### Stone and double Stone algebras: Boolean and Rough Set Representations, 3-valued and 4-valued Logics [article]

Arun Kumar
<span title="2017-10-05">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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
more &raquo; ... 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.
<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>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191014003520/https://arxiv.org/pdf/1710.02393v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bb/14/bb14019b139e4a579a7fae99928a84d02f8961e6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.02393v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>