The introduction of the chapter "The Logic of Quantum Mechanics" highlights the novel logical concepts in quantum theory, such as the uncertainty principle and the principle of non-commutativity of observations. The paper aims to explore the logical structure of physical theories that do not conform to classical logic, specifically quantum mechanics. It suggests that a calculus of propositions, similar to the calculus of linear subspaces, might be appropriate for quantum mechanics. The paper is divided into two parts: the first part discusses heuristic arguments supporting this calculus, while the second part reconstructs it from an axiomatic perspective, comparing it with classical mechanics and its propositional calculi. The chapter also introduces the concept of physical systems and observations, and the idea of phase spaces, which are common to both classical mechanics and quantum theory. In quantum theory, phase spaces are associated with wave functions, typically in Hilbert space.The introduction of the chapter "The Logic of Quantum Mechanics" highlights the novel logical concepts in quantum theory, such as the uncertainty principle and the principle of non-commutativity of observations. The paper aims to explore the logical structure of physical theories that do not conform to classical logic, specifically quantum mechanics. It suggests that a calculus of propositions, similar to the calculus of linear subspaces, might be appropriate for quantum mechanics. The paper is divided into two parts: the first part discusses heuristic arguments supporting this calculus, while the second part reconstructs it from an axiomatic perspective, comparing it with classical mechanics and its propositional calculi. The chapter also introduces the concept of physical systems and observations, and the idea of phase spaces, which are common to both classical mechanics and quantum theory. In quantum theory, phase spaces are associated with wave functions, typically in Hilbert space.