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Sigma Series in Stochastics, Volume 1, 73--93
Heldermann Verlag 2004

Reliability of Arguments

Jürg Kohlas
Dept. of Informatics, University of Fribourg, Fribourg, Switzerland

Inference under uncertainty was an important subject of philosophy already in the 17th and 18th century and especially in the enlightenment. Philosophers like Leibniz (1646--1716) and Jakob Bernoulli (1654--1705) and many others made important contributions to it. The subject has gained a new actuality in computer science. In the past as today, probability theory is used to formalize inference under uncertainty. Probability theory has originally been developed for the purpose of studying games of chance. Today probability theory is highly developed, but devoted mainly to the study of random phenomena. Inference under uncertainty however poses different problems, not related to chance, but to ignorance. Not surprisingly, alternative forms of probability like theory of evidence, probabilistic argumentation systems among others have evolved today. There are even formalisms for inference under uncertainty like different forms of non-monotonic logic, possibility theory and others, which avoid probability altogether. It is remarkable that the basic ideas underlying the new ways probability is applied to inference under uncertainty were already present in the beginnings of probability theory. They were however eliminated from the main stream of probability theory and surface again only in very recent developments.