View source for Philosophy:Regular modal logic

In [[Modal logic|modal logic]], a '''regular modal logic''' is a modal logic containing (as axiom or theorem) the [[Duality (mathematics)|duality]] of the modal operators:
<math>\Diamond A \leftrightarrow \lnot\Box\lnot A</math>

and closed under the rule

<math>\frac{(A\land B)\to C}{(\Box A\land\Box B)\to\Box C}.</math>

Every [[Philosophy:Normal modal logic|normal modal logic]] is regular, and every regular modal logic is [[Philosophy:Classical modal logic|classical]].

== References ==
*Chellas, Brian. ''Modal Logic: An Introduction''. Cambridge University Press, 1980.

[[Category:Logic]]
[[Category:Modal logic]]



{{Sourceattribution|Regular modal logic}}