This chapter introduces the concepts of discernibility matrices and functions in information systems, which are fundamental tools for understanding and manipulating knowledge represented in these systems. The authors, Andrzej Skowron and Cecylia Rauszer, present several properties of these notions and derive algorithms for solving problems related to rough definability, reducts, core, and dependencies generation. The chapter begins with an introduction to information systems, highlighting their role in representing knowledge and their connections to rough set theory. It discusses the importance of knowledge reduction and dependencies in information systems, emphasizing the need to identify and remove unnecessary attributes while preserving essential knowledge. The authors extend their previous work on discernibility matrices and functions, providing efficient methods for computing reducts, cores, and dependencies, with an upper bound on time complexity of order \( n^2 \). They also address the NP-hardness of generating minimal reducts and dependencies. The chapter concludes with a detailed definition of information systems and rough sets, including the concept of the \( B \)-indiscernibility relation.This chapter introduces the concepts of discernibility matrices and functions in information systems, which are fundamental tools for understanding and manipulating knowledge represented in these systems. The authors, Andrzej Skowron and Cecylia Rauszer, present several properties of these notions and derive algorithms for solving problems related to rough definability, reducts, core, and dependencies generation. The chapter begins with an introduction to information systems, highlighting their role in representing knowledge and their connections to rough set theory. It discusses the importance of knowledge reduction and dependencies in information systems, emphasizing the need to identify and remove unnecessary attributes while preserving essential knowledge. The authors extend their previous work on discernibility matrices and functions, providing efficient methods for computing reducts, cores, and dependencies, with an upper bound on time complexity of order \( n^2 \). They also address the NP-hardness of generating minimal reducts and dependencies. The chapter concludes with a detailed definition of information systems and rough sets, including the concept of the \( B \)-indiscernibility relation.