The paper introduces the discernibility matrix and discernibility function in information systems. These concepts are used to analyze and solve problems related to knowledge reduction, core, and dependencies in information systems. The discernibility matrix and function help in identifying redundant attributes and generating minimal descriptions of information systems. The paper presents algorithms for these tasks and provides an upper bound for their time complexity, which is generally of order n², where n is the number of objects in the system. The problem of generating reducts (minimal subsets of attributes that preserve the same classification as the full set) is shown to be polynomially equivalent to transforming the conjunctive form of a monotonic boolean function to disjunctive form. The paper also shows that generating minimal reduces and minimal dependencies are NP-hard. The paper extends the ideas from [Sk91], where the discernibility matrix and function were introduced. The paper discusses information systems and rough sets, defining an information system as a pair (U, A), where U is the universe and A is the set of attributes. The discernibility relation IND(B) is defined for subsets of attributes B, and is an equivalence relation. The paper provides a foundation for further research in information systems and rough set theory.The paper introduces the discernibility matrix and discernibility function in information systems. These concepts are used to analyze and solve problems related to knowledge reduction, core, and dependencies in information systems. The discernibility matrix and function help in identifying redundant attributes and generating minimal descriptions of information systems. The paper presents algorithms for these tasks and provides an upper bound for their time complexity, which is generally of order n², where n is the number of objects in the system. The problem of generating reducts (minimal subsets of attributes that preserve the same classification as the full set) is shown to be polynomially equivalent to transforming the conjunctive form of a monotonic boolean function to disjunctive form. The paper also shows that generating minimal reduces and minimal dependencies are NP-hard. The paper extends the ideas from [Sk91], where the discernibility matrix and function were introduced. The paper discusses information systems and rough sets, defining an information system as a pair (U, A), where U is the universe and A is the set of attributes. The discernibility relation IND(B) is defined for subsets of attributes B, and is an equivalence relation. The paper provides a foundation for further research in information systems and rough set theory.