QUANTUM LOGICS

Contents 1 Introduction 3 2 Orthomodular quantum logic and orthologic 11 3 The implication problem 22 4 Metalogical properties and anomalies 28 5 A modal interpretation of OL and OQL 32 6 An axiomatization of OL and OQL 35 7 The intractability of orthomodularity 40 8 Hilbert quantum logic and the orthomodular law 45 9 First-order quantum logic 50 10 Quantum set theories and theories of quasisets 56 11 The unsharp approaches 59 12 Effect structures 61 13 Paraconsistent quantum logic 70 14 The Brouwer-Zadeh logics 74 15 Partial qu antum logics 86 16 Lukasiewicz quantum logic 92 17 Conclusion 96