An Operational Approach to Quantum Probability
In the two preceding papers ‘Completeness of Quantum Logic’ (CQL) and ‘Quantum Logical Calculi and Lattice Structures’ (QLC) an operational approach to formal quantum logic was developed. Beginning with a pragmatic definition of quantum mechanical propositions by means of material dialogs a formal dialog-game was introduced for establishing formally true propositions. It was shown in CQL that the formal dialog-game can be replaced by a calculus T eff of effective (intuitionistic) quantum logic which is complete and consistent with respect to the dialogic procedure. In QLC we showed that T eff is equivalent to a propositional calculus Q eff Since the calculus Q eff is a model for a certain lattice structure, called quasi-implicative lattice (L eff), the connection between quantum logic and the quantum theoretical formalism is provided. L qi is a weaker algebraic structure than the orthomodular lattice of the subspaces of a Hilbert space L q which can be interpreted as the pro-positional calculus of value-definite quantum logic. This establishes a quantum logical interpretation of L q.
KeywordsOperational Approach Final Position Quantum Logic Individual System Orthomodular Lattice
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