The book explores the modal ideas and theories of the outstanding logic of the 20th century by Y. Lukasevich. The first two chapters analyze the two modal logics he built (three-digit and four-digit). The third chapter attempts to develop and formalize his intuitive ideas about determinism, truth, and causality. The book, which is the first study of this aspect of Lukasevich's work in logical literature, contains new ideas and logical results regarding widely understood modal logic, prognostic statements, ontological modalities, causality, time determination, causal definition of truth, etc.