Multiple Source Approximation Systems, Evolving Information Systems and Corresponding Logics: A Study in Rough Set Theory
Mathematical logic is used as a tool/language to reason about any kind of data. With the inception of rough set theory (RST) the question of a suitable logic for RST has attracted the attention of many researchers. One of the main contribution of the current article is the development of a logic that can describe aspects of information system such as attribute, attribute values, as well as the induced concept approximations. Moreover, the current article relates RST to some important issues in artificial intelligence such as multiple source (agent) knowledge bases, temporal evolution of knowledge bases, and information updates. For the multiple source case, we explored counterparts of standard rough set theoretic concepts such as concept approximations, definability of concepts, as well as corresponding logics that can express these notions. For the temporal situation, we proposed temporal logics for RST that bring temporal and approximation operators together, to enable reasoning about concept approximations relative to time. An update logic for RST is also introduced that can be used to study flow of information and its effect on concept approximations.
Trans. Rough Sets