Some implicative topological quasi-Boolean algebras and rough set models.

In this paper a number of implicative topological algebras have been developed which are based on the implicative quasi-Boolean algebra with operator (IqBaO) [10]. Their independence is established by several examples. Logics corresponding to these algebras are presented. Two new pairs of lower-upper approximations of a set have been introduced in order to develop the notion of duality with respect to the quasi-complementation. Set theoretic rough set models of some of the algebras are constructed using these lower-upper approximations and quasi-complementation. [ABSTRACT FROM AUTHOR]