(Non)compatibility in quantum logic

M. Navara (logic seminar)


We show why noncompatibility occurs not only in quantum mechanics, but also in social sciences, etc. As a consequence, the event structure is nondistributive - an orthomodular lattice. We show its basic properties. Measure theory on orthomodular lattices may be developed in an analogy with the classical case. However, we encounter new phenomena, e.g., the space of all probability measures need not be a simplex, but it can be any compact convex set.