## Handbook of Quantum Logic and Quantum Structures: Quantum LogicQuantum 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. |

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### Contents

1 | |

23 | |

49 | |

Chapter 4 Quantum Axiomatics | 79 |

Chapter 5 Quantum Logic and Nonclassical Logics | 127 |

Chapter 6 Gentzen Methods in Quantum Logic | 227 |

Chapter 7 Categorical Quantum Mechanics | 261 |

Chapter 8 Extending Classical Logic for Reasoning about Quantum Systems | 325 |

Chapter 9 Solèrs Theorem | 373 |

### Other editions - View all

Handbook of Quantum Logic and Quantum Structures: Quantum Logic Kurt Engesser,Dov M. Gabbay,Daniel Lehmann No preview available - 2008 |

Handbook of Quantum Logic and Quantum Structures: Quantum Logic Kurt Engesser,Dov M. Gabbay,Daniel Lehmann No preview available - 2008 |

### Common terms and phrases

Aerts atoms axiom axiomatics Birkhoff Boolean algebra classical logic closed subspaces Coecke compact closed category complete consequence relation Consider context corresponding defined DEFINITION denote disjunction elements entity equivalent example exists finite formula Foulis function geometry Giuntini given Greechie hence Hilbert lattices Hilbert space implies inference interpretation involution isomorphic Lemma linear linear logic mapping mathematical measurement monoidal Neumann notion observable operator ortho test orthoalgebra orthocomplemented orthogonal ortholattice orthomodular lattice outcome Pavicic physical system Piron poset probability projection Proof property space propositions prove quantum computation quantum logic quantum mechanics quantum structure quantum system qubit QZFZ real closed field Rédei represented satisfied sentence sequent Specker subset Suppose Svozil symmetric tensor product test space theorem theory topological valuations von Neumann algebras Wilce