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Moisil in 1941, while constructing the algebraic models of n-valued Łukasiewicz logic defined the set B^[n],where B is a Boolean algebra and 'n' being a natural number. Further it was proved by Moisil himself the representations of n-valued Łukasiewicz Moisil algebra in terms of B^[n]. In this article, structural representation results for Stone, dual Stone and double Stone algebras are proved similar to Moisil's work by showing that elements of these algebras can be looked upon as monotone<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.02393v1">arXiv:1710.02393v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yey4rlgdgvcg5hwywyhnehbe5u">fatcat:yey4rlgdgvcg5hwywyhnehbe5u</a> </span>
more »... red tuple of sets. 3-valued semantics of logic for Stone algebra, dual Stone algebras and 4-valued semantics of logic for double Stone algebras are proposed and established soundness and completeness results.
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