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Local hidden-variable model of singlet-state correlations discussed in M.Czachor, Arithmetic loophole in Bell's Theorem: Overlooked threat toentangled-state quantum cryptography, Acta Phys. Polon. A 139, 70-83 (2021), isshown to be a particular case of an infinite hierarchy of local hidden-variablemodels based on an infinite hierarchy of calculi. Violation of Bell-typeinequalities is shown to be a `confusion of languages' problem, a result ofmixing different but neighboring levels of the hierarchy. Mixing ofnon-neighboring levels results in violations beyond the Tsirelson bounds.

Imitating quantum probabilities: Beyond Bell's theorem and Tsirelson bounds