Titlebook: Quantum Logic; Peter Mittelstaedt Book 1978 D. Reidel Publishing Company, Dordrecht, Holland 1978 Interpretation.logic.proposition.quantum

箴言

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The Lattice of Effective Quantum Logic,bility and implicative sublattices and show that the lattice .. is a relaxation of the implicative lattice .. (Section 5.3). Finally, it will be shown that .. is also a relaxation of the orthocomplemented quasimodular lattice from which it differs by only the ‘tertium non datur’ law.

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Introduction,itions is established, which is slightly different from the calculus . of classical propositional logic but which is applicable to all quantum mechanical propositions (C.F. v. Weizs?cker, 1955). This calculus has sometimes been called ‘.’.

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Concluding Remarks: Classical Logic and Quantum Logic,ons. In particular, propositions about physical systems have this property to the extent that the system in question can be considered as a classical one. Consequently, from this point of view classical propositional logic turns out to be an idealisation, which has only approximate validity and, thus, no fundamental meaning.

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Book 1978at in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper- ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum

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0166-6991 statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are b978-94-009-9873-5978-94-009-9871-1Series ISSN 0166-6991 Series E-ISSN 2542-8292

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The Calculus of Full Quantum Logic,e availability propositions is re-established, it follows that the principle of excluded middle which is valid for elementary propositions, is, in fact, inherited by all finitely compound propositions. In this way, the calculus . of full quantum logic can be justified (Section 6.4).

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Book 1978to all quantum mechanical propositions (C. F. v. Weizsacker, 1955). This calculus has sometimes been called ‘quan- tum logic‘. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are b