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 of, order and/or precedence:
“It is with unfathomable love, pure joy and no regret that we leave this world. Men, do not cry for our fate, but cry for your own.”
—Members of the Order of the Solar T.. New York Times, p. 1 (October l4, 1994)
“What an infernal set of fools those schoolmarms must be! Well, if in order to please men they wish to live on air, let them. The sooner the present generation of women dies out, the better. We have idiots enough in the world now without such women propagating any more.”
—Elizabeth Cady Stanton (1815–1902)
“Let not England forget her precedence of teaching nations how to live.”
—John Milton (1608–1674)