Definition:Main Connective/Propositional Logic

Definition

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.

Also see

• Equivalence of Definitions of Main Connective
• Language of Propositional Logic has Unique Parsability

• Results about the main connective can be found here.