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Moisil in 1941, while constructing the algebraic models of n-valued{\L}ukasiewicz logic defined the set $B^{[n]}$,where $B$ is a Boolean algebraand `n' being a natural number. Further it was proved by Moisil himself therepresentations of n-valued {\L}ukasiewicz Moisil algebra in terms of$B^{[n]}$. In this article, structural representation results for Stone, dualStone and double Stone algebras are proved similar to Moisil's work by showingthat elements of these algebras can be looked upon as monotone ordered tuple ofsets. 3-valued semantics of logic for Stone algebra, dual Stone algebras and4-valued semantics of logic for double Stone algebras are proposed andestablished soundness and completeness results.

Stone and double Stone algebras: Boolean and Rough Set Representations, 3-valued and 4-valued Logics