Summary: While studying rough equality within the framework of the modal system
, an algebraic structure called rough algebra [M. Banerjee
and M. K. Chakraborty
, Bull. Pol. Acad. Sci., Math. 41, No. 4, 293-297 (1993; Zbl 0795.03035
)], came up. Its features were abstracted to yield a topological quasi-Boolean algebra (tqBa). In this paper, it is observed that rough algebra is more structured than a tqBa. Thus, enriching the tqBa with additional axioms, two more structures, viz. pre-rough algebra and rough algebra, are defined. Representation theorems of these algebras are also obtained. Further, the corresponding logical systems
are proposed and eventually,
is proved to be sound and complete with respect to a rough set semantics.