Handbook of Quantum Logic and Quantum Structures: Quantum Logic

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