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Among them, one is the weakly topological quasi-Boolean algebra. This paper studies the vicinity of weakly topological quasi-Boolean algebra from algebraic and logical perspectives. The weak pre-rough algebra is defined, and a cluster of intermediate algebras between it and the quasi-Boolean algebra is explored. The interrelationship and independence among them are presented. We also establish sound and complete sequential systems for these algebras. Further, we show the finite model property and construct decidable algorithms for weakly topological quasi-Boolean algebra and its weaker variants by context-free grammars. Rough set models of some of these algebras have been presented.<\/jats:p>","DOI":"10.1093\/jigpal\/jzag009","type":"journal-article","created":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:55:26Z","timestamp":1772283326000},"source":"Crossref","is-referenced-by-count":0,"title":["From weakly topological quasi-Boolean algebra to weak pre-rough algebra and closely related structures: an algebraic and logical investigation"],"prefix":"10.1093","volume":"34","author":[{"given":"Yiheng","family":"Wang","sequence":"first","affiliation":[{"name":"Institute of Logic and Cognition , Sun Yat-sen University, Xingang West Road No. 135, Guangzhou 510275, Guangdong China; Department of Philosophy, University of St Andrews, College Gate, St Andrews, KY16 9AJ, Fife Scotland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhe","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Philosophy , Xiamen University, Siming South Road No.422, Xiamen 361005 Fujian, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihir","family":"Kumar Chakraborty","sequence":"additional","affiliation":[{"name":"School of Cognitive Science , Jadavpur University, Kolkata 700032, West Bengal, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,25]]},"reference":[{"key":"2026052522103832900_ref1","first-page":"293","article-title":"Rough algebra","volume":"41","author":"Banerjee","year":"1993","journal-title":"Bull Pol Acad Sci"},{"key":"2026052522103832900_ref2","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1007\/978-1-4471-3238-7_24","article-title":"Rough consequence and rough algebra","volume-title":"Rough Sets, Fuzzy Sets and Knowledge Discovery: Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD\u201993)","author":"Banerjee","year":"1994"},{"key":"2026052522103832900_ref3","doi-asserted-by":"publisher","first-page":"211","DOI":"10.3233\/FI-1996-283401","article-title":"Rough sets through algebraic logic","volume":"28","author":"Banerjee","year":"1996","journal-title":"Fundam Inform"},{"key":"2026052522103832900_ref4","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/978-3-642-18859-6_7","article-title":"Algebras from rough sets","volume-title":"Rough-Neural Computing: Techniques for Computing With Words","author":"Banerjee","year":"2004"},{"key":"2026052522103832900_ref5","article-title":"The variety of topological quasi-Boolean algebras","volume-title":"Extended Abstract, Proceedings of Trends in Logic III","author":"Banerjee","year":"2005"},{"key":"2026052522103832900_ref6","first-page":"259","article-title":"On the representation of quasi-Boolean algebras","volume":"5","author":"Bialynicki-Birula","year":"1957","journal-title":"Bull Pol Acad Sci, Cl. 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