Covering-based rough sets and modal logics. Part I

Two conjectures on the covering-based rough set semantics for modal logics in [35] are answered. The C2 and C5 semantics give rise to the same modal system S4. There are Galois connections between C2 and C5 which lead to the covering-based semantics for the temporal logic system S4t. The P1 and C4 semantics give rise to the same modal system KTB.