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 Connective
Famous quotes containing the words order of, order and/or precedence:
“There is no permanent class of hired laborers amongst us. Twenty five years ago, I was a hired laborer. The hired laborer of yesterday, labors on his own account today; and will hire others to labor for him tomorrow. Advancement—improvement in condition—is the order of things in a society of equals.”
—Abraham Lincoln (1809–1865)
“Interpretation is the revenge of the intellect upon art. Even more. It is the revenge of the intellect upon the world. To interpret is to impoverish, to deplete the world—in order to set up a shadow world of “meanings.””
—Susan Sontag (b. 1933)
“Let not England forget her precedence of teaching nations how to live.”
—John Milton (1608–1674)