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:
“If we are the younger, we may envy the older. If we are the older, we may feel that the younger is always being indulged. In other words, no matter what position we hold in family order of birth, we can prove beyond a doubt that we’re being gypped.”
—Judith Viorst (20th century)
“The world men inhabit ... is rather bleak. It is a world full of doubt and confusion, where vulnerability must be hidden, not shared; where competition, not co-operation, is the order of the day; where men sacrifice the possibility of knowing their own children and sharing in their upbringing, for the sake of a job they may have chosen by chance, which may not suit them and which in many cases dominates their lives to the exclusion of much else.”
—Anna Ford (b. 1943)
“It is difficult to separate the tapestry
From the room or loom which takes precedence over it.”
—John Ashbery (b. 1927)