Definition:Binding Priority

Definition
The binding priority is the convention defining the order of binding strength of the individual connectives in a statement form.

Binding priorities can be overridden by using parenthesis in appropriate places. Parenthesis always takes priority over conventional binding priorities.

Logical Connectives
The convention which is almost universally used for the logical connectives of propositional calculus is:


 * $\neg$ binds more tightly than $\lor$ and $\land$
 * $\lor$ and $\land$ bind more tightly than $\implies$
 * $\implies$ binds more tightly than $\iff$

Note that there is no overall convention defining which of $\land$ and $\lor$ bears a higher binding priority, and therefore we consider them to have equal priority.

Because of this fact, unless specifically defined, expressions such as $p \land q \lor r$ can not be interpreted unambiguously, and parenthesis must be used to determine the exact priorities which are to be used to interpret particular statements which may otherwise be ambiguous.

Also known as

 * Precedence: a higher precedence is the same thing as a tighter binding priority.
 * Rank: a higher rank is the same thing as a tighter binding priority.

Also see

 * Parenthesis