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THE PROPOSITIONAL FORMULATION OF QUANTUM MECHANICS

We give a definition for the notion of statistics in the lattice-theoretical (or proposi-tional) formulation of quantum mechanics of Birchoff, von Neumann and Piron. We show that this formalism is compatible only with two types of statistics: Bose-Einstein and Fermi-Dirac. Some comments are made about the connection between this result and the existence of exotic statistics (para-statistics, infinite statistics, braid statistics). *