On modal logics characterized by models with relative accessibility relations. II (Q1595920)

The paper is a continuation of Part I [Stud. Log. 65, No.~3, 323-353 (2000; Zbl 0969.03028)]. Constructions from Part I are extended to the case of Rare-logics with nominals. The class of standard modal logics for which the universal modal operator can be eliminated (if satisfiability is concerned) is characterized. Proof systems for Rare-logics are proposed. A uniform method of proving decidability of Rare-logics and, in particular, information logics based on rough set theory is given.