modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...

, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators:

\Diamond A \leftrightarrow \lnot\Box\lnot A

and closed under the rule

\frac.

Every

normal modal logic In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains: * All propositional tautology (logic), tautologies; * All instances of the Kripke_semantics, Kripke schema: \Box(A\to B)\to(\Box A\to\Box B) and it is closed ...

is regular, and every regular modal logic is classical.

References

*Chellas, Brian. ''Modal Logic: An Introduction''. Cambridge University Press, 1980. Logic Modal logic {{logic-stub