Ebook: Current Issues in Quantum Logic

These are the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2 - 9, 1979, at the Ettore Hajorana Centre for Scientific Culture. A conference of this sort was originally proposed by Giuliano Toraldo di Francia, who suggested the idea to Antonino Zichichi, and thus laid the foundation for the Workshop. To both of them we express our appreciation and thanks, also on behalf of the other participants, for having made this conference possible. There were approximately fifty participants; their names and institutions are listed in the text. Quantum logic, which has now a history of some forty or more years, has seen remarkable growth during the sixties and seventies. The papers in the present volume presuppose, by and large, some acquaintance with the elements of the subject. These may be found in the well-known books by J.H. Jauch (Foundations of Quantum Hechanics; Reading, 1968), V.S. Varadarajan (Geometry of Quantum Theory: Princeton, 1968), and C. Piron (Foundations of Quantum Theory; New York, 1976). The initial program for the conference listed about twenty-five invited papers. But in the context of a very active and qualified attendance, other contributions were offered. This volume contains all of them. The program listed six main topics: I. Classification or different areas of quantum logic, and open problems. II. Comparison and unification of different approaches to quantum theories; problems of interpretation. III. Formal quantum logic; axiomatics. IV. Hodal interpretations of quantum logic. v vi FOREWORD V. Quantum set theory.

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Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Classification of Different Areas of Work Afferent to Quantum Logic....Pages 3-16
Assumptions and Interpretations of Quantum Logic....Pages 17-31
Front Matter....Pages 33-33
What are Quantum Logics and What Ought They to be?....Pages 35-52
Charting the Labyrinth of Quantum Logics: A Progress Report....Pages 53-76
Realism and Quantum Logic....Pages 77-87
What does Quantum Logic Explain?....Pages 89-100
A New Approach to Equivalence in Quantum Logic....Pages 101-113
How to Rewrite a Stochastic Dynamical Theory so as to Generate a Measurement Paradox....Pages 115-118
The Quantum Logical and the Operational Description for Physical Systems....Pages 119-127
Front Matter....Pages 129-129
Partial Referential Matrices for Quantum Logics....Pages 131-146
Some Metalogical Pathologies of Quantum Logic....Pages 147-159
Quantum Logic as an Extension of Classical Logic....Pages 161-171
Sequential Quantum Logic....Pages 173-191
Entailment and Quantum Logic....Pages 193-207
Some Problems and Methods in Formal Quantum Logic....Pages 209-225
Front Matter....Pages 227-227
A Modal Interpretation of Quantum Mechanics....Pages 229-258
The Dialogic Approach to Modalities in the Language of Quantum Physics....Pages 259-281
The Inner Language of Operational Quantum Mechanics....Pages 283-299
Front Matter....Pages 301-301
Quantum Set Theory....Pages 303-322
Quantum Sets, Assemblies and Plexi....Pages 323-331
Front Matter....Pages 301-301
Omologic as a Hilbert Type Calculus....Pages 333-340
Measure and Integration in Quantum Set Theory....Pages 341-352
Front Matter....Pages 353-353
Commutativity and Generalized Transition Probability in Quantum Logic....Pages 355-364
Representations of Baer *-Semigroups and Quantum Logics in Hilbert Space....Pages 365-373
A Non-Standard Quantum Logic with a Strong Set of States....Pages 375-380
Description of Compound Physical Systems and Logical Interaction of Physical Systems....Pages 381-403
Products of Logics....Pages 405-412
Space-Time Structure from Quantum Logic....Pages 413-418
Causal Logic of Minkowski Space....Pages 419-424
Propositional Systems in Field Theories and Lattice-Valued Quantum Logic....Pages 425-435
Non-Linear Integration and Signed Measures on Von Neumann Algebras....Pages 437-445
On the Inter-Relations of the Three Quantal Principles....Pages 447-454
On the Non-Unique Decomposability of Quantum Mixtures....Pages 455-464
Motion and Form....Pages 465-477
Back Matter....Pages 479-492

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Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Classification of Different Areas of Work Afferent to Quantum Logic....Pages 3-16
Assumptions and Interpretations of Quantum Logic....Pages 17-31
Front Matter....Pages 33-33
What are Quantum Logics and What Ought They to be?....Pages 35-52
Charting the Labyrinth of Quantum Logics: A Progress Report....Pages 53-76
Realism and Quantum Logic....Pages 77-87
What does Quantum Logic Explain?....Pages 89-100
A New Approach to Equivalence in Quantum Logic....Pages 101-113
How to Rewrite a Stochastic Dynamical Theory so as to Generate a Measurement Paradox....Pages 115-118
The Quantum Logical and the Operational Description for Physical Systems....Pages 119-127
Front Matter....Pages 129-129
Partial Referential Matrices for Quantum Logics....Pages 131-146
Some Metalogical Pathologies of Quantum Logic....Pages 147-159
Quantum Logic as an Extension of Classical Logic....Pages 161-171
Sequential Quantum Logic....Pages 173-191
Entailment and Quantum Logic....Pages 193-207
Some Problems and Methods in Formal Quantum Logic....Pages 209-225
Front Matter....Pages 227-227
A Modal Interpretation of Quantum Mechanics....Pages 229-258
The Dialogic Approach to Modalities in the Language of Quantum Physics....Pages 259-281
The Inner Language of Operational Quantum Mechanics....Pages 283-299
Front Matter....Pages 301-301
Quantum Set Theory....Pages 303-322
Quantum Sets, Assemblies and Plexi....Pages 323-331
Front Matter....Pages 301-301
Omologic as a Hilbert Type Calculus....Pages 333-340
Measure and Integration in Quantum Set Theory....Pages 341-352
Front Matter....Pages 353-353
Commutativity and Generalized Transition Probability in Quantum Logic....Pages 355-364
Representations of Baer *-Semigroups and Quantum Logics in Hilbert Space....Pages 365-373
A Non-Standard Quantum Logic with a Strong Set of States....Pages 375-380
Description of Compound Physical Systems and Logical Interaction of Physical Systems....Pages 381-403
Products of Logics....Pages 405-412
Space-Time Structure from Quantum Logic....Pages 413-418
Causal Logic of Minkowski Space....Pages 419-424
Propositional Systems in Field Theories and Lattice-Valued Quantum Logic....Pages 425-435
Non-Linear Integration and Signed Measures on Von Neumann Algebras....Pages 437-445
On the Inter-Relations of the Three Quantal Principles....Pages 447-454
On the Non-Unique Decomposability of Quantum Mixtures....Pages 455-464
Motion and Form....Pages 465-477
Back Matter....Pages 479-492
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