Abstract
These axioms reflect some important properties of implication in Boolean algebras. He further showed that there is a natural bijective correspondence between these groupoids and join semilattices with one every principal filter of which is a Boolean algebra. Abbott (1976) and Chajda, Halas, and Langer (2001) generalized these ideas and results from Boolean algebras to orthomodular lattices. Abbott (1976) defined orthoimplication algebras as groupoids (A, ·) satisfying (OI1) (xy)x = x , (OI2) (xy)y = (yx)x , and (OI3) x((yx)z) = xz.
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