Handbook of Quantum Logic and Quantum Structures

Quantum Logic

Kurt Engesser, Dov M. Gabbay, Daniel Lehmann

• Publisher: Elsevier Science
• Year: 2009
• Topic: Mathematics
• eBook ISBN:
  9780080931661
• Subtopic: Logic in Mathematics
• Index: Mathematics

Quantum mechanics is said to be the most successful physical theory ever. It is, in fact, unique in its success when applied to concrete physical problems. On the other hand, however, it raises profound conceptual problems that are equally unprecedented. Quantum logic, the topic of this volume, can be described as an attempt to cast light on the puzzle of quantum mechanics from the point of view of logic. Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled, "The logic of quantum mechanics, quantum logic has undergone an enormous development. Various schools of thought and approaches have emerged, and there are a variety of technical results. The chapters of this volume constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic. - Authored by eminent scholars in the field - Material presented is of recent origin representing the frontier of the subject - Provides the most comprehensive and varied discussion of Quantum Mechanics available

Table of contents

• Front Cover
• Handbook of Quantum Logic and Quantum Structures: Quantum Logic
• Copyright Page
• Contents
• Foreword
• Editorial Preface
• Chapter 1 The Birkhoff–von Neumann Concept of Quantum Logic
• Chapter 2 Is Quantum Logic a Logic?
• Chapter 3 Is Logic Empirical?
• Chapter 4 Quantum Axiomatics
• Chapter 5 Quantum Logic and Nonclassical Logics
• Chapter 6 Gentzen Methods in Quantum Logic
• Chapter 7 Categorical Quantum Mechanics
• Chapter 8 Extending Classical Logic for Reasoning about Quantum Systems
• Chapter 9 Solèr's Theorem
• Chapter 10 Operational Quantum Logic: A Survey and Analysis
• Chapter 11 Test Spaces
• Chapter 12 Contexts in Quantum, Classical and Partition Logic
• Chapter 13 Nonmonotonicity and Holicity in Quantum Logic
• Chapter 14 A Quantum Logic of Down Below
• Chapter 15 A Completeness Theorem of Quantum Set Theory
• Index