Probabilistic Logic in a Coherent Setting
The approach to probability theory followed in this book (which differs radically from the usual one, based on a measure-theoretic framework) characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence
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TRENDS IN LOGIC Studia Logica Library VOLUME 15 Managing Editor Ryszard W6jcicki, Institute of Philosophy and Sociology, Polish Academy ofSciences , Warsaw, Poland Editors Daniele Mundici , Department of Computer Sciences, University of Milan, Italy Ewa Orlowska, National Institute of Telecommunications , Warsaw, Poland Graham Priest, Department of Philosophy, University of Queensland, Brisbane, Australia Krister Segerberg, Department of Philosophy, Uppsala University, Sweden Alasdair Urquhart, Department of Philosophy, University of Toronto, Canada Heinrich Wansing, Institute of Philosophy, Dresden University of Technology, Germany
SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica - that is, contemporary formal logic and its applications and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time.
Volume Editor Heinrich Wansing
The titles publi shed in this series are listed at the end of this volume.
GJULIANELLA
COLElТI UlIiversity о/ Perugia, lю/у
ROMANO SCOZZAFAVA University о! Roma
"Lл Sapit!IIZi1",
/Ioly
PROBABILISTIC LOGIC IN А COHERENT SETTING
SPRINGER-SCIENCE+BUSINESS
МЕDIА, В . У .
А
C.I.P. Cata10gue record for this book is available from
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Library оС Congress.
ISBN 978-1-4020-0970-9 ISBN 978-94-010-0474-9 (eBook) DOI 10.1007/978-94-010-0474-9
Printed оп acid-free paper
Аll Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published Ьу Кluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover 1st edition 2002 No part оС this work mау ье reproduced, stored in а retrieval system, or transmitted in апу form or Ьу апу means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from те Publisher, with те exception оС anу material supplied specifically for те purpose оС being entered and executed оп а computer system, for exclusive use Ьу те purchaser оС те work.
Preface The theory of probability is usually based on very peculiar and restrictive assumptions: for example, it is maintained that the assessment of probabilities requires an overall design on the whole set of all possible envisaged situations. A "natural" consequence is that the use of probability in the management of uncertainty is often challenged, due to its (putative) lack of "flexibility" . Actually, many traditional aspects of probability theory are not so essential as they are usually considered; for example, the requirement that the set of all possible "outcomes" should be endowed with a beforehand given algebraic structure (such as a Boolean algebra), or the aim at getting, for these outcomes, uniqueness of their probability values, with the ensuing introduction of suitable relevant assumptions (such as a-additivity, condition
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