## A new postulational foundation of quantum mechanics |

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algebraic analogue arbitrary property symbol argument associated property symbols assume atomic systems axiom of modularity basic bility Boolean algebra classical and quantum compatible properties complete orthogonal set complex number consequence define demonstrate denote dimensional discussion equals relation experimental propositions experimentally testable false formal Foundations of Quantum further given physical greatest lower bound Hence Hilbert space ideal measurement postulate immediately Implies p(M indecomposable property symbols introduce lattice theory least upper bound linear sub-space M-determination ment mutually orthogonal property N-measurement nature Neumann and Birkhoff obtained operation orthogonal complement orthogonal property symbols Pa(M partially ordered set perty symbols physical system possible measurement results probabilistic probability amplitudes Proof property symbol associated propositional calculus quantum mechanical alternation quantum mechanical conjunction quantum mechanical negation quantum mechanically implies quantum physics real numbers refer remark satisfy set of numbers set of property statement structure sub-spaces of Hilbert suppose theorem tion uniquely determined usual validity viewpoint