Handbook of Epistemic Logic PDF
Preview Handbook of Epistemic Logic
E H p a i n s d t b e o m o i k c H W i a e J n b o s e s e L o p v f a o v h n Ba an g r Y D i t . e de it c ld r Ha m E l a d K Ho pe rs ito ooi ek rn ch rs: Pm OSE Ne ang, ST ener sane Sune aan S 2851099848187" 9 |= 2-451-09848-1-879 NBSI .yhpargoilbib deliated a dna ,secnerefer gnidulcni ,dnuorgkcab lacirotsih emos sedivorp taht seton fo noitces a htiw sdne retpahc hcaE .redro yma ni dna yltnednepedni daer eb nac yeht taht os nettirw neeb evah sretpahc ehT .slocotorp ytiruces dna ,ytiliba dna egdelwonk ,ycnega ,yroeht emaG ,gnikcehc ledom ,feileb fo dna egdelwonk fo scimanyd eht ,emit dna egdelwonk ,ytilibaborp dna egdelwonk ,ssenerawa ,gniwonk ylno fo scipot eht revoG ,)srehcraeser ro( rehcraeser gnidael a yb nettirw hcae ,sretpahc nevele gniwollof ehT .koob eht .ni derevoc lairetam eht dna aera eht fo weivrevo na sevig tij ;feileb dna egdelwonk fo scigol eht ot noitcudortni eltneg a htiw ,strats koob ehT .saera detaler ni krow etaicerppa ot ecnahc a strepxe evig dna ,dleif eh tretn es ortehcraeser wen ro freisae t iekam dluohs koob sihT .evitca yrev eb ot seunitnoc ,erutam erom elihw ,taht dleif a nsisergorp tnacifingi sstrop ekroobdnah si h.Tscimonoce dna ,ecnegilletni laicifitra ,ecneics retupmoC ni osla t,uybhposolihp ni ylno ton e ltonracifingis a deyalp evah scigol hcus ,neht ecniS .s0691 ylrae eht ni siweL divaD dna akkitniH okkaaJ sa hcus srehposolihp htiw detanigiro ,feileb dna egdelwonk fo scigol ,yllareneg erom ,dna cigol cimetsipE 21875i¢ Ca HY; 0225 H23 Handbook of Epistemic Logic Edited by Hans van Ditmarsch Joseph Y. Halpern Wiebe van der Hoek Barteld Kool © Individual authors and College Publications 2015. All rights reserved. ISBN 978-1-84890-158-2 College Publications Scientific Director: Dov Gabbay Managing Director: Jane Spurr http:/Avww.collegepublications.co.uk Cover produced by Laraine Welch Printed by Lightning Source, Milton Keynes, UK All rights reserved, No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form, or by any means, electronic, mechanical, photocopying, recording or otherwise without prior permission, in writing, from the publisher. Contents Preface xiii Contributors XV 1 An Introduction to Logics of Knowledge and Belief 1 Hans van Ditmarsch, Joseph Y. Halpern, Wiebe van der Hoek and Barteld Kooi 1.1 Introduction to the Book... ...............0.0.4 er 1.2. Basic Concepts and Tools .................04 N O 1.2.1 Language .. 2. O 1.2.2 Semantics .. 2... 2... ee C 1.2.3 Expressivity and Succinctness .. 2... 0.00004 21 1.2.4 Reasoning problems ...............004 26 1.2.5 Axiomatisation .... 0.0.000.0.. ee.e ee 32 13 Overview of the Book 2... 0.0... . 0... 0.000 A2 L4 Notes . 2... 45 References 00. 49 I Informational Attitudes 53 2 Only Knowing 55 Gerhard Lakemeyer and Hector J. Levesque 2.1 Introduction. 2... 2.2 Single-Agent Only Knowing ...........00.000. 2.2.1 Syntax and Semantics ........0.....00.. 2.2.2 Some properties of OL 2... ee 2.2.3 Proof Theory... 0... 2.24 Only Knowing and Autoepistemic Logic ....... 2.2.5 Honesty 2. vi CONTENTS 2.3 Multi-Agent Only Knowing ............0.0.04 65 2.3.1 The Canonical-Model Approach. ........... 66 2.3.2 Proof Theory .. 2.0... 0. ee 68 | 2.3.3 Honesty Revisited ©... 0.0.0.0... 0020004 69 24 Notes 2... 72 References... 0 74 3 Awareness 77 Burkhard C. Schipper 3.1 Introduction. 2... 77 3.2 Preliminary discussion .. 0... 0.0ee0 ee. 79 | 3.2.1 Some properties of awareness in natural languages . 79 | 3.2.2. Some properties of awareness in a formal language . 80 3.3 Awareness and knowledge ...........0....00004 82 | 3.3.1 Awareness structures 2.0.0.0e.e .ee.e 82 | 3.3.2 Impossibility of unawareness in Kripke frames... . 91 | 3.3.3 Unawareness frames 2... 0. ee 94 : 3.3.4 Unawareness structures . 1... 0..e.e e es 100 3.3.5 Generalized standard models ............. 104 3.3.6 Product models... 0... 0.0.0.0 .0..000.40 , 107 3.4 Awareness and probabilistic belief... ......0.000., 112 3.4.1 Type spaces with unawareness ............, 112 3.4.2 Speculative trade and agreement .....,..... 116 3.5 Awareness of unawareness .. 0... 0. ee 118 3.5.1 Propositional quantifiers and extended awareness structures ©. ao 118 3.5.2 First-order logic with unawareness of objects .... 121 3.5.3 Neighborhood semantics and first-order logic with a- WATENESS 127 3.5.4 Awareness of unawareness without quantifiers .... 129 3.6 Notes 2... es 133 References... 00. Ds 141 4 Epistemic Probabilistic Logic 147 Lorenz Demey and Joshua Sack 4,1 Introduction... 0... ee 148 4,2 Probabilistic Propositional Logic .... 0.0.0.0... 050. 150 4.2.1 Probabilistic Models 2... 151 4.2.2 Language and Semantics. 2... 0... 0. 152 4.2.3 The Expressivity of Linear Combinations ...... 155 CONTENTS vii 4.2.4 ProofSystem .. 0... ee 158 4.2.5 Decidability and Complexity .........0.... 160 4.3 Probabilistic Epistemic Logic .........0.0, 0.0004 161 4.3.1 Probabilistic Relational Models ..........2.. 161 4.3.2 Language and Semantics... 1... ee 162 4.3.3 Expressivity of Linear Combinations ......... 168 4.3.4 ProofSystem . 2... ee 169 4.3.5 Decidability and Complexity ............. 170 4.4 Probabilistic Interpreted Systems ............00. 171 4.4.1 Adding Probabilities to Interpreted Systems ..... 171 44.2 Language and Semantics... 2.0.0.0..00.0. 173 4.4.3. Temporal and Dynamic Epistemic Logic ....... 174 4.5 Probabilistic Public Announcement Logic .......... 176 4.5.1 Language and Semantics... ..........005. 176 4.5.2 Proof System .. 0... 0. 181 4.5.3 Decidability and Complexity .........0.., 182 4.5.4 Higher-Order Information in Public Announcements 182 4.6 Probabilistic Dynamic Epistemic Logic. .........0.. 185 4.6.1 Probabilistic Product Update .......0..0.020. 185 4.6.2 Language and Semantics... . 2.0.0.2. .0005 189 4.6.3 ProofSystem ... 2. 191 4,7 Further Developments and Applications ........... 193 4.8 Conclusion. 2... 194 4.9 Notes . 2... 195 References. 0 0 198 II Dynamics of Informational Attitudes 203 5 Knowledge and Time 205 Clare Divon, Cléudia Nalon and Ram Ramanujam 5.1 Introduction. 2... 206 5.1.1 A temporal logic of knowledge ............ 206 5.1.2 Structural investigations... 207 0.2 Language 2... 209 B.2.1 Syntax... 209 5.2.2 Semantics 6... 0. ee 210 5.3 Complexity 2... 213 5.4 Expressiveness 2.00 217 5.4.1 First order fragments. 2... 217 5.4.2 Quantified extensions ..........0. 0004 219 vill CONTENTS 5.5 Axiomatisation . 2... 219 5.6 Reasoning... 221 5.6.1 Resolution... 0.0... 223 5.6.2 Tableau... 227 5.7 Knowledge and communication ............000.4. 233 5.7.1 The history based model... .........00.., 234 5.8 Levels of knowledge... 0. 0 235 5.9 Knowledge based semantics ........0..0. 0.00040, 237 5.10 Automata theory of knowledge .............004 239 5.10.1 Epistemic automata ........2..0.... .00 4 240 5.10.2 Finite state automata . 2... 2... 0.00e.ee 240 5.10.3 Distributed alphabets ................ ., 241 5.10.4 Epistemic transition systems ...........04 242 5.10.56 Behaviours 2... ee 245 5.11 Applications... 0. ee 247 5.12 Inconclusion ©. 249 5.13 Notes 2 ee 250 References. .... ee 254 6 Dynamic Epistemic Logic 261 Lawrence S. Moss 6.1 Introduction... 0. ee 262 6.1.1 Scenarios 2... 263 6.1.2 General notes on this chapter ........... .. 267 6.2 Public Announcements and PAL .............0.4 268 6.2.1 Public Announcement Logic PAL ..... eas 271 6.2.2 Announcing a true fact might falsify io. 273 6.2.3 Sound and complete logical systems ......... 275 6.2.4 Succinctness and complexity. ............0. 282 6.2.5 The substitution core ..........0 0.0005 284 6.3 AdditionstoPAL 2.. 00.00..00.. e.ee 284 6.3.1 Common knowledge and relativized common knowledge285 6.3.2 Iterated announcements ........., as 288 6.3.3 Arbitrary announcement logic... .....0.004, 290 6.4 More General Epistemic Actions ............04., 291 6.4.1 Private announcements and more general epistemic ACTIONS . 291 6.4.2 The update product .......0..... 0.00 . 293 6.4.3 Slower version of the update product ......... 296 6.4.4 DEL based on epistemic actions ........... 299 6.5 Conclusions... 0 ee 305 CONTENTS ix 6.6 Notes... 307 References... ......0.. ee 310 7 Dynamic Logics of Belief Change 313 Johan van Benthem and Sonja Smets 7.1 Basics of belief revision. . 2... ee 314 7.1.1 The AGM account of belief revision ........., 314 7.1.2 Conditionals and the Ramsey Test .......... 317 7.2 Modal logics of belief revision... . 0.0. ee ee 318 7.3 Static base logics 2... 322 7.3.1 Static logic of knowledge and belief... ......, 322 7.3.2 Plausibility models... 2.0.2...... 0.000 4 323 7.4 Belief revision by model transformations ........... 330 7.4.1 From knowledge to belief, hard and soft information 330 7.4.2 Belief change under hard information. ........ 331 7.4.3 From dynamics to statics: safe and strong belief... 332 7.4.4 Belief change under soft information: radical upgrade 333 7.4.5 Conservative upgrade and other revision policies .. 336 7.5 General formats for belief revision... . 0... 00.0000. 337 7.5.1 Relation transformers as PDL programs........ 337 7.5.2 Product update in general dynamic-epistemic logic . 338 7.5.3 Priority update... 2... ee 342 7.6 Belief revision and probability dynamics .........., 345 7.7 Time, iterated update, and learning... ........... 349 7.7.1 Epistemic temporal logic. 2... 2... 350 7.7.2 Protocols in dynamic epistemic logic ........., 353 7.7.3 Representing DEL inside temporal logic... ..... 355 7.74 Beliefs over time ... 0.0.0e.e 0.ee 356 7.7.5 Iterated belief upgrades and limit behavior ..... 357 7.7.6 From belief revision to formal learning theory .... 360 7.8 Belief, games, and social agency... ........0,00 . 363 7.8.1 erated beliefs in games... 0...e e, 363 7.8.2 Belief change in social networks. ........... 366 7.8.3 Informational cascades... .. 0.0.0.. .0 . 366 7.8.4 Influence in social networks ...........0... 370 7.9 Further directions... 0.0. 372 7.9.1 Postulational and constructive approaches ...... 372 7.9.2 Belief revision versus nonstandard consequence ... 375 7.9.3 Belief revision and evidence ..............4 375 7.9.4 Combining information and preference ........ 376 7.9.5 Group belief and merge ............0004 377 FI x CONTENTS 7.9.6 Belief revision and social choice ............ 378 7.10 Notes 2... 379 ! References... ee 385 III Applications 395 8 Model Checking Temporal Epistemic Logic 397 Alessio Lomuscio and Wojciech Penczek 8.1 Introduction... .... ee 398 8.2 Syntax and Semantics . 0... 0... 00.ee0e .ee n 400 8.2.1 Syntax... 400 8.2.2 Interpreted systems semantics ............, A401 8.2.3 Interleaved interpreted systems ............ 402 8.2.4 ‘Temporal-epistemic specifications ........., .. 403 8.3 OBDD-based Symbolic Model Checking ........... 405 8.3.1 State space representation and labelling ....... 406 8.3.2 MCMAS... 0.0.00... cee 410 8.4 SAT-based Symbolic Model Checking. ............ Ail 8.4.1 Bounded Model Checking .........0....00, 412 | 8.4.2 Unbounded Model Checking. ............. 415 | B43 VelCS. 0. eee, 418 8.5 Extensions to Real-Time Epistemic Logic .......... 418 8.5.1 Example... 0... ee = 420 8.6 Partial Order Reductions .............0.0, oe ee AQ] 8.6.1 Evaluation... .. 0.0.000 0.. 0.ee e ew 423 8.7 Notes . 2... ee ee Lee ee ey 424 References... ee 433 9 Epistemic Foundations of Game Theory 443 Giacomo Bonanno 9.1 Introduction... .....0.....00, ee 444 9.2 Epistemic Models of Strategic-Form Games ......... 445 9.3 Common Belief of Rationality: Semantics ........., 449 9.4 Common Belief of Rationality: Syntax ...........0, 453 9.5 Common Belief versus Common Knowledge ......... 458 9.6 Probabilistic Beliefs and Payoffs................ 466 9.7 Dynamic Games with Perfect Information .......... 469 9.8 The Semantics of Belief Revision ..........,.... A73 9.9 Common Belief of Rationality ...............0., ATA 9.10 Notes 2... 480
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