This short paper proposes the project of a modal logical semantics that will represent not the classical modalities but the many-worlds interpretation for the physical theory of quantum mechanics. It also views some problematic methodological questions of the doctrine such as measurement and a role of an interpreter. Special attention is given to the famous paradoxes of the QM such as EPR Paradox and Schrodinger’s Cat. The paper will be interesting for logicians, physicists and philosophers of science.