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Journal of Bijie University

Probing into the Relating Problems between Restriction Logic and Computer Science

Xueming Wang

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Restriction logic,a rising field,is closely related to computer development.This mainly reflects in two aspects of connotation intelligence computer and quantum computer.The orthodox mathematical logic is not suitable for the need of intelligence computer and quantum computer,but restriction logic supplies it with a new theoretical foundation.

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§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff and von Neumann introduced quantum logic in a seminal paper in 1936 [1]. But the definition of quantum logic varies among authors (see [2]). How to capture the logic structure inherent in quantum mechanics is very interesting and challenging. Given the close connection between classical logic and theoretical computer science as exemplified by the coincidence of computable functions through Turing machines, recursive function theory, and λ-calculus, we are interested in how to gain some insights about quantum logic from quantum computing. In this note we make some observations about quantum logic as motivated by quantum computing (see [5]) and hope more people will explore this connection. The quantum logic as envisioned by Birkhoff and von Neumann is based on the lattice of closed subspaces of a Hilbert space, usually an infinite dimensional one. The quantum logic of a fixed Hilbert space ℍ in this note is the variety of all the true equations with finitely many variables using the connectives meet, join and negation. Quantum computing is theoretically based on quantum systems with finite dimensional Hilbert spaces, especially the states space of a qubit ℂ2. (Actually the qubit is merely a convenience.

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Keynotes and Industrial Talks

In this talk, we examine potential developments in the field of computing.Recall that Computer Science is defined as the science of algorithms.The development of Computer Science and its applications have relied on two cornerstones: Mathematical logic and semiconductor technology.Computing, i.e., execution of an algorithm, is a process of evaluating a logical expression.Thanks to semiconductor technology, logical operations can be implemented in a substantial manner with high density, high reliability, and low cost.Based on these two cornerstones, the complexity theory has been the major theoretical development of Computer Science.According to this theory, computing problems can be classified as "easy" and "hard".Easy ones are those in which the computation time is bounded by a polynomial of input size.Most computing applications today are in this category.In the future, we must focus on hard problems.One approach is to use nonsemiconductor-based physical devices; initial work in quantum computers would fall within this category.Another approach is to develop heuristic algorithms with much lower complexity; this is very much an objective of "Artificial Intelligence" development.The third approach is to leverage properties inherently embedded in input data, which calls for the development of Data Science.

IEEE International Conference on Networking, Architecture and Storage (NAS)•Oct 1, 2022•0 citations
Restriction logic,a rising field,is closely related to computer development.This mainly reflects in two aspects of connotation intelligence computer and quantum computer.The orthodox mathematical logic is not suitable for the need of intelligence computer and quantum computer,but restriction logic supplies it with a new theoretical foundation.
The emergence of quantum information and quantum computing is the inevitable choice in the development of information science. Introduces the historical development of quantum logic,research and the theoretical foundation of quantum logic related to orthomodular lattice on the basis of the closed subspace of Hilbert space and several open issues. Based on the above content,introduces the enormous computing power source of quantum computing and looks forward to the possibility of a quantum logic research.
§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff and von Neumann introduced quantum logic in a seminal paper in 1936 [1]. But the definition of quantum logic varies among authors (see [2]). How to capture the logic structure inherent in quantum mechanics is very interesting and challenging. Given the close connection between classical logic and theoretical computer science as exemplified by the coincidence of computable functions through Turing machines, recursive function theory, and λ-calculus, we are interested in how to gain some insights about quantum logic from quantum computing. In this note we make some observations about quantum logic as motivated by quantum computing (see [5]) and hope more people will explore this connection. The quantum logic as envisioned by Birkhoff and von Neumann is based on the lattice of closed subspaces of a Hilbert space, usually an infinite dimensional one. The quantum logic of a fixed Hilbert space ℍ in this note is the variety of all the true equations with finitely many variables using the connectives meet, join and negation. Quantum computing is theoretically based on quantum systems with finite dimensional Hilbert spaces, especially the states space of a qubit ℂ2. (Actually the qubit is merely a convenience.
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a mathematical universe different from that represented by set theory, we show that more thought and a better appreciation of the assumptions going into any mathematical model of the physical world are needed. We reflect on some of the mathematical consequences of this wider perspective of physics, explaining one interpretation of probabilistic values and numerical calculations in two mathematical universes governed by the less restrictive intuitionistic logic, and known to support the theory of synthetic differential geometry.
The quantum computer, is a "supercomputer" that relies on the phenomena of quantum mechanics to perform operations on data. Object of suppositions, sometimes farfetched, quantum mechanics gave birth to the quantum computer, a machine capable of processing data tens of millions of times faster than a conventional computer. A quantum computer doesn't use the same memory as a conventional computer. Rather than a sequence of 0 and 1, it works with qubits or quantum bits. The quantum computer is a combination of two major scientific fields: quantum mechanics and computer science. Quantum mechanics, on which this computer is based, governs the movement of bodies in the atomic, molecular and corpuscular domains, is a theory whose logic is totally contrary to intuition and it is essential to use mathematics to fully grasp it. Quantum computing is the sub-domain of computer science that deals with quantum computers using quantum mechanical phenomena, as opposed to those of electricity exclusively, for so-called "classical" computing. The quantum phenomena used are quantum entanglement and superposition. The article examines some aspects related to the development, operation, advantages and difficulties, applications and future of the quantum computer.
In this talk, we examine potential developments in the field of computing.Recall that Computer Science is defined as the science of algorithms.The development of Computer Science and its applications have relied on two cornerstones: Mathematical logic and semiconductor technology.Computing, i.e., execution of an algorithm, is a process of evaluating a logical expression.Thanks to semiconductor technology, logical operations can be implemented in a substantial manner with high density, high reliability, and low cost.Based on these two cornerstones, the complexity theory has been the major theoretical development of Computer Science.According to this theory, computing problems can be classified as "easy" and "hard".Easy ones are those in which the computation time is bounded by a polynomial of input size.Most computing applications today are in this category.In the future, we must focus on hard problems.One approach is to use nonsemiconductor-based physical devices; initial work in quantum computers would fall within this category.Another approach is to develop heuristic algorithms with much lower complexity; this is very much an objective of "Artificial Intelligence" development.The third approach is to leverage properties inherently embedded in input data, which calls for the development of Data Science.