Lattice sieving

In modal logic, a regular modal logic L is a modal logic closed under the duality of the modal operators:

$◊A\equiv \mathrm{\neg }◻\mathrm{\neg }A$

and the rule

$(A\wedge B)\to C⊢(◻A\wedge ◻B)\to ◻C.$

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.

Template:Logic-stub