Formal reasoning in preference-based multiple-source rough set model

We propose a generalization of Pawlak’s rough set model for the multi-agent situation, where information from an agent can be preferred over that of another agent of the system while deciding membership of objects. Notions of lower/upper approximations are given, which depend on the knowledge base of the sources as well as on the position of the sources in the hierarchy giving the preference of sources. A quantified modal logic is proposed to reason about the properties of the proposed approximations. A sound and complete deductive system for the logic is also presented. Moreover, it is shown how the properties of the proposed approximations can be deduced as theorems of this deductive system.