Definition:Scope (Logic)/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