Abstract
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.
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