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.
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