The principle of distributivity states that the algebraic distributive law is valid

Validity

In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....

 for classical logic

Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...

, where both logical conjunction

Logical conjunction

In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....

 and logical disjunction

Logical disjunction

In logic and mathematics, a two-place logical connective or, is a logical disjunction, also known as inclusive disjunction or alternation, that results in true whenever one or more of its operands are true. E.g. in this context, "A or B" is true if A is true, or if B is true, or if both A and B are...

 are distributive over each other so that for any proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

s A, B and C the equivalence

Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...

s
and
hold.

The principle of distributivity is valid in classical logic

Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...

, but invalid in quantum logic

Quantum logic

In quantum mechanics, quantum logic is a set of rules for reasoning about propositions which takes the principles of quantum theory into account...

. The article Is logic empirical?

Is logic empirical?

"Is logic empirical?" is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic...

discusses the case that quantum logic is the correct, empirical logic, on the grounds that the principle of distributivity is inconsistent

Consistency

Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...

 with a reasonable interpretation of quantum phenomena

Interpretation of quantum mechanics

An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...

.