  A class of ring-like event systems (RLSEs) is studied that generalizes
Boolean rings. Quantum logics represented by orthomodular lattices are
characterized within this class and the correspondence between Boolean algebras
and Boolean rings is enlarged to orthomodular lattices. The structure of RLSEs
and various subclasses is analysed and classical logics are especially
identified. Moreover, sets of numerical events within different contexts of
physical problems are described. A numerical event is defined as a function p
from a set S of states of a physical system to [0,1] such that p(s) is the
probability of the occurrence of an event when the system is in state s\in S.
In particular, the question is answered whether a given (small) set of
numerical events will give rise to the assumption that one deals with a
classical physical system or a quantum mechanical one.
