Propositional Connectives

Definition: Negation

A negation in the formal language of propositional logic ${\mathcal{L}}_{\text{PL}}$ is an expression of the form $\neg F$, where $F$ is some expression.

Definition: Conjunction

A conjunction in the formal Language of propositional logic ${\mathcal{L}}_{\text{PL}}$ is an expression of the form $P\wedge Q$, where $P$ and $Q$ are some expressions.

Definition: Disjunction

A disjunction in the formal Language of propositional logic ${\mathcal{L}}_{\text{PL}}$ is an expression of the form $P\vee Q$, where $P$ and $Q$ are some expressions.

Definition: Conditional

A conditional in the formal language of propositional logic ${\mathcal{L}}_{\text{LP}}$ is an expression of the form $P\to Q$, where $P$ and $Q$ are some expressions.

NOTE

Conditionals are also known as material implications, material conditionals and logical conditionals.

Definition: Biconditional

A biconditional in the formal language of propositional logic ${\mathcal{L}}_{\text{LP}}$ is an expression of the form $P\leftrightarrow Q$, where $P$ and $Q$ are some expressions.

NOTE

Biconditionals are also known as material biconditionals, logical biconditionals, equivalences, biimplications and bientailments.