Algebraic structures in the vicinity of pre-rough algebra and their logics

In this paper a cluster of algebraic structures weaker than pre-rough algebra has been studied. Their properties and interrelations are investigated. Logics, both Hilbert type axiomatization and sequent calculi for these algebras are presented. These algebraic structures may be considered as abstract generalizations of rough set algebra. In particular some of the algebras are observed to be quite rich in structure and hence bear the potentiality of generating concrete rough set models for specific usages.