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.
Read more about this topic: Logical Connectives
Famous quotes containing the words order and/or precedence:
“When we walk the streets at night in safety, it does not strike us that this might be otherwise. This habit of feeling safe has become second nature, and we do not reflect on just how this is due solely to the working of special institutions. Commonplace thinking often has the impression that force holds the state together, but in fact its only bond is the fundamental sense of order which everybody possesses.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Let not England forget her precedence of teaching nations how to live.”
—John Milton (1608–1674)