Ideals of core regular double Stone algebra

A regular double Stone algebra with nonvoid core is called core regular double Stone algebra (CRDSA) [6] and this particular core element affects the behavior of the algebra in certain aspects especially in characterization of maximal and prime ideals. In this paper, an elegant characterization for maximal and prime ideals of a CRDSA is established.

Generalized Rough Logics with Rough Algebraic Semantics

The collection of the rough set pairs <lower approximation, upper approximation> of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (RSL), Stone logic (SL), rough double Stone logic (RDSL), and double Stone Logic (DSL). The languages, axioms and rules are presented. The soundness and completeness of the logics are proved.

Generalized Rough Logics with Rough Algebraic Semantics

The collection of the rough set pairs <lower approximation, upper approximation> of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (RSL), Stone logic (SL), rough double Stone logic (RDSL), and double Stone Logic (DSL). The languages, axioms and rules are presented. The soundness and completeness of the logics are proved.

A class of projective Stone algebras

We prove that a regular double Stone algebra is protective in the category of Stone algebras if and only if its centre is a projective Boolean algebra and its dense set is countably generated as a filter. It follows that every countable regular double Stone algebra is projective as a Stone algebra.