Formal Theories of Information

It is commonly assumed that computers process information. But what is inf- mation? In a technical, important, but nevertheless rather narrow sense, Sh- non’sinformationtheorygivesa?rstanswertothisquestion.Thistheoryfocuses on measuring the information content of a message. Essentially this measure is the reduction of the uncertainty obtained by receiving a message. The unc- tainty of a situation of ignorance in turn is measured by entropy. This theory hashad an immense impact on the technologyof information storage,data c- pression, information transmission and coding and still is a very active domain of research. Shannon’s theory has also attractedmuch interest in a more philosophic look at information, although it was readily remarked that it is only a “syntactic” theory of information and neglects “semantic” issues. Several attempts have been made in philosophy to give information theory a semantic ?avor, but still mostly based on or at least linked to Shannon’s theory. Approaches to semantic informationtheoryalsoveryoftenmakeuseofformallogic.Thereby,information is linked to reasoning, deduction and inference, as well as to decision making. Further, entropy and related measure were soon found to have important connotations with regard to statistical inference. Surely, statistical data and observation represent information, information about unknown, hidden para- ters. Thus a whole branch of statistics developed around concepts of Shannon’s information theory or derived from them. Also some proper measurements - propriate for statistics, like Fisher’s information, were proposed.