Logical Connectives - Order of Precedence

Order of Precedence

As a way of reducing the number of necessary parentheses, one may introduce precedence rules: ¬ has higher precedence than, higher than, and higher than →. So for example, P Q ¬R → S is short for (P (Q (¬R))) → S.

Here is a table that shows a commonly used precedence of logical operators.

Operator	Precedence
¬	1
	2
	3
→	4
	5

The order of precedence determines which connective is the "main connective" when interpreting a non-atomic formula.