How do necessity and possibility extend the scope of logic?

Necessity and possibility extend the scope of logic by enabling the formal study of modal logic, which incorporates concepts beyond the standard nonmodal systems of classical propositional calculus.12

By introducing primitive operators—such as L for "it is necessary that" and M for "it is possible that"—logicians can classify propositions based on their modal status:
* Necessary propositions: True by logical necessity (e.g., $2+2=4$).2
* Impossible propositions: False by logical necessity (e.g., $2+2=5$).2
* Contingent propositions: Neither necessary nor impossible; they are true or false depending on the circumstances.2

This framework allows for the analysis of strict implication, where one proposition necessitates another, and provides a foundation for possible-worlds semantics. These developments have expanded logic into diverse fields, including epistemic logic (the study of knowledge and belief) and deontic logic (the study of obligation and permission), allowing for the rigorous examination of philosophically central concepts that exhibit similar logical behavior.345