Definition:Scope (Logic)
Definition
Let $\LL_0$ be the language of propositional logic.
Let $\circ$ be a connective of $\LL_0$.
Let $\mathbf W$ be a wellformed formula of $\LL_0$.
Connective of Propositional Logic
The scope of an occurrence of $\circ$ in $\mathbf W$ is defined as:
 the smallest wellformed part of $\mathbf W$ containing this occurrence of $\circ$.
Quantifier of Predicate Logic
Let $\mathbf A$ be a WFF of the language of predicate logic.
Let $Q$ be an occurrence of a quantifier in $\mathbf A$.
Let $\mathbf B$ be a wellformed part of $\mathbf A$ such that $\mathbf B$ begins (omitting outer parentheses) with $Q x$.
That is, such that $\mathbf B = \paren {Q x: \mathbf C}$ for some WFF $\mathbf C$.
$\mathbf B$ is called the scope of the quantifier $Q$.
Examples
Arbitrary Example $1$
Let $\circ$ be a binary logical connective in a compound statement $p \circ q$.
The scope of $\circ$ is $p$ and $q$.
Arbitrary Example $2$
Consider the statement:
 $\paren {p \land \paren {q \lor r} } \implies \paren {s \iff \neg \, t}$
We have:
 $(1): \quad$ The scope of $\land$ is $p$ and $\paren {q \lor r}$.
 $(2): \quad$ The scope of $\lor$ is $q$ and $r$.
 $(3): \quad$ The scope of $\implies$ is $\paren {p \land \paren {q \lor r} }$ and $\paren {s \iff \neg \, t}$.
 $(4): \quad$ The scope of $\iff$ is $s$ and $\neg \, t$.
 $(5): \quad$ The scope of $\neg$ is $t$.
Arbitrary Example $3$
Consider the statement:
 $\exists x: \paren {x < y} \lor y = 0$
We have:
 $(1): \quad$ The scope of $\exists$ is $x$.
 $(2): \quad$ The scope of $\exists x$ is $\exists x: \paren {x < y}$.
 $(3): \quad$ The scope of $=$ is $y$ and $0$.
 $(4): \quad$ The scope of $\lor$ is $\exists x: \paren {x < y}$ and $y = 0$.
Scope (Logic)/Connective


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 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 5$: Using Brackets
 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): scope