This monograph presents a systematic, exhaustive and up-to-date overview of formal methods and theories for data analysis and inference inspired by the concept of rough set. The book studies structures with incomplete information from the logical, algebraic and computational perspective. The formalisms developed are non-invasive in that only the actual information is needed in the process of analysis without external sources of information being required. The book is intended for researchers, lecturers and graduate students who wish to get acquainted with the rough set style approach to information systems with incomplete information.