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:
 * $$\left({p \and \left({q \or r}\right)}\right) \implies \left({s \iff \neg \, t}\right)$$


 * 1) The scope of $$\and$$ is $$p$$ and $$\left({q \or r}\right)$$.
 * 2) The scope of $$\or$$ is $$q$$ and $$r$$.
 * 3) The scope of $$\implies$$ is $$\left({p \and \left({q \or r}\right)}\right)$$ 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.