Reasoning with Incomplete Information: Rough Set Based Information Logics

The representation of uncertain information is a central task of AI systems and many different methods have been developed to address this issue. In this paper we discuss a rough set [27] perspective on uncertainty and we present a survey of logics that provide foundations for reasoning with incomplete information that is a source of that uncertainty. The rough set paradigm is based on the observation that characterization of individuals in observational terms is usually incomplete. Trying to describe continuous domains with discrete means we are faced with the problem of indiscernibility: We might not have enough discriminative resources to discern each individual in a domain under consideration from any others. In various fields of applications indiscernibility arises from different reasons. For instance, in information systems some objects might be indiscernible because they have the same description in terms of the attributes admitted in the system. In a more general setting, indiscernibility is determined by some parameters which reflect expressive and discriminative resources of a domain under consideration. Objects may be discernible with respect to one subset of parameters but indiscernible with respect to another. Whether or not objects are discernible from one another is thus a function of these parameters, or in other words, indiscernibility is relative to these parameters. In this paper several examples are discussed where relative indiscernibility plays a crucial role.