Banerjee, Mohua; Chakraborty, Mihir K. Rough sets through algebraic logic. (English) Zbl 0864.03041 Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 28, No. 3-4, 211-221 (1996). Summary: While studying rough equality within the framework of the modal system \(S_5\), an algebraic structure called rough algebra [M. Banerjee and M. K. Chakraborty, Bull. Pol. Acad. Sci., Math. 41, No. 4, 293-297 (1993; Zbl 0795.03035)], came up. Its features were abstracted to yield a topological quasi-Boolean algebra (tqBa). In this paper, it is observed that rough algebra is more structured than a tqBa. Thus, enriching the tqBa with additional axioms, two more structures, viz. pre-rough algebra and rough algebra, are defined. Representation theorems of these algebras are also obtained. Further, the corresponding logical systems \({\mathcal L}_1\), \({\mathcal L}_2\) are proposed and eventually, \({\mathcal L}_2\) is proved to be sound and complete with respect to a rough set semantics. Cited in 3 ReviewsCited in 40 Documents MSC: 03G25 Other algebras related to logic 03B45 Modal logic (including the logic of norms) 68T27 Logic in artificial intelligence 68T30 Knowledge representation Keywords:rough sets; representation; modal logic; rough equality; rough algebra; pre-rough algebra; semantics Citations:Zbl 0795.03035 PDFBibTeX XMLCite \textit{M. Banerjee} and \textit{M. K. Chakraborty}, Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 28, No. 3--4, 211--221 (1996; Zbl 0864.03041)