Rough set theory (RST) focuses on forming posets of equivalence relations to describe sets with increasing accuracy. The connection between modal logics and RST is well known and has been extensively studied in their relation algebraic (RA) formalisation. RST has also been interpreted as a variant of intuitionistic or multi-valued logics and has even been studied in the context of logic programming. This paper presents a detailed formalisation of RST in RA by way of residuals, motivates its generalisation and shows how results can be used to prove many RST properties in a simple algebraic manner (as opposed to many tedious and error-prone set-theoretic proofs). A further abstraction to an entirely point-free representation shows the correspondence to Kleene algebras with domain. Finally, we show how an RA-perspective on RST allows to derive an abstract algorithm for finding reducts from a mere analysis of the properties of the RA-construction rather than by a data-driven approach.
展开▼
