Journal of Philosophical Logic 5 (2):237 - 280 (1976)
AbstractThis 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
Similar books and articles
Combining Derivations and Refutations for Cut-Free Completeness in Bi-Intuitionistic Logic.Linda Postniece - unknown
The Principle of Excluded Middle in Quantum Logic.P. Mittelstaedt & E. -W. Stachow - 1978 - Journal of Philosophical Logic 7 (1):181 - 208.
A Model Theoretic Semantics for Quantum Logic.E. -W. Stachow - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:272 - 280.
Quantum Logic and the Classical Propositional Calculus.Othman Qasim Malhas - 1987 - Journal of Symbolic Logic 52 (3):834-841.
Three-Valued Logic, Indeterminacy and Quantum Mechanics.Tomasz Bigaj - 2001 - Journal of Philosophical Logic 30 (2):97-119.
Abacus Logic: The Lattice of Quantum Propositions as the Poset of a Theory.Othman Qasim Malhas - 1994 - Journal of Symbolic Logic 59 (2):501-515.
Added to PP
Historical graph of downloads
Citations of this work
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.
Perhaps (?), New logical foundations are needed for quantum mechanics.J. Almog - 1978 - Logique Et Analyse 21 (82):251.
Reviews. [REVIEW]Peter Gibbins - 1982 - British Journal for the Philosophy of Science 33 (2):209-217.
References found in this work
No references found.