Definition:Binding Priority
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Definition
The binding priority is the convention defining the order of binding strength of the individual connectives in a compound logical or mathematical statement.
Binding priorities can be overridden by inserting parentheses in appropriate places. Parentheses always take priority over conventional binding priorities.
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.
Logical Connectives
The convention which is almost universally used 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 are going to assume they have equal priority.
Because of this fact, unless specifically defined, expressions such as $p \land q \lor r$ can not be interpreted unambiguously, and we brackets must be used to determine the exact priorities which are to be used to interpret particular statements which may otherwise be ambiguous, and therefore ill-formed.
Sources
- E.J. Lemmon: Beginning Logic (1965): $\S 2.1$
- Michael R.A. Huth and Mark D. Ryan: Logic in Computer Science: Modelling and reasoning about systems (2000): $\S 1.1$: Convention $1.3$
