On a Certain Logic of Information

Abstract

The main aim of the present article is an outline of an intuitively adequate system of logic of the operator „being informed”. Such a system should be different from the familiar systems of epistemic and doxastic logic. The principle of veracity occurring in epistemic logics does not describe adequately the information operator, since the information may be true as well as false. On the other hand, the principle of consistency of beliefs, occurring in doxastic logics, cannot be applied to information, because the information can be inconsistent. Our logic of information, although it is based on Kripke’s semantics, includes principles not occurring in the systems of epistemic and doxastic logics, such as the principle of incompleteness of information and the Brouwerian Axiom. We prove that this system is incomplete. We also suggest that it can be generalized to a dynamic logic in the sense of van Benthem.