Towards Information Logics

Abstract

The information operators presented in Chap. 4 are intensional operators in that the result of applying an operator to a compound set of objects depends not only on the component sets but also on an information relation. From a logical perspective, it follows that information operators have the status of modal connectives. It is therefore natural to postulate that information logics be modal-like logics. However, reasoning about the objects and relations of an information system often requires more subtle means than ordinary monomodal logics can offer. For example, we might need an explicit representation of compound information relations obtained by performing some relational operations on the component relations. This is needed, for instance, for reasoning about definability of sets of objects in information systems. Similarly, it might not be sufficient to consider only the modal connectives analogous to possibility and necessity. For instance, the operators of sufficiency needed for a characterisation of complementarity relations are not among the classical modal connectives. In this chapter we present a general scheme of modal logics. The scheme captures the classes of information logics considered in this book as well as most modal logics from the literature. Our definition of modal logics is semantic. This enables us to stress the links between the logics under consideration and their intended use in information systems.