In the first Part of this paper Property Systems are investigated in order to define intensional and extensional operators fulfilling adjointness properties. On this basis a set of operators are defined which are able to determine non-classical upper and lower approximations of subsets of objects or properties. But in order to bypass "discontinuity" of such operators we introduce, in the second Part, the higher order notion of an "Information Quantum". This way we can account for Attribute Systems as well as Property Systems by transforming them into new structures called "Information Quantum Relational Systems" in which adjointness makes operators fulfill continuity and makes it possible to define a class of Generalised Approximation Spaces. ©2005 IEEE.