A logical connection between statements.
| Connective | Description | Type | Notation |
|---|---|---|---|
| negation | not | unary | \(\lnot\) |
| conjunction | and | binary | \(\land\) |
| disjunction | or | binary | \(\lor\) |
| exclusive disjunction | either, or | binary | \(\oplus\) |
| conditional | if, then | binary | \(\implies\) |
| biconditional | if and only if, then | binary | \(\iff\) |
By type,
| Type | Connects |
|---|---|
| unary | one statement with itself |
| binary | two statements with each other |
By precedence, first to last,
| Precedence | Connective |
|---|---|
| 1 | negation |
| 2 | conjunction |
| 3 | disjunction |
| 4 | conditional |
| 5 | biconditional |
Parentheses bring the precedence to zero, like in arithmetic.
(Levin, 2021, sec. 0.2; Poole & Mackworth, 2017, sec. 5.1.1)