Choice inclusive general rough semantics

Similarity based rough set theory (RST) involving choice in the formation of approximations was recently introduced by the present author. Though the theory can be used to develop improved semantics and models of knowledge and belief with ontology, application requires a priori concepts of granules and granulation as opposed to the more common a posteriori or not a priori concepts of the same prevalent in the literature. In this research, we clarify the desirable semantic features of a context for seamless application of the theory to more general situations, formalise them and refine the semantics. A new axiomatic theory of granules in general RST (including hybrid versions involving fuzzy set theories) is also developed in the process. Interesting new applications to human learning are also illustrated in this paper.