Knowledge Contributors

208 Pages·2003·1.931 MB·English

by  V. F. Hendricks, K. F. Jørgensen, S. A. Pedersen (auth.), Vincent F. Hendricks, Klaus Frovin Jørgensen, Stig Andur Pedersen (eds.)

KNOWLEDGE CONTRIBUTORS
SYNTHESE LIBRARY
STUDIES IN EPISTEMOLOGY,
LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Editor-in-Chief:
JOHN SYMONS,University of Texas at El Paso, U.S.A.
VINCENT F. HENDRICKS,Roskilde University, Denmark
Honorary Editor:
JAAKKO HINTIKKA, Boston University, U.S.A.
Editors:
DIRK VAN DALEN, University of Utrecht, The Netherlands
THEO A.F. KUIPERS, University of Groningen, The Netherlands
TEDDY SEIDENFELD, Carnegie Mellon University, U.S.A.
PATRICK SUPPES, Stanford University, California, U.S.A.
JAN WOLEN´SKI,Jagiellonian University, Kraków, Poland
VOLUME 322
KNOWLEDGE
CONTRIBUTORS
Edited by
VINCENT F. HENDRICKS
Roskilde University,
Denmark
KLAUS FROVIN JØRGENSEN
Roskilde University,
Denmark
and
STIG ANDUR PEDERSEN
Roskilde University,
Denmark
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4020-1748-3 ISBN978-94-007-1001-6 (eBook)
DOI 10.1007/978-94-007-1001-6
Printed on acid-free paper
All Rights Reserved
©2003Springer Science+Business M edia D ordr echt
Originally published byKluwer Academic Publishers in 2003
Softcover reprint of the hardcover 1st edition 2003
No part of this work may be reproduced, stored in a retrieval system, or transmitted
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CONTENTS
Preface............................................................... ix
V.F. HENDRICKS, K.F. JØRGENSEN AND
S.A. PEDERSEN/ Introduction...................................... 1
1. Agent and System ............................................. 1
2. Active Agenthood ............................................. 6
3. Multiple Active Agents ........................................ 9
4. Multi-Modalities ............................................. 11
5. Conclusion ................................................... 13
Notes ........................................................... 13
References ...................................................... 14
W.LENZEN/Knowledge,Belief,andSubjectiveProbability: Outlinesof
a Unified System of Epistemic/DoxasticLogic ....................... 17
1. The Logic of Conviction ...................................... 17
2. The Logic of Knowledge ...................................... 21
3. The Logic of (‘Weak’) Belief.................................. 24
4. The Pragmaticsof Epistemic Sentences....................... 26
Notes ........................................................... 30
References ...................................................... 30
J. HINTIKKA / A Second Generation Epistemic Logic and Its General
Significance.......................................................... 33
1. The Prima Facie Conundrum of Epistemic Logic .............. 33
2. The Promises ................................................ 37
3. PromisesFulfilled by Means of the Notion of Independence ... 46
References ...................................................... 54
H.ROTT/EconomicsandEconomyintheTheoryofBeliefRevision. 57
1. Introduction ................................................. 57
2. What is Economics? ......................................... 58
3. Acting Economically,A Second View:
“InformationalEconomy” ................................... 60
4. Economicand EconomicalConsiderationsin
Belief Revision Theory ...................................... 61
5. InformationalEconomywith Respect to Beliefs:
What has been done? ....................................... 65
6. InformationalEconomywith Respect to Beliefs:
What should be done? ...................................... 68
v
vi
7. Conservatismwith Respect to Belief-Revision Guiding Structures:
What has been done? ....................................... 69
8. Conservatismwith Respect to Belief-Revision Guiding Structures:
What should be done? ...................................... 71
9. RationalChoices and LogicalProperties:
What has been done? ....................................... 74
10. Rational Choices and LogicalProperties:
What should be done? ...................................... 76
11. Conclusion .................................................. 79
Notes ........................................................... 80
References ...................................................... 83
R. FAGIN, J.Y. HALPERN, Y. MOSES AND M.Y. VARDI / Common
KnowledgeRevisited .................................................87
1. Introduction ................................................. 87
2. TwoPuzzles ................................................. 88
3. Common Knowledgeand Uncertainty ........................ 90
4. Simultaneous Events ......................................... 91
5. TemporalImprecision ........................................ 95
6. The Granularityof Time ..................................... 96
7. Approximationsof Common Knowledge ...................... 98
8. Summary ................................................... 101
Notes .......................................................... 102
References ..................................................... 103
H.P.VAN DITMARSCH, W. VAN DER HOEKAND B.P.KOOI/ Con-
currentDynamic Epistemic Logic .................................. 105
1. Introduction ................................................ 105
2. Languageand Semantics .................................... 107
3. ProofSystem ............................................... 119
4. Completeness ............................................... 130
5. Applications ................................................ 136
6. Conclusions ................................................. 140
References ..................................................... 141
J.F. SOWA / Laws, Facts, and Contexts: Foundations of Multimodal
Reasoning .......................................................... 145
1. ReplacingPossible Worlds with Contexts .................... 145
2. Dunn’s Lawsand Facts ...................................... 147
3. Contexts by Peirceand McCarthy ........................... 149
4. Tarski’sMetalevels .......................................... 155
5. Nested Graph Models ....................................... 157
6. BeyondKripke Semantics ................................... 165
vii
7. The Intended Interpretation ................................. 174
References ..................................................... 183
R. WO´JCICKI / Referential Semantics ............................. 185
1. The General Idea of Referential Semantics ................... 185
2. Language ................................................... 186
3. Components of Referential Semantics ........................ 187
4. Substitutions ................................................ 187
5. Some Notation .............................................. 188
6. The Definition Completed ................................... 188
7. A Few Examples ............................................ 189
8. Four Principlesof LogicalAnalysis .......................... 190
9. LogicalConsequences ....................................... 192
10. A Few Comments on the Peculiar Status
of the Identity Predicate ................................... 192
11. General Propertiesof Consequence Operations ............. 193
12. The Truth PreservingConsequenceOperations ............. 194
13. The Problemof Adequacy ................................. 194
14. Self-ExtensionalConsequence Operations ................... 195
15. Adequacy Theorem ........................................ 195
16. The Need for Referential Semantics ........................ 195
17. Notes and References ...................................... 197
References ..................................................... 198
Index .............................................................. 199
PREFACE
Inthe1950’sGeorgvonWrightprovidedthefirstsurveysinepistemiclogic.
Roughly10yearslaterJaakkoHintikkapublishedhisseminalworkonthe
logic of knowledge and belief. Epistemic and doxastic logics have since
then growninto mature disciplines enjoying many important applications
inphilosophy,computerscience,gametheory,economicsandlinguisticsto
mention of few fields of applications.
Knowledge Contributors is based on the Dimensions in Epistemic
Logic conferencehostedbyΦLOG—The Danish Network for Philosophical
Logic and Its Applications in May2002at Roskilde University,Denmark.
The conference featured lectures by such recognized experts in epistemic
logic as Joseph Y. Halpern (Cornell University, USA), Jaakko Hintikka
(Boston University, USA), Wiebe van der Hoek (University of Liverpool,
UK), Wolfgang Lenzen (University of Osnabru¨ck, DE), Hans Rott (Uni-
versity of Regensburg, DE), Krister Segerberg (Uppsala University, SE),
JohnF.Sowa(USA),MosheY.Vardi(RiceUniversity,USA)andRyszard
Wo´jcicki (Polish Academy of Sciences, PL).
The conference had three aims which are reflected in the current vol-
ume and its organizationof the contributions: (1) To track the history of
epistemic logic, (2) to consider important applications of epistemic logic
in a variety of fields and (3) to discuss future directions of research in
epistemic logicwith particularemphasis on ‘activeagenthood’ and multi-
modalsystems. The editors wouldlike tothank the invited speakers,and
their co-authors, for contributing, in the most lucid and inspiring way, to
the fulfillment of the conference aims and for making their contributions
availablefor publication.
The editors wouldalsolike to extend their gratitude to ΦLOG’s orga-
nizationalcommitteeconsistingofTorbenBrau¨ner,HenningChristiansen
(RoskildeUniversity), JanRiis Flor(University of Copenhagen),Cynthia
M.Grund(UniversityofSouthernDenmark),LarsBoGundersen(Aarhus
University), Per Hasle (University of Southern Denmark), K. Hvidtfeldt
Nielsen (Aarhus University), Peter Øhrstrøm (Aalborg University) and
ΦLOG’s secretaryPelle Guldborg Hansen (Roskilde University). ΦLOG is
onlymadepossiblebyaresearchgrantfromtheDanish Research Council
for the Humanities for which the editors and the network remain grate-
ful. The editors would like to thank Lise Sonne-Hansen for her careful
BIBTEX’ing of the manuscript. Finally we would like to extend our grat-
itude to Kluwer Academic Publishers and in particular acquisition editor
FloorOosting for taking on this project.
Vincent F. Hendricks Klaus Frovin Jørgensen
Stig Andur Pedersen
September 2003
ix
V.F. HENDRICKS, K.F. JØRGENSEN AND S.A. PEDERSEN
INTRODUCTION
The study of epistemic attitudes – in particular knowledge and belief –
dates at least back to the Scholaticism of the Middles Ages. The formal
study of the same attitudes was then largely initiated by von Wright’s
seminal paper from the 1950’s (37). The formal systematic study of
knowledgeandbelief sawthe lightof daybyHintikka’s bookbythe same
nameKnowledge and Belief: An Introduction to the Logic of the Two No-
tions from1962(16). Hardlyapublicationinepistemiclogichassurfaced
sincewithoutreferencetothisground-breakinginvestigation. Morerecent
monographsdedicatedtoepistemicand/ordoxasticlogic1 includenotably
Lenzen(22),Schlesinger(25),Boh(3),Knuuttila(19),Meyerandvander
Hoek (35), Fagin et al. (6), Sowa (30), Hendricks (12), (14), and Halpern
(11).
The contemporary logics of knowledge and belief are advanced and
sophisticated. Epistemic and doxastics logics for single agents have been
catalogued;logicsformulti-agentsystemshavebeencatalogued;epistemic
modalitieshavebeen combinedwith temporalandalethicmodalities, etc.
These advances make the way for multiple epistemic operators, multi-
ple doxastic operators, common knowledge operators, alethic and tempo-
ral operators, mono-modal systems, multi-modal systems, dynamic epis-
temic/doxasticsystems, belief revision features and agentsequipped with
learning mechanisms. This is not an exhaustive list. There is a vast fan
of important applications and models utilizing these powerful logics of
knowledge and belief. Examples range from robots on assembly lines, so-
cialandcoalitionalinteractions,cardgames,‘live’situationsineconomics,
miscellaneouslinguistic practicesand so on.
Itisnotthepurposeofthisintroductiontoreviewepistemiclogicfrom
its date of birth to this day and age in detail.2 Certain distinctive devel-
opmentalfeaturesstandoutasparticularlypertinenttoboththeresearch
progressionanddirectionaswellasthegeneralepistemologicalandappli-
cationalrelevanceofepistemiclogic. Thesemaybesubsumedunder‘agent
andsystem’,‘activeagenthood’,‘multipleactiveagents’,‘multi-modalites’
andconstitutethefeatureswithrespecttowhichthisintroductionandthe
contributionsin this volume are organized.
1. AGENT AND SYSTEM
The formalsystematic surveysof epistemic and doxasticlogicswereearly
on largely influenced by the advances in (alethic) modal logic. Standard
systemsof modal logicwerefurnished with epistemic interpretations,and
some fundamental results of epistemic logiccould then be extracted.
Syntactically,thelanguageofpropositionalepistemiclogicisobtained
byaugmentingthe languageofpropositionallogicwith a unaryepistemic
1
V.F.Hendricks,K.F.JørgensenandS.A.Pedersen(eds.),KnowledgeContributors,1–15.
©2003KluwerAcademicPublishers.PrintedintheNetherlands.