# 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 $\mathbf C$.

Otherwise, 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 $T$.

## Also known as

The **main connective** is sometimes also called the **principal operator**.

## Sources

- 1980: D.J. O'Connor and Betty Powell:
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