Symmetries of physical theories

A physical theory is, by definition, a complete orthomodular atomic lattice having the covering property. GivenL a quantum logic andS _L the set of all its states, a theorem is proved which asserts that, if certain reasonable assumptions concerningS _L are satisfied, then for any bijective convex mappingU: S _LS_L, satisfying also certain physically meaningful conditions, there exists a unique automorphismV: L L such thatU(p)=p oV ^–1 for allp S _L.