Abstract
In the empirical logic approach to quantum mechanics, the physical system under consideration is given in terms of a manual of sample spaces. The resulting propositional structure has been shown to form an orthoalgebra, generalizing the structure of an orthomodular poset. An orthoalgebra satisfies the unique Mackey decomposition (UMD) property if, given two commuting propositions a and b, there is a unique jointly orthogonal triple (e, f, c) such that a=e⊕c and b=f⊕c. In a manual, E is refined by F if E is logically equivalent to some partition of F, making results from F at least as informative as those from E. The main result is a characterization of the UMD property in terms of the refinement structure of an underlying manual, provided the manual is event saturated and orthogonally additive.
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Younce, M.B. Refinement and unique Mackey decomposition for manuals and orthalogebras. Found Phys 20, 691–700 (1990). https://doi.org/10.1007/BF01889455
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DOI: https://doi.org/10.1007/BF01889455