Idempotence (Propositional Logic)

Definition

Idempotence (Propositional Logic)

Idempotence is the property of the connectives $\vee$ and $\wedge$ that combining a formula with itself yields the formula itself:

$$P\vee P\equiv P,P\wedge P\equiv P.$$

For every interpretation $v$,

$$v(P\vee P)=v(P)=v(P\wedge P).$$

No information is gained by repeating an operand, because both connectives ignore multiplicity: only the truth value of $P$ matters.