Giovanni Sommaruga

This book presents the scientific outcome of a joint effort of the computer science departments of the universities of Berne, Fribourg and Neuchâtel. Within an initiative devoted to "Information and Knowledge", these research groups collaborated over several years on issues of logic, probability, inference, and deduction. The goal of this volume is to examine whether there is any common ground between the different approaches to the concept of information. The structure of this book could be represented by a circular model, with an innermost syntactical circle, comprising statistical and algorithmic approaches; a second, larger circle, the semantical one, in which "meaning" enters the stage; and finally an outermost circle, the pragmatic one, casting light on real-life logical reasoning. These articles are complemented by two philosophical contributions exploring the wide conceptual field as well as taking stock of the articles on the various formal theories of information.

From Shannon to Semantic Information Theory and General Concepts of Information

Formal Theories of Information

Thomas Strahm

This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of computability theory as well as on generalised Turing computability. By looking at the roots and at the philosophical and technical influence of Turing’s work, it is possible to gather new perspectives and new research topics which might be considered as a continuation of Turing’s working ideas well into the 21st century.

The Impact of His Ideas about Computability

Turing’s Revolution

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.

Giovanni Sommaruga

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