This work employs the empirical logic approach of D. Foulis and C. Randall to compare non-relativistic, conservative, non-compound physical systems (universes) in classical and quantum mechanics. We present definitions of test spaces, propositions, proposition logics, statistical states, observables, and dynamical systems. Then we try to identify their mathematical representatives for both, classical and quantum universes. Except for the case of the dynamical system, which is not defined for classical universes, the definitions prove to be general enough to apply to both cases.
Necessary mathematical tools not generally known to physicists are also treated in a concise fashion. These include some basic theory of partially ordered sets (posets) and lattices, in particular boolean and orthomodular lattices.