Definition:Main Connective

Definition

In a compound statement, exactly one of its logical connectives has the largest scope.

That connective is called the main connective.

The scope of the main connective comprises the entire compound statement.

Propositional Logic

Definition 1

Let $\mathbf C$ be a WFF of propositional logic.

Let $\circ$ be a binary connective.

Then $\circ$ is the main connective if and only if the scope of $\circ$ is $\mathbf C$.

Definition 2

Let $\mathbf C$ be a WFF of propositional logic such that:

$\mathbf C = \left({\mathbf A \circ \mathbf B}\right)$

where both $\mathbf A$ and $\mathbf B$ are both WFFs and $\circ$ is a binary connective.

Then $\circ$ is the main connective of $\mathbf C$.

Alternatively, let $\mathbf A$ be a WFF of propositional logic such that:

$\mathbf A = \neg \mathbf B$

where $\mathbf B$ is a WFF.

Then $\neg$ is the main connective of $\mathbf A$.

Definition 3

Let $T$ be a WFF of propositional logic in the labeled tree specification.

Suppose $T$ has more than one node.

Then the label of the root of $T$ is called the main connective of $T$.