Games, norms and reasons: Logic at the crossroads PDF
Preview Games, norms and reasons: Logic at the crossroads
Games, Norms and Reasons SYNTHESE LIBRARY STUDIESINEPISTEMOLOGY, LOGIC,METHODOLOGY,ANDPHILOSOPHYOF SCIENCE Editors-in-Chief: VINCENT F. HENDRICKS, University of Copenhagen, Denmark JOHN SYMONS, University of Texas at El Paso, U.S.A. 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, Krako´w, Poland VOLUME 353 For further volumes: http://www.springer.com/series/6607 Games, Norms and Reasons Logic at the Crossroads Editedby Johan van Benthem ILLC,UniversityofAmsterdam,TheNetherlandsandStanfordUniversity,USA Amitabha Gupta IndianInstituteofTechnologyBombay,India and Eric Pacuit TilburgUniversity,TilburgInstituteforLogicandPhilosophyofScience, TheNetherlands 123 Editors Prof.JohanvanBenthem Prof.AmitabhaGupta UniversityofAmsterdam AdiShankaracharyaMarg InstituteforLogic 503WhisperingWoods LanguageandComputation(ILLC) PowaiVihar,Bldg.3 SciencePark,P.O.Box94242 700076Powai,Mumbai 1090GEAmsterdam India TheNetherlands [email protected] [email protected] Asst.Prof.EricPacuit TilburgUniversity TilburgInstituteforLogic andPhilosophyofScience Warandelaan2 5037ABTilburg TheNetherlands [email protected] ISBN978-94-007-0713-9 e-ISBN978-94-007-0714-6 SetISBN978-94-007-0920-1 DOI10.1007/978-94-007-0714-6 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2011923658 (cid:2)c SpringerScience+BusinessMediaB.V.2011 Nopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorby anymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwritten permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Thisbookcontinuesaseriescalled“LogicattheCrossroads”ofwhichthefirstvol- umeappearedin2007.1Theseriestitlereflectsaviewofourdisciplineasavantage point for seeing new developments across academic fields, as well as a catalyst in making them happen. In particular, the editors feel that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, moreambitiousresearchagendaofunderstandingandenhancinghumanreasoning andintelligentinteractionintheirfullextent,whenceourtitle“Games,Normsand Reasons”. ThisbroadviewoflogicanimatedtheSecondIndianConferenceon“Logicand its Relationship with other Disciplines” held at IIT Bombay, Mumbai 2007, the originofmostofthepapersinthisvolume,whileafewadditionaloneshavebeen solicited by the editors to round out coverage. But the Mumbai conference also added a very concrete focus, by honouring one person who embodies the general trenddescribed,namelyProfessorRohitJivanlalParikh.Rohitstandsatthecross- roadsofmanyacademicdisciplines,andoftwomajorhumancultures,andwhyand howthisisso,isadmirablyexplainedintheCongratulatoryCitationthatwasread ataspecialeventatIITBombaycelebratingRohit’s70thbirthday.Thisdocument hasbeenreprintedhere,afterthefollowingbriefeditorialdescriptionofcontents. The papers in this volume do two things. First, they paint a lively portrait of modern logic as it is expanding today with many new themes and concerns. But at the same time, they include a gallery of friends and colleagues of Rohit’s who eagerly responded to our call for honouring him. The chapters to follow highlight major dimensions of his work and influence, in particular, his “Social Software” program for studying the procedural behaviour of interactive human agents with beliefsandpreferences. Horacio Arlo´ Costa and Arthur Paul Pedersen start off with a key interest of Parikh’s,viz.bridgingbetweenrealisticmodelsofhumanbehaviourandlogicbased 1LogicattheCrossroads:AnInterdisciplinaryView,AmitabhaGupta,RohitParikhandJohanvan Benthem,editors,AlliedPublishers,NewDelhi.RecentlyreissuedbySpringerPublishersunder thenewtitleProof,ComputationandAgency:LogicattheCrossroads. v vi Preface ones.TheyanalyzeGigerenzer’s“TaketheBest”algorithmforsuccessfuldecisions by bounded-rational agents, and show how it can be understood and taken further using formal models of choice and preference. Sergei Artemov continues with an account of “justification logics”, which merge ideas from proof theory and prov- ability logic with epistemic logic to arrive at rich and more realistic accounts of evidence in human reasoning that link up with formal epistemology. Next, Akeel Bilgramidiscussesakeyaspectofwhatholdscommunicationtogether,viz.mean- ingfuldiscourse,andarguesthatlinguisticmeaningsarenotnormativeinanydeep sense – while still fully acknowledging Wittgenstein’s insights about the norma- tivity of human intentions. Melvin Fitting follows up on his long-standing formal studies of logics of proofs, and gives a new proof of a “realization theorem” link- ing the epistemic logic S5 to its justification counterpart. Next, Sujata Ghosh and Fernando Vela´zquez-Quesada discuss current models of belief and belief change basedonnetworks,andrelatethesetothemorequalitativeonesfoundinepistemic and doxastic logic, including an account of successive dynamic steps that change a current belief network. Patrick Girard analyzes another crucial dynamic social scenario,viz.mergeofindividualpreferencesintoagroup-basedoneoverasetof outcomes. He shows how preference merging in structured groups receives a per- spicuoussemanticandaxiomaticformulationusingthetoolsofmodalanddynamic preferencelogic.AmyGreenwald,AmirJafariandCaseyMarksdevelopnewlinks between the fields of game theory and computational learning theory, both crucial ingredientsofintelligentinteraction–basedonanewnotionof“no-Φ-regret”.Vin- cent Hendricks returns to Parikh’s interests in the fit between formal models and ournaturalwaysofunderstandingknowledgeandinformation.Hegivesaninsight- fuldiscussionoftheintuitivedistinctionbetween“firstperson”and“thirdperson” perspectives,linkingthistoawiderangeofissuesfromphilosophytoeconomics. Dexter Kozen and Ganesh Ramanarayanan present another innovative social use of classical ideas from proof theory, developing a universal Horn equational logic with dynamic operations of “publish”, “cite” and “forget” which describe the ac- tualconstructionandmaintenanceofmathematicalknowledge.LawrenceMossre- turnstotheuseofnaturallanguageinhumaninteraction,andshowshowreasoning in natural language has interesting syllogistic subsystems allowing for negations that form a hitherto hardly explored level in between the classical Syllogistic and full-fledgedfirst-orderpredicatelogic.JeffParisandAlenaVencovska´consideran- othermajoraspectofournaturalreasoning,namely,itsuseofprobabilisticfeatures, whether quantitative, or qualitative with tags like “probably”. Linking up with De Finetti’s foundations of probability, they develop a sophisticated new version of Carnap’s inductive logic for monadic predicates which handles the right inference relations between agents’ degrees of belief. They also generalize this approach to binaryandhigher-orderpredicates,anddevelopitsmathematicaltheoryfurther,us- ing a new principle of “Spectrum Exchangeability”. Finally, R. Ramanujam and S.P. Suresh look at the central role of knowledge in reasoning about security pro- tocols.Thesemanticsofconventionalepistemiclogicsthrowsupchallenges,since cryptographicprimitivesincommunicationleadtoproblemsofunboundednessand Preface vii undecidability.Theauthorsproposeanalternativeepistemiclogicwhichisexpres- siveenoughwhileitsprotocolverificationprocedureisdecidable. Taken together, these papers show how logic can extend its scope without any sacrificeinrigourorfocus.Moreover,theirquality,andtheircastofauthors,speaks foritselfaboutRohitParikh’sintellectualbreadthandinfluence.Ithasbeenaplea- suretoarrangethistribute,andbeyondlogistics,theeditorshavelearnedalotinthe process. We end with a citation which was read during the 2007 Mumbai conference. The present volume has taken some time to appear, due to circumstances beyond ourcontrol,buttheeditorsfeelthatthesentimentsexpressedthenareasfreshand appropriateasever. Stanford JohanvanBenthem Bombay AmitabhaGupta Tilburg EricPacuit Dedication Ontheoccasionofhisseventiethbirthday,we,theparticipantsandorganizersofthe “SecondIndianConferenceonLogicanditsRelationshipwithOtherDisciplines”, acclaimandhonourProfessorRohitJivanlalParikhandcelebratehismanyextraor- dinaryachievementsandoutstandingcontributionsinhispursuitofknowledge. BornonNovember20,1936,hewaseducatedatMumbai,andthenatHarvard University, where he obtained degrees with highest honors in Physics (A.B.) and Mathematics(Ph.D.).Parikh’sromancewithLogicbeganwithacoursebyQuine. LateronhewassupervisedbyBurtonDrebenandHartleyRogers,writinghisdis- sertationontransfiniteprogressions,influencedbyandextendingworkofKreisel. Subsequently,RohitParikhtaughtatseveralprestigiousinstitutions,includingStan- ford, Boston and Punjab University. He has had a long and distinguished profes- sionalcareerthatcontinuestobeproductiveandinfluential.Afullsurveywouldbe lengthyindeed,butthefollowingmaybehighlighted: • formallanguagetheory,especiallyinherentlyambiguouslanguagesandsemilin- earsets, • mathematicallogic,specificallylengthsofproofsandfeasiblearithmetic, • logicincomputerscience,specificallydynamiclogicandlogicsofknowledge, • philosophical logic, especially vagueness, nonmonotonic reasoning, and belief revision, • socialsoftware,includingthelogicofgames. In a research career spanning five decades, these contributions were not only seminal, but shaped the direction of a field, sometimes even creating it. The work rangesbroadly,frommathematics,tocomputerscience,economics,andphilosophy. Nowonderthenthathiscurrentaffiliationis:“DistinguishedProfessorofComputer viii Preface Science,MathematicsandPhilosophy,GraduateCenter,andDept.ofComputerSci- ence,BrooklynCollege,CityUniversityNewYork.” AtthestartofhiscareerwhenworkingwithNoamChomskyasaresearchassis- tant,Parikhpublishedafundamentalpaperinautomatatheory.Thissubjectessen- tiallystartedwithapaperofKleenein1956,andParikh’spaperappearedin1966, so he was there almost at the beginning. Today Parikh’s theorem and the Parikh maparestandardtools.TheParikhmapsendseachwordoverann-letteralphabet to an n-dimensional vector whose components give the number of occurrences of thelettersintheword.Histheoremsays,inpart,thattheimageunderthismapof anycontext-freelanguageisalwaysasemi-linearset,afiniteunionoflinearsets.It followsthattheemptinessproblemforcontext-freelanguagesisdecidable.Aswith many of Parikh’s contributions, this was not an end-point, but a starting point for others. A quick internet search turns up many current papers using the automata- theoretictoolsthatParikhintroduced. It is a common observation today that some things computable in principle are not so in practice. Here Parikh made important early contributions. To study the strengthofexponentiationrelativetoadditionandmultiplication,oneneedsaweak background theory. In 1971 Parikh introduced bounded arithmetic, which is both weak and strong enough for the purpose. A vast stream of research in the founda- tionsofproofandcomputationhasmadeessentialuseofthistheory.Onefascinating resultfromParikh’s1971paperishisdemonstrationthatthereisatheoremofPeano Arithmeticforwhichanyproofissubstantiallylongerthanaproofthattheformula hasaproof.Anotherconcerns“feasible”integers,andisrelatedtotheSoritespara- dox. Suppose we add to Peano Arithmetic conditions asserting that 0 is a feasible number,adding1toafeasiblenumberyieldsanotherfeasiblenumber,andthereis anexplicitlydesignatedhugenumberthatisnotfeasible.Ofcoursethisisanincon- sistenttheory,butParikhshowedthatanyresultprovableinthistheorywithoutthe useofthenotionoffeasibilityininductions,andwhoseproofisoffeasiblelength, willinfactbeatheoremofPeanoArithmeticitself.Inparticular,provablecontra- dictionsmusthaveinfeasibleprooflengths–thefeasiblepartofthetheoryissafeto use. Movingtologicsofcomputation,propositionaldynamiclogicisafamouslogic ofaction,designedtoestablishfactsaboutcomputerprogrambehavior.Complete- nessofaproposedaxiomatizationwasadifficultproblem,withmorethanonein- correctsolutionproposedatthetime.Parikh(andindependently,Gabbay)gavethe firstcorrectcompletenessproof,thenhegaveasecondalongdifferentlinesinajoint paperwithDexterKozen.Inadditiontoitsimpactondynamiclogicitself,thiswork hashadasubstantialspill-overeffect,sinceParikh’smethodsturnedoutapplicable tosimilarlogicsaswell. In recent years, much of Parikh’s work has fallen under the general program of “social software.” Here the idea is to investigate the reasoning used by people in social interactions. Many apparently separate topics come together under this rubric.Ourreasoningofteninvolvesvagueterms.Parikhhascreatedandanalyzed algorithmsthatworkevenwithvaguenesspresent(inonepaperthisiswhimsically appliedtosortingsocksintopairs,wherecolormatchingcanbeonlyapproximate). Preface ix Also, everyday reasoning is often non-monotonic—we tend to make plausible de- faultassumptions,butmayhavetoretractthemwhenfurtherinformationcomesin, andParikhhasworkedonthis,aswellaswellastherelatedareaofbeliefrevision. Next,commonsensereasoningmaybeapproximate,buttheapproximationmaybe improved at the cost of further work. Parikh has, with his colleagues, created an interestingfamilyoflogicsthattakeexpenditureofeffortintoaccount.Finally,how societyvaluesthings,fromelectioncandidatestostocksandnormsofsocialbehav- ior, is studied mathematically in terms of game theory. In recent years, Parikh has made interesting contributions to game theory, and has trained students who have continuedthiswork. It is not easy to say, in simple terms, what the common thread to an oevre of Parikh’s scope and depth might be, over many years and across several areas. But perhaps it is this. Our actual reasoning, as opposed to the ideal represented by the tradition beginning with Principia Mathematica, is subject to limitations of time, space,uncertaintyofreal-worldfacts,vaguenessofconcepts,andthecomplexityof interaction between people. Parikh has made a series of formal contributions that, together, say that what we do in practice is not without form. There is logic and structurethere,thoughitmaybecomplexandstillimperfectlyunderstood.Parikh hasletthelightofreasonshineonsomeoftheterraincognitaofhumanthoughtand understanding.Thus,heisaninvestigatorintheWittgensteintradition,ratherthan inthatofRussell. Today,hisstudents,colleaguesandfriendswishtoexpresstheiradmirationfor allthatRohitParikhhasdoneandthemanycontributionshehasmade.Hehasbeen asourceofinspirationforallofus. Alsopractically,theideaofcreatingalogicbaseatIITBombayisasmuchhis as ours. He has been instrumental in urging his Indian colleagues to put in place anambitiousplanofnotmerelyorganizingConferencesandSchools,butbuilding something that will last for years, eventually becoming the foundation of a strong IndianSchoolinLogic.Hesays:“TherearealreadystrongIndianlogiciansoutside India.WhatweneednowisastronggroupinsideIndiatotrainbrilliantIndianminds andtotakeourrightfulplaceinthisrichintellectualcommunityintheworld.” This citation is presented to Professor Rohit Jivanlal Parikh in recognition of his seminal contributions and outstanding achievements in research, teaching, in- stitution building, and especially, for his dedication and wisdom, admired by his colleaguesandstudents,andrespectedbyall. TheParticipantsofICLA2 IITBombay,Mumbai,January9-11,2007
The list of books you might like
