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 and/or precedence:
“The profoundest thoughts of the philosophers have something tricklike about them. A lot disappears in order for something to suddenly appear in the palm of the hand.”
—Elias Canetti (b. 1905)
“What is line? It is life. A line must live at each point along its course in such a way that the artist’s presence makes itself felt above that of the model.... With the writer, line takes precedence over form and content. It runs through the words he assembles. It strikes a continuous note unperceived by ear or eye. It is, in a way, the soul’s style, and if the line ceases to have a life of its own, if it only describes an arabesque, the soul is missing and the writing dies.”
—Jean Cocteau (1889–1963)