  It is shown that quantum-type coherence, leading to indeterminism and
interference of probabilities, may in principle exist in the absence of the
Planck constant and a Hamiltonian. Such coherence is a combined effect of a
symmetry (not necessary physical) and semantics. The crucial condition is that
symmetries should apply to logical statements about observables. A theoretical
example of a non-quantum system with quantum-type properties is analysed.
