# Definition:Binding Priority

## Definition

The **binding priority** is the convention defining the order of **binding strength** of the individual connectives in a logical formula.

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

### Binding Priority of Connectives of Propositional Logic

The binding priority convention which is almost universally used for the connectives of propositional logic is:

- $(1): \quad \neg$ binds more tightly than $\lor$ and $\land$
- $(2): \quad \lor$ and $\land$ bind more tightly than $\implies$ and $\impliedby$
- $(3): \quad \implies$ and $\impliedby$ bind 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.

Most sources do not recognise the use of $\impliedby$ as a separate connective from $\implies$, so the priority of one over the other is rarely a question.

## 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

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $1$ Formation Rules - 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.1$: Simple and Compound Statements - 1993: M. Ben-Ari:
*Mathematical Logic for Computer Science*... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.2$: Propositional formulas - 2000: Michael R.A. Huth and Mark D. Ryan:
*Logic in Computer Science: Modelling and reasoning about systems*... (previous) ... (next): $\S 1.1$: Declarative sentences - 2012: M. Ben-Ari:
*Mathematical Logic for Computer Science*(3rd ed.) ... (previous) ... (next): $\S 2.1.3$