Logics for quantum mechanics

Foundations of Physics 3 (2):265-276 (1973)

The two concepts of probability used in physics are analyzed from the formal and the material points of view. The standard theory corresponds toprob 1 (probability of the coexistence of two properties). A general logicomathematical theory ofprob 2 (probability of transition between states) is presented in axiomatic form. The underlying state algebra is neither Boolean nor Birkhoff-von Neumann but partial Boolean. In the Boolean subalgebras,prob 1 theory holds. The theory presented contains the logicomathematical foundations of quantum mechanics and, as degenerate cases, the theories of stochastic games and of Markov chains
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DOI 10.1007/BF00708444
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