RIKEN team shows classical logic is 6:1 compression of quantum context

A new arXiv preprint from Haruki Emori, Atsushi Iriki, Andrei Khrennikov, and Kazunori Kondo (RIKEN) turns the usual understanding of quantum logic on its head. Traditionally, quantum logic is presented as a non-classical departure from ordinary Boolean reasoning forced by quantum mechanics. The authors argue the opposite: quantum logic – specifically a finite, fully computable orthomodular lattice – is the fundamental logic of contexts, and classical logic is merely a derived, information-losing projection. They analyze the free orthomodular lattice on two generators, which has exactly 96 elements. This lattice factorizes into a direct product of a six-element non-distributive orthomodular lattice (which registers contexts) and a sixteen-element Boolean algebra (which stores logical content). Each element is thus a context–bit-vector pair, with operations acting componentwise.

The paper establishes three main results. First, by classifying the six layers (elements of the context factor) according to commutativity, they identify a central, context-neutral kernel (propositions true in all contexts) and a dual central layer where all complementary contexts are present. Second, they show that orthocomplementation (the logical NOT operation) rearranges these layers exactly as complementation in the small six-element factor does, making the layer duality structurally rigid rather than accidental. Third, and most strikingly, they prove that the operation of forgetting the context (projecting out the context factor) is a surjective homomorphism of orthocomplemented lattices whose quotient is the classical Boolean algebra. In other words, classical logic is a six-to-one, information-losing image of the full contextual calculus. This reframes quantum logic not as an exotic deviation but as the basic fabric of reasoning, with classical logic as a coarse-grained approximation.