Definition:Scope (Logic)

Definition

The scope of a logical connective is defined as the statements that it connects, whether this be simple or compound.

In the case of a unary connective, there will be only one such statement.

Examples

• Let $\circ$ be a binary logical connective in a compound statement $p \circ q$.

The scope of $\circ$ is $p$ and $q$.

• Consider the statement:

$\left({p \land \left({q \lor r}\right)}\right) \implies \left({s \iff \neg \, t}\right)$

1. The scope of $\land$ is $p$ and $\left({q \lor r}\right)$.
2. The scope of $\lor$ is $q$ and $r$.
3. The scope of $\implies$ is $\left({p \land \left({q \lor r}\right)}\right)$ and $\left({s \iff \neg \, t}\right)$.
4. The scope of $\iff$ is $s$ and $\neg \, t$.
5. The scope of $\neg$ is $t$.

Also see

It can be seen that this definition is consistent with the definition of scope in propositional calculus.

Sources

• D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.5$