Definition:Scope of Connective/Definition 2
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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 $\LL_0$.
The scope of an occurrence of $\circ$ in $\mathbf W$ is defined as:
- the set of statements that it connects, whether simple or compound.
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The arity of $\circ$ determines the cardinality of this set.
In the case of a unary connective, there will be only one such statement.
Non-Equivalence of Definitions
Definition:Scope of Connective/Non-Equivalence
Also see