Handbook of Quantum Logic and Quantum Structures

1st Edition

Quantum Structures

Editors: Kurt Engesser Dov M. Gabbay Daniel Lehmann
Hardcover ISBN: 9780444528704
eBook ISBN: 9780080550381
Imprint: Elsevier Science
Published Date: 1st August 2007
Page Count: 818
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Description

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics” quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.

Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate.

The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject.

The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.

Key Features

  • Written by eminent scholars in the field of logic
  • A comprehensive presentation of the theory, approaches and results in the field of quantum logic
  • Volume focuses on quantum structures

Readership

Libraries, scholars from various fields as logic, philosophy of science, mathematics, physics, computer science, artificial intelligence

Table of Contents

Foreword (A. Dvurecenskij) Editorial Preface (K. Engesser, D. Gabbay and D. Lehmann) New Quantum Structures (A. Dvurecenskij) Quantum Structures and Fuzzy Set Theory (J. Pykasz) Algebraic and Measure-theoretic Properties of Classes of Subspaces of an Inner Product Space (D. Buhagiar, E. Chetcuti and A. Dvurecenskij) Quantum Probability (S. Gudder) Orthomodular Lattices and Orthomodular Posets (P. Ptak and S. Pulmannova) Quantum Logic and Partially Ordered Abelian Groups (D.J. Foulis and R.J. Greechie) Operator Algebras (J. Hamhalter) Constructions of Quantum Structures (M. Navara) D-Posets (F. Chovanec and F. Kopka) Wigner's Theorem and its Generalisations (G. Chevalier) Hilbert Lattices (I. Stubbe and B. van Steirteghem) Ortholattice Equations and Hilbert Lattices (R. Mayet) Decomposition in QL (J. Harding) Starting from the Convex Set of States (E. Beltrametti) QL and Automata Theory (M. Ying) QL and Quantum Computation (N.D. Megill and M. Pavicic) Index

Details

No. of pages:
818
Language:
English
Copyright:
© Elsevier Science 2007
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080550381
Hardcover ISBN:
9780444528704

About the Editor

Kurt Engesser

Affiliations and Expertise

Kings College London, London, UK

Dov M. Gabbay

Dov M. Gabbay is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. He has authored over four hundred and fifty research papers and over thirty research monographs. He is editor of several international Journals, and many reference works and Handbooks of Logic.

Affiliations and Expertise

King's College London, UK

Daniel Lehmann

Affiliations and Expertise

Hebrew University of Jerusalem, Israel