A number of low and high-level models of general rough sets can be used to represent knowledge. Often binary relations between attributes or collections thereof have deeper properties related to decisions, inference or vision that can be expressed in ternary functional relationships (or groupoid operations) – this is investigated from a minimalist perspective in this research by the present author. General approximation spaces and reflexive up-directed versions thereof are used by her as the basic frameworks. Related semantic models are invented and an interpretation is proposed in this research. Further granular operator spaces and variants are shown to be representable as partial algebras through the method. An analogous representation for all covering spaces does not necessarily hold. Applications to education research contexts that possibly presume a distributed cognition perspective are also outlined.
Functional Extensions of Knowledge Representation in General Rough Sets