# Definition:Scope (Logic)/Connective

< Definition:Scope (Logic)(Redirected from Definition:Scope of Connective)

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## Definition

Let $\LL_0$ be the language of propositional logic.

Let $\circ$ be a connective of $\LL_0$.

Let $\mathbf W$ be a well-formed formula of $\LL_0$.

### Definition 1

The **scope** of an occurrence of $\circ$ in $\mathbf W$ is defined as:

- the smallest well-formed part of $\mathbf W$ containing this occurrence of $\circ$.

### Definition 2

The **scope** of an occurrence of $\circ$ in $\mathbf W$ is defined as:

- the set of statements that it connects, whether simple or compound.

### Non-Equivalence of Definitions

Definition:Scope of Connective/Non-Equivalence

## Also see

## Sources

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- 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 3.2$: Logical Punctuation and the Scope of Constants - 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $1$ Formation Rules