This book is the first to present quantum logic in relation to von Neumann algebra theory. Based on developing quantum logic in terms of operator algebras, the book reconstructs and reevaluates the Birkhoff — von Neumann concept of quantum logic. It also covers recent results such as the violation of Bell's inequality in relativistic quantum field theory, the logical independence of von Neumann lattices and the status of the common cause principle in quantum field theory. Other topics treated include the theory of quantum conditional and statistical inference, an operator algebraic treatment of the hidden variable problem and the semantic approach to physical theories. Audience: This volume will be of interest to mathematicians, physicists, mathematical physicists and historians and philosophers of science involved in interpretational problems of quantum mechanics and quantum field theory.