia//