Philosophy:Regular modal logic

From HandWiki

In modal logic, a regular modal logic is a modal logic closed under the duality of the modal operators: [math]\displaystyle{ \Diamond A \equiv \lnot\Box\lnot A }[/math]

and the rule

[math]\displaystyle{ (A\land B)\to C \vdash (\Box A\land\Box B)\to\Box C. }[/math]

Every regular modal logic is classical, and every normal modal logic is regular and hence classical.

References

  • Chellas, Brian. Modal Logic: An Introduction. Cambridge University Press, 1980.