Theprinciple of distributivity states that the algebraicdistributive law isvalid, where bothlogical conjunction andlogical disjunction are distributive over each other so that for anypropositionsA,B andC theequivalences

${\displaystyle A\wedge (B\vee C)⟺(A\wedge B)\vee (A\wedge C)}$

and

${\displaystyle A\vee (B\wedge C)⟺(A\vee B)\wedge (A\vee C)}$

hold.

The principle of distributivity is valid inclassical logic, but both valid and invalid inquantum logic.

The article "Is Logic Empirical?" discusses the case that quantum logic is the correct, empirical logic, on the grounds that the principle of distributivity isinconsistent with a reasonableinterpretation of quantum phenomena.^[1]

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