Quantum Logic and Probability Theory

[Revised entry by Alexander Wilce on January 26, 2017. Changes to: Main text, Bibliography, notes.html, supplement.html] Mathematically, quantum mechanics can be regarded as a non-classical
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[Revised entry by Alexander Wilce on January 26, 2017. Changes to: Main text, Bibliography, notes.html, supplement.html] Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. More specifically, in quantum mechanics each probability-bearing proposition of the form "the value of physical quantity (A) lies in the range (B)" is represented by a projection operator on a Hilbert space (mathbf{H}). These form a non-Boolean - in particular, non-distributive - orthocomplemented lattice. Quantum-mechanical states correspond exactly to probability measures...

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News source: Stanford Encyclopedia of Philosophy

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