Compatibility in physical theories

Only those physical theories are considered which may be constructed from atomic ortholattices. It is proved that an atomic ortholattice becomes a physical theory (i.e. an atomic orthomodular having the covering property lattice) if an appropriate denumerable family {F-p subset of L x L; p greater than or equal to 0} of symmetric relations, with F, describing different ''degrees of incompatibility'', may be defined on it. It is shown that such a family may be explicitly constructed if certain easily understandable physical reasons are taken into account.