The principle of distributivity states that the algebraic distributive law is valid for classical logic, where both logical conjunction and logical disjunction are distributive over each other so that for any propositions A, B and C the equivalences
\( A\land (B\lor C)\iff (A\land B)\lor (A\land C) \)
and
\( A\lor (B\land C)\iff (A\lor B)\land (A\lor C) \)
hold.
The principle of distributivity is valid in classical logic, but invalid in quantum 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 is inconsistent with a reasonable interpretation of quantum phenomena.[1]
References
Putnam, H. (1969). "Is Logic Empirical?". Boston Studies in the Philosophy of Science. 5.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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