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1. Two further postulates for a Boolean ring with a unit element. If addition, subtraction, and multiplication are properly defined in logic, it may be shown* that the postulates for these operations are identical with those in a ring, in which every element is idempotent, satisfying the postulate XX ~— X . Such a ring is called a Boolean ring. The postulates for a Boolean ring with a unit element are therefore the following :

Algebraic postulates and a geometric interpretation for the Lewis calculus of strict implication