The logic of quantum mechanics - Take II
This work addresses foundational issues in quantum mechanics and logic for researchers in theoretical physics and logic, but it appears incremental as it builds on existing views like Schroedinger's.
The paper tackles the problem of defining quantum logic by proposing a new approach based on composition rather than propositional structure, resulting in a quantitative logic that models natural language meaning, supports automation, and enables probabilistic inference.
We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of superpositions, as proposed by Birkhoff and von Neumann. This gives rise to an intrinsically quantitative kind of logic, which truly deserves the name `logic' in that it also models meaning in natural language, the latter being the origin of logic, that it supports automation, the most prominent practical use of logic, and that it supports probabilistic inference.