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.