Table Of ContentTrends in Logic 46
Sven Ove Hansson
Descriptor
Revision
Belief Change Through Direct Choice
Trends in Logic
Volume 46
TRENDS IN LOGIC
Studia Logica Library
VOLUME 46
Editor-in-chief
HeinrichWansing, Ruhr-University Bochum, Bochum,Germany
Editorial Assistant
Andrea Robitzsch, University ofOsnabrück, Osnabrück,Germany
EditorialBoard
Wesley Holliday, University of California, Berkeley, USA
Arnon Avron,University of TelAviv, TelAviv, Israel
Katalin Bimbó,University of Alberta,Edmonton, Canada
Giovanna Corsi, University of Bologna,Bologna,Italy
JanuszCzelakowski, University of Opole, Opole, Poland
Roberto Giuntini,University of Cagliari,Cagliari, Italy
RajeevGoré,Australian National University, Canberra, Australia
Andreas Herzig, University ofToulouse, Toulouse, France
Andrzej Indrzejczak, University of Łodz, Łodz,Poland
Daniele Mundici,University ofFlorence,Florence, Italy
SergeiOdintsov, SobolevInstitute of Mathematics, Novosibirsk, Russia
EwaOrłowska, Institute ofTelecommunications, Warsaw,Poland
PeterSchroeder-Heister, University of Tübingen, Tübingen, Germany
Yde Venema,University of Amsterdam, Amsterdam, TheNetherlands
Andreas Weiermann, University of Ghent, Ghent, Belgium
Frank Wolter,University of Liverpool, Liverpool,UK
Ming Xu,WuhanUniversity, Wuhan, People’s Republic ofChina
Foundingeditor
Ryszard Wójcicki, Polish Academy ofSciences, Warsaw, Poland
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moreover, the range of applications, comparisons and sources of inspiration is open and
evolves overtime.
More information about this series at http://www.springer.com/series/6645
Sven Ove Hansson
Descriptor Revision
Belief Change Through Direct Choice
123
SvenOve Hansson
Division of Philosophy
RoyalInstitute ofTechnology
Stockholm
Sweden
ISSN 1572-6126 ISSN 2212-7313 (electronic)
Trends inLogic
ISBN978-3-319-53060-4 ISBN978-3-319-53061-1 (eBook)
DOI 10.1007/978-3-319-53061-1
LibraryofCongressControlNumber:2017933665
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Preface
The use of logical modelling to study belief change is a well-established research
area since more than three decades. The focus is mostly on operations that take us
fromabeliefstateinwhichaparticularsentenceisbelievedtooneinwhichitisnot
believed,ortheotherway around. Inthemajormodels,theseoperationsarebased
on a mechanism that can be constructed as a choice among maximally consistent
sets of sentences, “possible worlds.” The development of these models has been
accompanied by a critical discussion in which the resulting operations of change
have been shown to have implausible properties.
Thisbookproposes aretake for thelogicof belief change. From a formal point
ofview,twoinnovationsarecombinedtoarriveatanewtypeofmodel,descriptor
revision,inwhichtheimplausiblepropertiesareavoided.Oneoftheseinnovations
consistsinbasingtheoperationonadirectchoiceamongpotentialoutcomes(belief
states)ratherthanindirectlyonachoiceamongpossibleworldsortheirequivalents.
The other innovation is a new formal device, belief descriptors, that is used for
describing the goals of a belief change. They allow us to represent a much wider
array of belief changes than the incorporation or rejection of a single sentence. In
combination with the new choice mechanism, they also allow us to perform all
these changes in a unified way.
All formal proofs are deferred to an appendix. A list of symbols and a general
index are included in order to facilitate the reader’s orientation in the book.
This book has grown out of several years of research. References are given
throughoutthetexttopreviouspublicationswherethisworkwasreportedatearlier
stages.Readerswishingtocomparethebooktoitsprecursorsmayhaveuseforthe
following references to the Bibliography: Sections 4.1–4.2 [135], Sections 4.3–4.5
and 5.1–5.2 [124], Section 5.4 [130], Section 5.5 [126], Sections 6.1–6.3 and
7.2–7.3 [132], Section 7.4 [129], Section 7.5 [131], Section 8.1 [124], Section 8.2
[124, 128], Section 8.3 [132], Section 8.4 [126], Section 9.1 [124], Section 9.3
[126], Section 10.3 [134], Section 10.5 [120], and Section 10.6 [117].
I have benefitted greatly in this work from critical discussions on seminars and
workshops in Stockholm, Lund, Copenhagen, Amsterdam, Schloss Dagstuhl,
Munich,Nancy,ACaruña,Madeira,Pittsburgh,SãoPaulo,Campinas,Beijing,and
v
vi Preface
several other places. I am grateful to everyone who took part in these discussions.
Special thanks go to Johan van Benthem, Gregor Betz, John Cantwell, Hans van
Ditmarsch,EduardoFermé,Valentin Goranko,DavidMakinson,andZhangLifor
their comments on an earlier version of the manuscript.
Stockholm, Sweden Sven Ove Hansson
December 2016
Contents
Symbols.. .... .... .... .... ..... .... .... .... .... .... ..... .... xi
Preview .. .... .... .... .... ..... .... .... .... .... .... ..... .... xv
Part I Why a New Approach?
1 The State of the Art .... ..... .... .... .... .... .... ..... .... 3
1.1 A Sentential, Input-Assimilating Approach.... .... ..... .... 3
1.2 The AGM Construction .. .... .... .... .... .... ..... .... 6
1.3 The AGM Postulates .... .... .... .... .... .... ..... .... 7
1.4 Possible World Models... .... .... .... .... .... ..... .... 9
1.5 Epistemic Entrenchment.. .... .... .... .... .... ..... .... 15
1.6 Conclusion ... .... ..... .... .... .... .... .... ..... .... 16
2 Inside the Black Box.... ..... .... .... .... .... .... ..... .... 17
2.1 Epistemic Choice .. ..... .... .... .... .... .... ..... .... 18
2.2 The Select-and-Intersect Method.... .... .... .... ..... .... 19
2.3 Is the Intersection as Good as Its Origins?.... .... ..... .... 21
2.4 Do All Success Conditions Withstand Intersection?. ..... .... 22
2.5 Do We Select Among the Right Objects?. .... .... ..... .... 23
3 Questionable Patterns of Change... .... .... .... .... ..... .... 27
3.1 The Postulates of Finite-Based Outcome . .... .... ..... .... 27
3.2 The Success Postulates... .... .... .... .... .... ..... .... 29
3.3 The Recovery Postulate .. .... .... .... .... .... ..... .... 30
3.4 Pure Contraction and the Inclusion Postulate .. .... ..... .... 31
3.5 The Expansion Property.. .... .... .... .... .... ..... .... 33
3.6 Extending the Language.. .... .... .... .... .... ..... .... 34
3.7 Iterated Change.... ..... .... .... .... .... .... ..... .... 37
3.8 Ten Desiderata for an Alternative Framework . .... ..... .... 42
vii
viii Contents
Part II Descriptor Revision
4 Putting the Building-Blocks Together ... .... .... .... ..... .... 45
4.1 Beginning Without Sentences.. .... .... .... .... ..... .... 45
4.2 Support Functions.. ..... .... .... .... .... .... ..... .... 49
4.3 Belief Descriptors.. ..... .... .... .... .... .... ..... .... 53
4.4 Properties of Descriptors.. .... .... .... .... .... ..... .... 55
4.5 Descriptor Revision Introduced. .... .... .... .... ..... .... 58
4.6 Conclusion ... .... ..... .... .... .... .... .... ..... .... 60
5 Local Descriptor Revision..... .... .... .... .... .... ..... .... 63
5.1 Monoselective Descriptor Revision.. .... .... .... ..... .... 64
5.2 Linear and Centrolinear Revision... .... .... .... ..... .... 67
5.3 Indeterministic Descriptor Revision . .... .... .... ..... .... 70
5.4 Blockage Revision . ..... .... .... .... .... .... ..... .... 73
5.5 Relations of Epistemic Proximity... .... .... .... ..... .... 78
6 Global Descriptor Revision.... .... .... .... .... .... ..... .... 85
6.1 Global Monoselective and Centrolinear Revision... ..... .... 86
6.2 Distance-Based Global Revision.... .... .... .... ..... .... 87
6.3 Global Blockage Revision .... .... .... .... .... ..... .... 91
7 Dynamic Descriptors.... ..... .... .... .... .... .... ..... .... 95
7.1 Representing Autoepistemic Beliefs . .... .... .... ..... .... 96
7.2 Ramsey Descriptors ..... .... .... .... .... .... ..... .... 98
7.3 The Logic of Ramsey Descriptors .. .... .... .... ..... .... 100
7.4 Alternative Approaches to Conditionals .. .... .... ..... .... 105
7.5 Non-Monotonic Inference. .... .... .... .... .... ..... .... 107
7.6 Modalities of Belief ..... .... .... .... .... .... ..... .... 111
Part III Sentential Change Revisited
8 Sentential Revision . .... ..... .... .... .... .... .... ..... .... 117
8.1 Sentential Monoselective Revision.. .... .... .... ..... .... 118
8.2 Sentential Centrolinear Revision.... .... .... .... ..... .... 120
8.3 Global Sentential Revision.... .... .... .... .... ..... .... 126
8.4 Believability Relations ... .... .... .... .... .... ..... .... 127
8.5 Multiple Revision and Making up One’s Mind. .... ..... .... 130
9 Revocation.... .... .... ..... .... .... .... .... .... ..... .... 133
9.1 Monoselective Revocation .... .... .... .... .... ..... .... 134
9.2 Centrolinear Revocation.. .... .... .... .... .... ..... .... 135
9.3 Entrenchment . .... ..... .... .... .... .... .... ..... .... 139
9.4 Multiple Revocation and Entrenchment .. .... .... ..... .... 143
9.5 A Revisionary Account of Giving up Beliefs.. .... ..... .... 146
Contents ix
10 Contraction ... .... .... ..... .... .... .... .... .... ..... .... 151
10.1 How to Construct Contraction . .... .... .... .... ..... .... 151
10.2 Centrolinear and Maximal Contraction... .... .... ..... .... 152
10.3 Two Impossibility Theorems .. .... .... .... .... ..... .... 154
10.4 Monomaximal Contraction.... .... .... .... .... ..... .... 155
10.5 Perimaximal Contraction.. .... .... .... .... .... ..... .... 156
10.6 Bootstrap Contraction.... .... .... .... .... .... ..... .... 159
Part IV Epilogue
11 Looking Back – and Ahead ... .... .... .... .... .... ..... .... 165
11.1 Looking Back. .... ..... .... .... .... .... .... ..... .... 165
11.2 Looking Ahead.... ..... .... .... .... .... .... ..... .... 166
Appendices
Proofs.... .... .... .... .... ..... .... .... .... .... .... ..... .... 171
Bibliography .. .... .... .... ..... .... .... .... .... .... ..... .... 219
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 231
