Definition:Scope of Connective/Definition 1

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 $\LL_0$.

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 $\circ$.

where:

smallest means the well-formed part of $\mathbf W$ whose length is least

containing means such that it is a substring of $\mathbf W$.

Also see

• Definition:Main Connective

Sources

• 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