  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.
