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1
Content available remote From quantum logic to quantum computational logic
100%
Caponigro M. , Mancini S.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2006
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tom Vol. 10, No 1
5-19
EN
We overview the main concepts of quantum logic ranging from the orthodox formulation to the quantum computational aspects.
2
Content available remote Neurčité situace a logika
80%
Dvořák P.
Filosofický časopis (Philosophical Journal)
|
2015
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tom 63
|
nr 3, Special No: Sedmkrát z logiky a metodologie vědy
9-38
EN
The article surveys and evaluates various approaches to the logic of indeterminate situations. Two types of such situations are discussed: future contingents and quantum indeterminacy. Approaches differ according to whether they can salvage (i) classical tautologies (such as the law of excluded middle) as logical truths, (ii) bivalence and (iii) truth-functionality. What I call “the first solution” denies bivalence and either saves classical logical truths (supervaluations) or truth-functionality (multi-valued approach), but not both. The so-called “second solution”, saving all aforementioned features, harbors difficulties for the contingency of future contingents and is inapplicable in the quantum realm. Finally, the third solution saves bivalence but, at least in the case of quantum logic, abandons truth-functionality.
3
Content available Ring-like structures with unique symmetric difference related to quantum logic
80%
Dorninger D. , Länger H. , Maczyński M.
Discussiones Mathematicae - General Algebra and Applications
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2001
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tom 21
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nr 2
239-253
EN
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
4
Content available No-signaling in topos formulation and a common ontological basis for classical and non-classical physical theories
80%
Kuś M.
Zagadnienia Filozoficzne w Nauce
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2020
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nr 69
129-143
EN
Starting from logical structures of classical and quantum mechanics we reconstruct the logic of so-called no-signaling theories, where the correlations among subsystems of a composite system are restricted only by a simplest form of causality forbidding an instantaneous communication. Although such theories are, as it seems, irrelevant for the description of physical reality, they are helpful in understanding the relevance of quantum mechanics. The logical structure of each theory has an epistemological flavor, as it is based on analysis of possible results of experiments. In this note we emphasize that not only logical structures of classical, quantum and no-signaling theory may be treated on the same ground but it is also possible to give to all of them a common ontological basis by constructing a “phase space” in all cases. In non-classical cases the phase space is not a set, as in classical theory, but a more general object obtained by means of category theory, but conceptually it plays the same role as the phase space in classical physics.
5
Content available remote The Vitali-Hahn-Saks theorem for the product of quantum logics
80%
De Simone A. , Navara M. , Pták P.
Demonstratio Mathematica
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2002
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tom Vol. 35, nr 4
717-725
EN
We show as a main result that if each quantum logic of a given collection of quantum logics satisfies the Vitali-Hahn-Saks theorem, then so does their product. As a consequence we formulate a dual result for the sum of a collection of Dynkin systems.
6
Content available remote Synthesis of Transition Systems from Quantum Logics
70%
Bernardinello L. , Ferigato C. , Pomello L. , Puerto Aubel A.
Fundamenta Informaticae
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2017
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tom Vol. 154, nr 1/4
25--36
EN
The set of elementary regions of a transition system, ordered by set inclusion, forms an orthomodular poset, also referred to as quantum logic, which is regular and rich. Starting from an abstract regular and rich quantum logic, one can construct an elementary transition system such that the orginal logic embeds into its set of regions, and which is saturated of transitions. We study the problem of selecting subsets of transitions on the same set of states, which generate the same set of regions.
7
Content available Labeled Sequent Calculus for Orthologic
70%
Kawano T.
Bulletin of the Section of Logic
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2018
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tom 47
|
nr 4
EN
Orthologic (OL) is non-classical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic. Sequent calculus is used as a tool for proof in logic and has been examinedfor several decades. Although there are many studies on sequent calculus forOL, these sequent calculi have some problems. In particular, they do not includeimplication connective and they are mostly incompatible with the cut-eliminationtheorem. In this paper, we introduce new labeled sequent calculus called LGOI, and show that this sequent calculus solve the above problems. It is alreadyknown that OL is decidable. We prove that decidability is preserved when theimplication connective is added to OL.
8
Content available Is Schrödinger's cat dead oa alive?
70%
Grygiel W.
Zagadnienia Filozoficzne w Nauce
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2005
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nr 37
119-139
PL
The Schrödinger's Cat paradox was proposed in 1935 by Edwin Schrodinger, one of the founders of quantum mechanics, as an attempt to visualize the macroscopic realization of a quantum superposition state. A cat is placed in a sealed box together with a vial of poison. A two-state particle (e.g. an electron) is sent into a detector in the box resulting either in a broken or an intact vial and a dead or live cat, respectively. The main problem consists in whether the superposition state of a microscopic particle can be transferred upon the macroscopic cat, that is, whether the cat can exist in a superposition state, being simultaneously dead and alive. Since the standard Copenhagen interpretation is unable to assign any reality to the quantum superposition state, the paradox finds no resolution within the regime of this interpretation. Von Neumann's insistence on the uniform treatment of both microscopic (quantum) and macroscopic (classical) objects according to the laws of quantum mechanics provides a more consistent framework for the resolution of the paradox. In particular, the discovery of the phenomenon of decoherence, whereby the disappearance of the quantum interferences at the macro level is accounted for, suggests the onset of an extremely efficient interference relaxation process (10-23 s) upon the interaction of the two state particle with the detector. As a result, Schrodinger's cat can exist macroscopically either as dead or alive and never as a combination of both. Decoherence not only aids the resolution of the Schrodinger's Cat paradox but also sheds light upon the mechanisms by which the macro-world emerges from the microscopic quantum realm.
9
Content available Probability measures and logical connectives on quantum logics
70%
Nánásiová O. , Valášková Ľ. , Čerňanová V.
Journal of Automation Mobile Robotics and Intelligent Systems
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2019
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tom Vol. 13, No. 3
64--73
EN
The present paper is devoted to modelling of a probabi‐ lity measure of logical connectives on a quantum logic via a G‐map, which is a special map on it. We follow the work in which the probability of logical conjunction (AND), dis‐ junction (OR), symmetric difference (XOR) and their nega‐ tions for non‐compatible propositions are studied. Now we study all remaining cases of G‐maps on quantum lo‐ gic, namely a probability measure of projections, of impli‐ cations, and of their negations. We show that unlike clas‐ sical (Boolean) logic, probability measures of projections on a quantum logic are not necessarilly pure projections. We indicate how it is possible to define a probability me‐ asure of implication using a G‐map in the quantum logic, and then we study some properties of this measure which are different from a measure of implication in a Boolean algebra. Finally, we compare the properties of a G‐map with the properties of a probability measure related to logical connectives on a Boolean algebra.
10
Content available Some distributivities in GBbi-QRs characterizing Boolean rings
60%
Kaleta J.
Discussiones Mathematicae - General Algebra and Applications
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2004
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tom 24
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nr 1
115-124
EN
This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.
11
Content available Logika podejmowania decyzji (podejmowanie decyzji w aspekcie klasycznej i kwantowej logiki)
60%
Kałuski J.
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska
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2012
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tom z. 61
191--219
PL
W pracy obszernie omówiono stosowanie logiki kwantowej do podejmowania decyzji na tle logiki klasycznej w szerokim zakresie teoretycznym i praktycznym. Wychodząc od samych początków teorii kwantowej, a więc od eksperymentu myślowego EPR, prac Heisenberga, Bohra, Borna, Schroedingera, von Neumanna, Paulli’ego i innych znakomitych teoretyków fizyki kwantowej lat 20 i 30 ubiegłego stulecia, aż do słynnego twierdzenia J. Bella (1964) i jego nierówności i kończąc eksperymentami A. Aspecta i A. Zeillingera, pokazano skomplikowaną drogę rozwoju logiki kwantowej w podejmowaniu decyzji w naukach kognitywnych, ekonomii i technice. Równolegle analizowano pojęcia logiki klasycznej i kwantowej w aspekcie filozoficznym, począwszy od I. Kanta i jego logiki formalnej, poprzez logikę Łukasiewicza – Tarskiego, kosmologię Jacyny – Onyszkiewicza, aż po filozofię buddyzmu oraz różnych, współczesnych nurtów myślenia „kwantowego”. Do podejmowania decyzji w konkretnych sytuacjach służą modele na bazie kwantowej teorii informacji, kwantowego prawdopodobieństwa a przede wszystkim kwantowej teorii gier. Na przykładach szczegółowych obliczeń prawdopodobieństw kwantowych i budowy strategii kwantowych na użytek gier zobrazowano proces postępowania, który zasadniczo różni się od modelu klasycznego.
EN
In the work some problems of quantum decision making with comparing to the classical logic are presented. Based to Bell’s theorem (1964) and many works of famous physicians as Einstein, Bohr, Heisenberg, Born, Schroedinger, von Neumann and others which hold fast to the concept of new logic, the hard way of development of quantum logic in decision making is discussed. Simultaneously in the paper the I. Kant’s formal logic, Łukasiewicz-Tarski’s truth theory and logic across the Jacyna-Onyszkiewicz’s cosmological theory and Buddism’s philosophy are presented. To decision making in the concrete situations some models of quantum information theory, quantum probability and first of all quantum game are used. On the number of examples according to detailed computing of the quantum probability and construction of the quantum strategies in the games, the methods of calculating are showed. In all mentioned discussion shows that these methods are different from classical methods.
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