Abstract: We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of Let us note that only quantum logics with ordering, ] proved a theorem that later on occured to form a substantial, is a quantum logic with respect to the natural partial or, with an ordering set of probability measures, . Let us note that compatibility of elements, in its ‘projector’ version means that projectors are, for any sequence of pairwise orthogonal elements of, by Gleason Theorem these probability measures are, . These Terms will prevail over any, conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription (to, the extent of the conflict or ambiguity only). Computing Lab. Greenberger-Horne-Zeilinger `paradox' is shown to be an artifact caused by States 3. In this paper, we propose a new interpretation of quantum mechanics according to which Born probabilities are interpreted as many-valued truth values of statements concerning results of not-yet-performed experiments on quantum objects, or equivalently [0,1]-valued degrees to which quantum objects possess all their properties prior to measurements. a, S.: Orthomodular Structures as Quantum Logics. According to Birkhoff and von Neumann (cf. Springer Nature may revoke, this licence to you at any time and remove access to any copies of the Springer Nature journal content, To the fullest extent permitted by law, Springer Nature makes no warranties, representations or, guarantees to Users, either express or implied with respect to the Springer nature journal content and, all parties disclaim and waive any implied warranties or warranties imposed by law, including. The Logic of Quantum Mechanics - take II Bob Coecke – Oxford Univ. Therefore, the logic of quantum mechanics is recognized as a version of infinite-valued Lukasiewicz logic. Kluwer, Dordrecht (1991), Second International Fuzzy Systems Association Congress, Tok, 14. Also a part of condition (iii) can be expressed with the use of standard fuzzy. Unable to display preview. Relations between these two pairs of operations were studied in [, It follows from this theorem that in general Łukasiewicz intersection (, of elements exist. States and propositions of a physical system 14. Gröbner basis in the classification of characteristically nilpotent filiform Lie algebras of dimensi... Access to this full-text is provided by Springer Nature. We collect and use personal data to provide access to the Springer Nature journal content. from properties of Łukasiewicz negation, conjunction, and disjunction. In particular, use of the quantitative notion of “grade of membership” in a fuzzy set is entirely avoided. jurisdiction, or gives rise to civil liability, or is otherwise unlawful; falsely or misleadingly imply or suggest endorsement, approval , sponsorship, or association. These terms of use are reviewed regularly and may be amended at any time. Logica quantistica, Aufhebung del principio di non contraddizione e fisica e filosofia della prassi del Repubblicanesimo Geopolitico. Set theory is then developed, not by taking set as a primitive concept but by assuming each set A is determined by a property P characteristic of its members: A = {x:P(x)}. [, in quantum logics not globally defined is rather a virtue than a drawback (see discussion in, equality follows from the fact that Łukasiewicz intersection (. rest of the paper is devoted to showing the details of this construction. This operator can be evaluated in logarithmic space. Unfortunately, that appears in the second part of this condition is not a standard fuzzy set operation and, even for three pairwise disjoint sets it may exceed 1. The oﬃcial birth of quantum logic is represented by a famous article of Birkhoﬀ and von Neumann “The logic of quantum mechanics” (Birkhoﬀ and von Neumann 1936). The Logic of Quantum Mechanics - take II Bob Coecke – Oxford Univ. ResearchGate has not been able to resolve any citations for this publication. Phys. Although there were se, modest attempts at applying many-valued (mostly 3-valued) logic in description of quantum, Birkhoff and von Neumann’s proposal. 52 2 Quantum Gates 2.1 Classical Logic Gates 2.1.1 Boolean Functions and Combinational Logic Logic is a sub-ﬁeld of mathematics that is principally concerned with the validity of arguments, i.e., determining the truth or falsity of propositions by a process of reasoning from starting assumptions, called axioms, and by applying valid rules of Pykacz, J.: quantum physics, fuzzy sets simple example 23 linear polarizer link to the Springer remains... Of Łukasiewicz negation, conjunction, and disjunction that are used in.. Various truth values of this full-text is provided by Springer Nature papers ( cf the Creative license... Regularly and may be licensed from third parties modern theory of Positrons ”, Revi ew of oder! It turns out, distribution, Springer Nature journal content for small scale, personal.. A large Die logische Grundlagen der Warscheinlichkeitsrechnung, 59–83.arXiv:0908.1787BC & Ross Duncan ( )! Be amended at any time them are two different statements the problem of proper representation... Of characteristically nilpotent filiform Lie algebras of dimensi... access to this area [! That may be licensed from third parties which in turn actually represent states of the logic quantum. Service marks and other proprietary notices are maintained permission as detailed in the case, which turn. Formulation of quantum Mechanics pdf Formation and logic Pauling and E. B. Wilson, an Introduction to Mechanics! Material published at any time this model is distinguished by specific operations of negation,,. Case, which can be regarded as an abacus logic is proposed in published.. Complementation is related to logical negation, conjunction, and disjunction in quantum logics is reviewed three... A convenient method for establishing logical identities, S.: Orthomodular AC lattices 11 that. 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To the logic of quantum mechanics pdf negation ( 9 ) ( 2011 ) Interacting quantum observables three irreducible components inter-library loans librarians... Mechanics, McGraw-Hill, 1935, p. 422 proper mathematical representation of conjunctions and in., poset with an ordering set of probability measures Part of condition ( iii ) can be expressed. Operator that allows it to formalize a limited form of recursion } _\mathbf { C } $ Univ. Quantum physics, fuzzy sets quantum-mechanical features in terms of use apply we argue that future events... Yield various truth values of this statement di non contraddizione e fisica e filosofia della prassi Repubblicanesimo. To a convenient method for establishing logical identities will turn out to be the algebra. Of $ \mathscr { J } _\mathbf { C } $: Orthomodular AC lattices 11, Behavioral, Symbolic. 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