دانلود کتاب Handbook of Quantum Logic and Quantum Structures: Quantum Logic

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Front Cover
Handbook of Quantum Logic and Quantum Structures – Quantum Logic
Copyright Page
Table of Contents
Foreword
Editorial Preface
Chapter 1 The Birkhoff–von Neumann Concept of Quantum Logic
1 INTRODUCTION
2 QUANTUM LOGIC: LOGICIZATION OF NON-BOOLEAN ALGEBRAIC STRUCTURES. THE STANDARD VIEW
3 THE BIRKHOFF-VON NEUMANN CONCEPT OF QUANTUM LOGIC
4 VON NEUMANN\'S POST 1936 STRUGGLE WITH QUANTUM LOGIC
5 SUMMARY AND CONCLUDING REMARKS
ACKNOWLEDGEMENTS
BIBLIOGRAPHY
Chapter 2 Is Quantum Logic a Logic?
1 INTRODUCTION
2 LATTICES
3 LOGICS
4 THE SOUNDNESS OF QL: ORTHOMODULARITY LOST
5 THE SOUNDNESS OF CL: DISTRIBUTIVITY LOST
6 THE COMPLETENESS OF QL FOR WOML MODELS: NON-ORTHOMODULARITY CONFIRMED
7 THE COMPLETENESS OF CL FOR WDOL MODELS: NON-DISTRIBUTIVITY CONFIRMED
8 THE COMPLETENESS OF QL FOR OML MODELS: ORTHOMODULARITY REGAINED
9 THE COMPLETENESS OF CL FOR BOOLEAN ALGEBRA MODELS: DISTRIBUTIVITY REGAINED
10 DISCUSSION
ACKNOWLEDGEMENT
BIBLIOGRAPHY
Chapter 3 Is Logic Empirical?
1 INTRODUCTION
2 QUANTUM MECHANICS IN A NUTSHELL
3 QUANTUM LOGIC IN A NUTSHELL
4 STANDARD INTERPRETATION AND MEASUREMENT PROBLEM OF QUANTUM MECHANICS
5 QUANTUM LOGIC AND THE STANDARD INTERPRETATION OF QUANTUM MECHANICS
6 QUANTUM LOGIC AND CLASSICAL PROPOSITIONS
7 QUANTUM LOGIC IN OTHER APPROACHES TO QUANTUM MECHANICS
8 CONCLUSION
ACKNOWLEDGEMENTS
BIBLIOGRAPHY
Chapter 4 Quantum Axiomatics
1 INTRODUCTION
2 STATE PROPERTY SPACES
3 A SET OF AXIOMS
4 MORPHISMS
5 DECOMPOSITION OF A STATE PROPERTY SPACE
6 ADDITIONAL AXIOMS
7 SUPERPOSITION
8 HILBERT SPACE REPRESENTATIONS
BIBLIOGRAPHY
Chapter 5 Quantum Logic and Nonclassical Logics
1 INTRODUCTION
2 HOW QUANTUM LOGIC EMERGES FROM QUANTUM EVENT-STATE SYSTEMS
3 QUANTUM LOGIC VS POSITIVE, MINIMAL AND INTUITIONISTIC LOGIC
4 THE \"LINDENBAUM-ANOMALY\"
5 QUANTUM LOGIC AND THE HIDDEN VARIABLE PROBLEM
6 THE UNSHARP APPROACHES TO QT
7 UNSHARP QUANTUM LOGICS
8 QUANTUM LOGIC AND PARACONSISTENT LOGIC
9 QUANTUM LOGIC AND LINEAR LOGIC
10 QUANTUM LOGIC AND QUANTUM COMPUTATION
11 MATHEMATICAL APPENDIX
ACKNOWLEDGEMENTS
BIBLIOGRAPHY
ACKNOWLEDGEMENTS
BIBLIOGRAPHY
Chapter 6 Gentzen Methods in Quantum Logic
1 INTRODUCTION
2 MINIMAL QUANTUM LOGIC IN GENTZEN STYLE
3 THE CONTRAPOSITION THEOREM
4 THE DUALITY THEOREM
5 THE CUT-ELIMINATION THEOREM
6 THE COMPLETENESS THEOREM
BIBLIOGRAPHY
Chapter 7 Categorical Quantum Mechanics
1 INTRODUCTION
2 REVIEW OF QUANTUM MECHANICS AND TELEPORTATION
3 COMPACT CLOSED CATEGORIES AND THE LOGIC OF ENTANGLEMENT
4 STRONGLY COMPACT CLOSED CATEGORIES AND 2-DIMENSIONAL DIRAC NOTATION
5 BIPRODUCTS, BRANCHING AND MEASUREMENTS
6 ABSTRACT QUANTUM MECHANICS: AXIOMATICS AND QUANTUM PROTOCOLS
7 EXTENSIONS AND FURTHER DEVELOPMENTS
BIBLIOGRAPHY
Chapter 8 Extending Classical Logic for Reasoning about Quantum Systems
1 INTRODUCTION
2 EXOGENOUS APPROACH
3 DECIDABLE FRAGMENT OF EQPL
4 COMPLETENESS AND DECIDABILITY
5 APPLICATION EXAMPLES
6 CONCLUDING REMARKS
ACKNOWLEDGMENTS
BIBLIOGRAPHY
Chapter 9 Solèr\'s Theorem
1 PRELIMINARIES AND STRUCTURE OF THE PROOF
2 CONSTRUCTION OF THE SEMI-ORDERING ON F
3 ARCHIMEDEANITY AND COMPLETENESS OF (F,≤)
4 THE NON-COMMUTATIVE CASE
BIBLIOGRAPHY
Chapter 10 Operational Quantum Logic: A Survey and Analysis
1 INTRODUCTION
2 SOME HISTORICAL REMARKS
3 QUANTUM OBJECTS
4 MORPHISMS
5 DYNAMICAL EVOLUTION
6 FROM BEING TO BECOMING
7 COMPOSITE QUANTUM OBJECTS
8 QUANTUM PROCESSES
ACKNOWLEDGEMENTS
BIBLIOGRAPHY
Chapter 11 Test Spaces
0 INTRODUCTION AND OVERVIEW
1 BACKGROUND ON QUANTUM LOGICS
2 TEST SPACE BASICS
3 LOGICS OF TEST SPACE
4 SUPPORTS AND ENTITIES
5 TENSOR PRODUCTS OF QUANTUM LOGICS
6 SYMMETRIC TEST SPACES
7 TOPOLOGICAL CONSIDERATIONS
ACKNOWLEDGEMENTS
BIBLIOGRAPHY
Chapter 12 Contexts in Quantum, Classical and Partition Logic
1 MOTIVATION
2 CLASSICAL CONTEXTS
3 QUANTUM CONTEXTS
4 AUTOMATA AND GENERALIZED URN LOGIC
5 SUMMARY
BIBLIOGRAPHY
Chapter 13 Nonmonotonicity and Holicity in Quantum Logic
INTRODUCTION
1 STRUCTURE OF THIS CHAPTER
2 BASICS OF NONMONOTONIC LOGIC
3 CONSEQUENCE REVISION SYSTEMS
4 HOLISTIC LOGICS: EVERYTHING IS ENCODED IN EVERYTHING
5 SOME HILBERT SPACE THEORY
6 TOWARDS HILBERT SPACE
BIBLIOGRAPHY
Chapter 14 A Quantum Logic of Down Below
1 INTRODUCTION
2 AGENCY
3 SEMANTIC SPACE: COMPUTATIONAL APPROXIMATIONS OF CONCEPTUAL SPACE
4 BRIDGING SEMANTIC SPACE AND QUANTUM MECHANICS
5 QUANTUM LOGIC AND CONCEPTUAL GENERALIZATION
6 SUMMARY AND CONCLUSIONS
ACKNOWLEDGMENTS
BIBLIOGRAPHY
Chapter 15 A Completeness Theorem of Quantum Set Theory
1 INTRODUCTION
2 COMPLETE ORTHOMODULAR LATTICES
3 QUANTUM LOGIC QL
4 QUANTUM SET THEORY QZFZ
5 A COMPLETENESS THEOREM OF QZFZ
BIBLIOGRAPHY
Index