General Introduction; D. Aerts. Quantum Physics and the Nature of Reality. Editorial; D. Aerts, J. Pykacz. A half-century of Quantum Logic - what have we learned? D. Foulis. Quantum mechanical measurements; S. Gudder. From Logic to Physics: the logico-algebraic foundations of quantum theory; G. Cattaneo, F. Laudisa. Non-classical logics, non-classical sets, and non-classical physics; J. Pykacz. Against `Paradoxes': A new quantum philosophy for quantum mechanics; C. Garola. Quantum mechanics: Structures, Axioms and Paradoxes; D. Aerts. Orthogonality relations: From classical to quantum; T. Durt. Quantum logical semantics, historical truths and interpretations in Arts; M.L. Dalla Chiara, R. Giuntini.