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.
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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:
“All the sciences are now under an obligation to prepare for the future task of philosopher, which is to solve the problem of value, to determine the rank order of values.”
—Friedrich Nietzsche (1844–1900)
“Therefore doth heaven divide
The state of man in divers functions,
Setting endeavor in continual motion,
To which is fixed, as an aim or butt,
Obedience; for so work the honeybees,
Creatures that by a rule in nature teach
The act of order to a peopled kingdom.”
—William Shakespeare (1564–1616)
“It is difficult to separate the tapestry
From the room or loom which takes precedence over it.”
—John Ashbery (b. 1927)