====== Junctor (logic) ======

From Lat. “<i :la>iungo</i>”: to join, to connect. General expression for a logical operator.

For example, in a logical [[glossary:disjunction|disjunction]] like “A //or// B”, the word “or” represents the junctor.

Relevant for us is not which specific symbol is used (e.g. the word “''or''”, or a logical symbol like “''∨''”), but the semantic meaning which is represented by this symbol.

The following table shows an overview over the most commonly used junctors of propositional logic:

^ Name ^  Logical symbols  ^^^ Description ^
^ ::: ^ <small>preferred</small>   ^ <small>also in use</small>   ^ <small>not recommended</small>   ^ ::: ^
^ [[glossary:conditional|Conditional]] | ''→'', ''⟶'' | ''⇒'', ''⟹'' | <u questionable "not recommended because it is ambiguous">''⊃''</u>, <u questionable "not recommended because it is ambiguous">''⊨''</u> | if …, then … |
^ [[glossary:biconditional|Biconditional]] | ''↔'', ''⟷'' | ''⇔'', ''⟺'', ''≡''((This is actually the symbol for [[glossary:logical_equivalence|logical equivalence]]; however this is ironically in many contexts //logically equivalent// to the [[glossary:biconditional|biconditional]].)), <span :en "if and only if">''iff''</span> | <u questionable "not recommended because it is ambiguous">''=''</u>, <u questionable "not recommended because it is ambiguous">''~''</u> | … exactly, when … |
^ [[glossary:conjunction|Conjunction]] | <span "et">''∧''</span> | <span "Kaufmanns-Und">''&''</span> | <u questionable "not recommended because it is ambiguous">''∩''</u>, <u questionable "not recommended because it is ambiguous">''∙''</u> | … and … |
^ [[glossary:adjunction|Adjunktion]] | ''∨'' | <span "Parallelen">''∥''</span> | <u questionable "not recommended because it is ambiguous">''+''</u> | … oder … [//or both//] |
^ [[glossary:contravalence|Contravalence]] | ''⊻'' | <span "O-Plus">''⊕''</span>, ''⩒'', ''≢'', ''xor'' | <u questionable "not recommended because it is ambiguous">''%%><%%''</u> | … or … [//but not both//] |
^ Negation | ''¬'' | ''!'' | <u questionable "Overline: not recommended because it has also numerous other meanings, especially in mathematics">''‾‾''</u>, <u questionable "not recommended, as it is also used as “follows the distribution of” (and sometimes also for the biconditional">''∼''</u> | not … |

===== Other junctors =====

In addition to the aforementioned ones, used here to illustrate logical fallacies, there is also a whole range of other junctors, which are usually only relevant in very specific applications, depending on the specific application. 

For example, in programming languages, the comparison operators (''='', ''<'', ''≤'', ''≥'', ''>'' and ''≠'') are usually understood as //junctors//, as they result in a truth value (e.g.: ''i %%<=%% 5'' can be //true// or //false//, depending on the value of ''i'').

In addition to the contravalence ([[wp>XOR gate|XOR]]), the Peirce function ([[wp>NOR gate|NOR]]) and the Sheffer function ([[wp>NAND gate|NAND]]) are also relevant as basic building blocks of digital [[wp>Logic gate|logic gates]].

Other junctors address, among other things, multi-valued logics ( meaning that there are other states besides true and false) or even [[glossary:intension|intensional]] aspects of propositions. However, these are outside the scope of this website.

===== See also =====

  * [[meta:logical_symbols|Logical symbols]]
  * [[glossary:quantifier|Quantifier]]