Completeness of quantum logic

Journal of Philosophical Logic 5 (2):237 - 280 (1976)
This paper is based on a semantic foundation of quantum logic which makes use of dialog-games. In the first part of the paper the dialogic method is introduced and under the conditions of quantum mechanical measurements the rules of a dialog-game about quantum mechanical propositions are established. In the second part of the paper the quantum mechanical dialog-game is replaced by a calculus of quantum logic. As the main part of the paper we show that the calculus of quantum logic is complete and consistent with respect to the dialogic semantics. Since the dialoggame does not involve the 'excluded middle' the calculus represents a calculus of effective (intuitionistic) quantum logic. In a forthcoming paper it is shown that this calculus is equivalent to a calculus of sequents and more interestingly to a calculus of propositions. With the addition of the 'excluded middle' the latter calculus is a model for the lattice of subspaces of a Hilbert space
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DOI 10.1007/BF00248731
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Matrix-Based Logic for Application in Physics.Paul Weingartner - 2009 - Review of Symbolic Logic 2 (1):132-163.
Are the Laws of Quantum Logic Laws of Nature?Peter Mittelstaedt - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (2):215-222.
How Does Quantum Logic Correspond to Physical Reality?Ernst-Walther Stachow - 1977 - Journal of Philosophical Logic 6 (1):485 - 496.

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