Junctor (logic)
From Lat. “iungo”: to join, to connect. General expression for a logical operator.
For example, in a logical 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 | ||
|---|---|---|---|---|
| preferred | also in use | not recommended | ||
| Conditional | →, ⟶ | ⇒, ⟹ | ⊃, ⊨ | if …, then … |
| Biconditional | ↔, ⟷ | ⇔, ⟺, ≡1), iff | =, ~ | … exactly, when … |
| Conjunction | ∧ | & | ∩, ∙ | … and … |
| Adjunktion | ∨ | ∥ | + | … oder … [or both] |
| Contravalence | ⊻ | ⊕, ⩒, ≢, xor | >< | … or … [but not both] |
| Negation | ¬ | ! | ‾‾, ∼ | 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 (XOR), the Peirce function (NOR) and the Sheffer function (NAND) are also relevant as basic building blocks of digital logic gates.
Other junctors address, among other things, multi-valued logics ( meaning that there are other states besides true and false) or even intensional aspects of propositions. However, these are outside the scope of this website.