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:
“The universal principle of etymology in all languages: words are carried over from bodies and from the properties of bodies to express the things of the mind and spirit. The order of ideas must follow the order of things.”
—Giambattista Vico (16881744)
“In order to master the unruly torrent of life the learned man meditates, the poet quivers, and the political hero erects the fortress of his will.”
—José Ortega Y Gasset (18831955)
“Let not England forget her precedence of teaching nations how to live.”
—John Milton (16081674)