engleski

Quantum and Classical Implication Algebras with Primitive Implications

Join in an orthomodular lattice is obtained in the same form for all five quantum implications. The form holds for the classical implication in a distributive lattice as well. Even more, the definition added to an ortholattice makes it orthomodular for quantum implications and distributive for the classical one. Based on this result a quantum implication algebra with a single primitive---and in this sense unique---implication is formulated. A corresponding classical implication algebra is also formulated. The algebras are shown to be special cases of a universal implication algebra.

implication algebra; orthomodular lattices; quantum logic; classical logic

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