Modal logic
Incomplete Information: Structure, Inference, Complexity
Incomplete Information: Structure, Inference, Complexity
Approaches to Conflict Dynamics Based on Rough Sets
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Approximate boolean reasoning: foundations and applications in data mining
Transactions on Rough Sets V
Approximation of sets based on partial covering
Transactions on Rough Sets XVI
| Hi-index | 0.00 |
The natural modal logic corresponding to Pawlak's approximationspaces is S5, based on the box modality [R]A (and the diamondmodality )R*A=¬[R]¬A), where R is the correspondingindiscernibility relation of the approximation space S=(W,R).However the expressive power of S5 is too weak and, for instance,we cannot express that the space S has exactly n equivalenceclasses (we say that S is roughly-finite and n is therough cardinality of S). For this reason we extend the modallogic S5 with a new box modality [S]A, where S is the complement ofR i.e. the discernibility relation of W. We propose acomplete axiomatization, in this new language, of the logicROUGHn corresponding to the class of approximationspaces with rough cardinality n. We prove that the satisfiabilityproblem for ROUGHn is NP-complete.