scholarly journals Quantum-Inspired Uncertainty Quantification

2022 ◽  
Vol 3 ◽  
Author(s):  
Günther Wirsching
Keyword(s):  
Uncertainty Quantification ◽  
Quantum Logic ◽  
Similarity Measure ◽  
Classical Logic ◽  
Quantum Physics ◽  
Axiomatic Approach ◽  
Axiomatic Method ◽  
Successful Communication ◽  
Incoming Signal

Reasonable quantification of uncertainty is a major issue of cognitive infocommunications, and logic is a backbone for successful communication. Here, an axiomatic approach to quantum logic, which highlights similarity to and differences to classical logic, is presented. The axiomatic method ensures that applications are not restricted to quantum physics. Based on this, algorithms are developed that assign to an incoming signal a similarity measure to a pattern generated by a set of training signals.

The Use of the Axiomatic Method in Quantum Physics

1971 ◽  
Vol 38 (3) ◽  
pp. 429-437 ◽  
Author(s):  
Yvon Gauthier
Keyword(s):  
Quantum Physics ◽  
Axiomatic Method

scholarly journals Classical Logic and Quantum Logic with Multiple and Common Lattice Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Mladen Pavičić
Keyword(s):  
Quantum Logic ◽  
Classical Logic ◽  
Orthomodular Lattice ◽  
Lattice Models ◽  
Quantum Space ◽  
Technical Terms

We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical logic which turns out to have disjoint distributive and nondistributive ortholattices. In particular, we prove that both classical logic and quantum logic are sound and complete with respect to each of these lattices. We also show that there is one common nonorthomodular lattice that is a model of both quantum and classical logic. In technical terms, that enables us to run the same classical logic on both a digital (standard, two-subset, 0-1-bit) computer and a nondigital (say, a six-subset) computer (with appropriate chips and circuits). With quantum logic, the same six-element common lattice can serve us as a benchmark for an efficient evaluation of equations of bigger lattice models or theorems of the logic.

scholarly journals Classical Logic in the Quantum Context

2020 ◽  
Vol 2 (4) ◽  
pp. 600-616
Author(s):  
Andrea Oldofredi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Logic ◽  
Classical Logic ◽  
Theory Of Measurement ◽  
Propositional Calculus ◽  
Bohmian Mechanics ◽  
Physical Content ◽  
Present Essay ◽  
Classical Propositional Calculus

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.

scholarly journals Ensembles and Experiments in Classical and Quantum Physics

2003 ◽  
Vol 17 (16) ◽  
pp. 2937-2980
Author(s):  
Arnold Neumaier
Keyword(s):  
Quantum Mechanics ◽  
Quantum Physics ◽  
Law Of Large Numbers ◽  
Correspondence Principle ◽  
Axiomatic Approach ◽  
Mathematical Concepts ◽  
Large Numbers ◽  
The Universe ◽  
Classical And Quantum Mechanics ◽  
Elegant Solution

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization. Extending the ''probability via expectation'' approach of Whittle to noncommuting quantities, this paper defines quantities, ensembles, and experiments as mathematical concepts and shows how to model complementarity, uncertainty, probability, nonlocality and dynamics in these terms. The approach carries no connotation of unlimited repeatability; hence it can be applied to unique systems such as the universe. Consistent experiments provide an elegant solution to the reality problem, confirming the insistence of the orthodox Copenhagen interpretation on that there is nothing but ensembles, while avoiding its elusive reality picture. The weak law of large numbers explains the emergence of classical properties for macroscopic systems.

MATRIX-BASED LOGIC FOR APPLICATION IN PHYSICS

2009 ◽  
Vol 2 (1) ◽  
pp. 132-163 ◽  
Author(s):  
PAUL WEINGARTNER
Keyword(s):  
Classical Logic ◽  
Quantum Physics ◽  
Finite Model ◽  
Model Property ◽  
Bell’S Inequalities ◽  
Finite Model Property ◽  
Matrix Calculus ◽  
Bell's Inequalities ◽  
Matrix Quantum

The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense “irrelevant” from those which are “relevant” or “nonredundant” in the sense of allowing only the most informative consequences in the derivations. The latter derivations are strictly valid inRMQ, whereas the former are only materially valid.RMQis a decidable matrix calculus which possesses a semantics and has the finite model property. It is shown in the paper howRMQby its strictly valid derivations can avoid the difficulties with commensurability, distributivity, and Bell's inequalities when it is applied to quantum physics.

scholarly journals Fuzzy Axiomatic Approach to Blue-green Infrastructure Strategy Selection: A Sustainability Perspective

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Desmond Ighravwe ◽  
Daniel Mashao
Keyword(s):  
Green Infrastructure ◽  
Flood Management ◽  
Axiomatic Approach ◽  
Green Technology ◽  
Technology Selection ◽  
Axiomatic Method ◽  
Data Sets ◽  
Green Technologies ◽  
Sustainable Solutions ◽  
Aid Decision

Flood management is a global problem that has created immense contributions from researchers and practitioners, especially those in developing countries. These people often seek ways to minimise the aftermath of a flood. Recently, they are making a case for sustainable solutions to flood management. This study, therefore, contributes a sustainability model that addresses the problem of blue-green technology selection to the current discussion on flood management. It coupled the techno-economic, social, and environmental impact of a blue-green technology using the unique attributions of three multi-criteria decision-making tools: best-worst method, fuzzy axiomatic method and VIKOR; its performance was investigated with qualitative data sets that were obtained from experts. The outcomes of the investigation showed that techno-economic criteria contributed about 88.18% to the ranking of blue-green technology. The most and least suitable blue-green technologies for a community in Nigeria are Rainwater and floodwater harvesting and Retention lake, respectively. With these results, the proposed model will aid decision-makers strategic and tactical criteria that can be used to evaluate blue-green technology selection.

scholarly journals Logical Paradoxes in Non-Classical Logic Systems

2021 ◽  
Author(s):  
Serge Dolgikh
Keyword(s):  
Quantum Logic ◽  
Classical Logic ◽  
Logic Systems ◽  
Logical Paradoxes

It is shown that well-known logical paradoxes such as Barber paradox can be interpreted differently in non-classical logic systems such as multi-valued, continuous and quantum logic with possibility of solutions of the paradox. The results of this research can have applications in investigations of completeness of logic systems.

scholarly journals An Application of Quantum Logic to Experimental Behavioral Science

2021 ◽  
Vol 3 (4) ◽  
pp. 643-655
Author(s):  
Louis Narens
Keyword(s):  
Hilbert Space ◽  
Quantum Logic ◽  
Additive Function ◽  
Quantum Physics ◽  
Behavioral Science ◽  
Slight Modification ◽  
Quantum Probability ◽  
Rational Approach ◽  
Dutch Book Argument ◽  
Von Neumann

In 1933, Kolmogorov synthesized the basic concepts of probability that were in general use at the time into concepts and deductions from a simple set of axioms that said probability was a σ-additive function from a boolean algebra of events into [0, 1]. In 1932, von Neumann realized that the use of probability in quantum mechanics required a different concept that he formulated as a σ-additive function from the closed subspaces of a Hilbert space onto [0,1]. In 1935, Birkhoff & von Neumann replaced Hilbert space with an algebraic generalization. Today, a slight modification of the Birkhoff-von Neumann generalization is called “quantum logic”. A central problem in the philosophy of probability is the justification of the definition of probability used in a given application. This is usually done by arguing for the rationality of that approach to the situation under consideration. A version of the Dutch book argument given by de Finetti in 1972 is often used to justify the Kolmogorov theory, especially in scientific applications. As von Neumann in 1955 noted, and his criticisms still hold, there is no acceptable foundation for quantum logic. While it is not argued here that a rational approach has been carried out for quantum physics, it is argued that (1) for many important situations found in behavioral science that quantum probability theory is a reasonable choice, and (2) that it has an arguably rational foundation to certain areas of behavioral science, for example, the behavioral paradigm of Between Subjects experiments.

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