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.
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Operator Precedence ¬ 1 2 3 → 4 5
The order of precedence determines which connective is the "main connective" when interpreting a non-atomic formula.
Read more about this topic: Logical Connectives
Famous quotes containing the words order and/or precedence:
“Compassion has no place in the natural order of the world which operates on the basis of necessity. Compassion opposes this order and is therefore best thought of as being in some way supernatural.”
—John Berger (b. 1926)
“Let not England forget her precedence of teaching nations how to live.”
—John Milton (1608–1674)