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:
“Out of the slimy mud of words, out of the sleet and hail of verbal imprecisions,
Approximate thoughts and feelings, words that have taken the place of thoughts and feelings,
There springs the perfect order of speech, and the beauty of incantation.”
—T.S. (Thomas Stearns)
“It is necessary, in order to know things well, to know the particulars of them; and these, being infinite, make our knowledge ever superficial and imperfect.”
—François, Duc De La Rochefoucauld (1613–1680)
“It is difficult to separate the tapestry
From the room or loom which takes precedence over it.”
—John Ashbery (b. 1927)