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Rough set theory has already been algebraically investigated for decades and quasi-Boolean algebra has formed a basis for a number of structures emerging out of rough sets. Pre-rough algebra is one such algebra amongst them. A number of structures based on quasi-Boolean algebra but weaker than pre-rough algebra already exist. In this paper some algebras and their logics are added. Rough set models of the newly created algebras and some of the existing algebras are presented. [ABSTRACT FROM AUTHOR]

In this paper a number of implicative topological algebras have been developed which are based on the implicative quasi-Boolean algebra with operator (IqBaO) [10]. Their independence is established by several examples. Logics corresponding to these algebras are presented. Two new pairs of lower-upper approximations of a set have been introduced in order to develop the notion of duality with respect to the quasi-complementation. Set theoretic rough set models of some of the algebras are constructed using these lower-upper approximations and quasi-complementation. [ABSTRACT FROM AUTHOR]

The covering-based rough sets in the system C 2 and bounded N -morphisms form a category C F N . This category is dually equivalent to the category K F S4 in which objects are Kripke S 4-frames and arrows are bounded morphisms. Morphisms over covering structures are defined in order to characterize the modal C 2 -definability of classes of finite covering frames. [ABSTRACT FROM AUTHOR]

Two conjectures on the covering-based rough set semantics for modal logics in [35] are answered. The C 2 and C 5 semantics give rise to the same modal system S4 . There are Galois connections between C 2 and C 5 which lead to the covering-based semantics for the temporal logic system S4 t . The P 1 and C 4 semantics give rise to the same modal system KTB . [ABSTRACT FROM AUTHOR]

Pre-rough algebra has emerged from the rough set theory, which is a quasi-Boolean algebra with a few additional axioms. Four types of abstract rough inclusion are defined in pre-rough algebra which give rise to four different implication operators within this algebra. Properties of these four implications are studied from the angle of residuation. Logics of pre-rough algebra with respect to different implications are presented. [ABSTRACT FROM AUTHOR]

Towards the study of covering based rough set semantics for modal logic [39] , we present a modal system corresponding to the covering systems P 3 , C 1 , and C Gr. We also study the modal systems for boundary operators based on generalized approximation spaces as well as covering systems. Our study also leads to covering semantics for some contingency logics and provide its connection with rough set theory. Further, an alternative modal system based on the contingency modal operator is provided corresponding to the covering system P 4. [ABSTRACT FROM AUTHOR]

The paper is a continuation of the type of research that has been initiated in our previous paper (Saha et al., 2014) [23]. Algebraic structures weaker than pre-rough algebra have been studied intending availability of an implication operation suitable for developing Hilbert type logic systems. [ABSTRACT FROM AUTHOR]

In this paper a cluster of algebraic structures weaker than pre-rough algebra has been studied. Their properties and interrelations are investigated. Logics, both Hilbert type axiomatization and sequent calculi for these algebras are presented. These algebraic structures may be considered as abstract generalizations of rough set algebra. In particular some of the algebras are observed to be quite rich in structure and hence bear the potentiality of generating concrete rough set models for specific usages. [ABSTRACT FROM AUTHOR]