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Belief Revision Meets Philosophy of Science LOGIC,EPISTEMOLOGY,ANDTHEUNITYOFSCIENCE VOLUME21 Editors ShahidRahman,UniversityofLilleIII,France JohnSymons,UniversityofTexasatElPaso,U.S.A. EditorialBoard JeanPaulvanBendegem,FreeUniversityofBrussels,Belgium JohanvanBenthem,UniversityofAmsterdam,theNetherlands JacquesDubucs,UniversityofParisI-Sorbonne,France AnneFagot-LargeaultCollègedeFrance,France BasvanFraassen,PrincetonUniversity,U.S.A. DovGabbay,King’sCollegeLondon,U.K. JaakkoHintikka,BostonUniversity,U.S.A. KarelLambert,UniversityofCalifornia,Irvine,U.S.A. GrahamPriest,UniversityofMelbourne,Australia GabrielSandu,UniversityofHelsinki,Finland HeinrichWansing,TechnicalUniversityDresden,Germany TimothyWilliamson,OxfordUniversity,U.K. Logic,Epistemology,andtheUnityofScienceaimstoreconsiderthequestionoftheunityofscience in light of recent developments in logic. At present, no single logical, semantical or methodological frameworkdominatesthephilosophyofscience.However,theeditorsofthisseriesbelievethatformal techniqueslike,forexample,independencefriendlylogic,dialogicallogics,multimodallogics,game theoreticsemanticsandlinearlogics,havethepotentialtocastnewlightonbasicissuesinthediscussion oftheunityofscience. Thisseriesprovidesavenuewherephilosophersandlogicianscanapplyspecifictechnicalinsightsto fundamentalphilosophicalproblems.Whiletheseriesisopentoawidevarietyofperspectives,including thestudyandanalysisofargumentationandthecriticaldiscussionoftherelationshipbetweenlogicand thephilosophyofscience,theaimistoprovideanintegratedpictureofthescientificenterpriseinallits diversity. Forfurthervolumes: http://www.springer.com/series/6936 · Erik J. Olsson Sebastian Enqvist Editors Belief Revision Meets Philosophy of Science 123 Editors Prof.ErikJ.Olsson SebastianEnqvist UniversityofLund UniversityofLund Dept.Philosophy Dept.Philosophy Kungshuset Kungshuset 22222Lund 22222Lund Sweden Sweden erik_j.olsson@fil.lu.se Sebastian.Enqvist@fil.lu.se ISBN978-90-481-9608-1 e-ISBN978-90-481-9609-8 DOI10.1007/978-90-481-9609-8 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2010938250 ©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) Editor’s Introduction Belief revision theory and philosophy of science both aspire to shed light on the dynamicsofknowledge–onhowourviewoftheworldchanges(typically)inthe lightofnewevidence.Yetthesetwoareasofresearchhavelongseemedstrangely detachedfromeachother,aswitnessedbythesmallnumberofcross-referencesand researchers working in both domains. One may speculate as to what has brought about this surprising, and perhaps unfortunate, state of affairs. One factor may be thatwhilebeliefrevisiontheoryhastraditionallybeenpursuedinabottom-upman- ner,focusingontheendeavorsofsingleinquirers,philosophersofscience,inspired bylogicalempiricism,havetendedtobemoreinterestedinscienceasamulti-agent oragent-independentphenomenon. The aim of this volume is to build bridges between these two areas of study, the basic question being how they can inform each other. The contributors seek their answers by relating the logic of belief revision to such concepts as expla- nation, coherence, induction, abduction, interrogative logic, conceptual spaces, structuralism, idealization, research agendas, minimal change and informational economy. Our aim in putting together this volume has been to provide a number of new perspectives that are likely to stir research in new directions, as well as to estab- lish new connections between areas previously assumed unrelated, e.g. between belief revision, conceptual spaces and structuralism. The result is, we believe, a coherent volume of individual papers complementing and shedding light on each other. Wehavebeenveryfortunatetobeabletoattract,ascontributorstothisvolume, some of the best researchers in their respective fields of philosophy, cognitive sci- enceandlogic,aswellassomeexceptionalscholarsintheyoungergeneration.We areextremelyproudtohavetheirarticlesinthevolume,andwethankthemallfor theirdedicationandfinescholarship. We hope that this volume will contribute to a greater degree of interaction betweenthefieldsofbeliefrevisiontheoryandthephilosophyofscience.Forthis reason, we hope that the essays included here will be read by researchers in both fields. However, the fundamental concepts in the philosophy of science are prob- ably known to a significantly wider audience than belief revision theory. For this v vi Editor’sIntroduction reason,inordertofacilitateforthosereadersnotpreviouslyacquaintedwithbelief revisiontheory,abriefintroductionseemsinorder. Belief revision theory is a branch of formal epistemology that studies rational changesinstatesofbelief,orrationaltheorychanges.Theclassicframeworkhere, andthebestknownone,isthesocalledAGMtheory,namedafteritscreatorsCarlos Alchourrón,PeterGärdenforsandDavidMakinson,whichoriginatedinaseriesof papersintheeighties.Sincethen,aratherlargenumberofalternativeframeworks haveemerged,whichgeneralizeordeviatefromAGMinvariousways.Butforthe purposeofintroducingthenovicetobeliefrevisiontheory,asummaryoftheAGM theory will be enough to give a sense of how belief revision works and what it is about. The basic way of representing belief states in the AGM theory is to equate an agent’sstateofbelief(atsomegiventime)withalogicallyclosedsetofsentences K,i.e.suchthatK=Cn(K)whereCndenotestheoperationoflogicalclosure.Thus, thelogicalconsequencesofanagent’sbeliefsarealsocountedasbeliefsinAGM. SuchasetKissometimesreferredtoasa“theory”,sometimesasa“beliefset”. Let α = “Charles is in his office” and let β = “Charles is at home”. Let K = 1 Cn({∼α→β}). Then K expresses the state of belief where it is believed that “if 1 Charlesisnotinhisoffice,thenheisathome”.Now,saythatwelearnthatCharles is not in his office. Then we need to alter our initial belief state K to include this 1 new belief. How do we do this, rationally? Simply adding the sentence ∼α to K 1 willnotdo,sincethesetK ∪{∼α}isnotlogicallyclosed,i.e.itisnotabonafide 1 beliefset.Whatweneedtodoistofirstadd∼αtoK ,andthenclosetheresultunder 1 logicalconsequences.Thisgeneralrecipegivesrisetotheoperationofexpansion, oneofthethreebasicoperationsonbeliefsetsinAGM.Theexpansionofabelief setKbyasentenceα,denotedK+α,isdefinedbysetting K+α = Cn(K∪{α}) df. In our case, the new belief set K +∼α after learning that Charles is not in his 1 officeisCn({∼α →β,∼α}).Thisnewbeliefsetincludesthesentenceβ,i.e.upon learning that Charles is not in his office, we come to believe that Charles is not at home. Let us denote this new belief set by K . Say that we now learn that Charles is 2 not at home. Then we want to add the sentence ∼β to K . If we expand again at 2 this point, we run into some trouble: since β is in K , the expanded set K + ∼ β 2 2 contains a contradiction, and so by logical closure (assuming that the underlying logic contains the classical validities) K + ∼ β will contain all sentences in the 2 language – it is a state where we believe everything. This awkward situation has been referred to as “epistemic hell”, and is clearly unattractive. We would like to avoid this consequence, and update the initial state K with ∼β while preserving 2 consistency. This enters us into the area where belief revision theory becomes interesting. The operation used for updating a belief state while maintaing consistency in cases like the one above is called revision. The revision of a belief set K by a sentence α is denoted K∗α. A useful way of analysing the problem of revision is Editor’sIntroduction vii byintroducingathirdoperator:contraction.TakethebeliefsetK again;wewould 2 like to add ∼β to this belief set without creating an inconsistency. In order to do this,wehavetoremovesomething,inparticularwehavetoremovethenegationof ∼β, or equivalently, β. Inorder to do this,we have toremove some of our earlier beliefs,∼α and∼ α → β sincetheyjointlyimplyβ.Now,wecouldremoveboth these beliefs of course – this would certainly make room for ∼β – but that would not be very economical, since removing either of ∼α or ∼ α → β while keeping theotherwouldsuffice.Beliefsarevaluablethings,andarationalagentshouldnot bewillingtogiveupmoreofhisbeliefsthanwhatisnecessary.Thisintuitionisone oftheguidingprinciplesinAGM,andusuallygoesunderthenameoftheprinciple ofminimalchange.Contractionisintendedasanoperationthatremovesasentence fromagivenbeliefsetinaccordancewiththisprinciple. The contraction of a belief set K by a sentence α is denoted K ÷ α. Given a suitable operator ÷ of contraction, we can define a revision operator ∗ by setting, forallα: K∗α = .(K÷∼α)+α df Intuitively:toreviseKbyαistofirstremovethenegationofα(to“makeroom” for α) and then expand with α. The definition is commonly known as the Levi identity,afterIsaacLevi. Withthisdefinition inplace, the problem of revisionreduces totheproblem of contraction. Thus we are left with the task of devising a satisfactory account of contraction. The way AGM handles this problem can be divided into two distinct approaches:wemaycallonetheaxiomaticapproach,andtheothertheconstructive approach. The axiomatic approach consists in narrowing down the class of ratio- nallyadmissiblecontractionfunctionsbysettingupalistof(intuitivelyplausible) postulatesforcontraction.ThefollowingsixpostulatesareknownasthebasicAGM postulatesforcontraction: (closure) K÷α =Cn(K÷α) (success)α ∈/ Cn(Ø)impliesα ∈/ K÷α (inclusion)K÷α ⊆K (vacuity)α ∈/ K impliesK÷α =K (extensionality)Cn(α)=Cn(β)impliesK÷α =K÷β (recovery)K ⊆(K÷α)+ α ·· Thislistisusuallyextendedwiththefollowingtwosupplementarypostulates: (conjunctiveinclusion)α ∈/ K÷(α∧β)impliesK÷(α∧β)⊆K÷α (conjunctiveoverlap)K÷α∩K÷β ⊆K÷(α∧β) Thepostulatesallhavesomeintuitivejustification.Forinstance,thesuccesspos- tulate says that an admissible contraction operator ÷ should do its job properly wheneverpossible,i.e.ifα isnotatautologyandsocanberemovedfromKwhile maintaininglogicalclosure,then÷shouldsuccesfullyremoveit.The(highlycon- troversial) recovery postulate gives a first formal expresssion to the principle of viii Editor’sIntroduction minimalchange:whenwecontractbyα,weshouldkeepsomuchinformationthat wecanregainallourinitialbeliefsbyexpandingwithαagain.Asimilarsetofpos- tulatesforrevisionexists,andthesepostulatesaresatisfiedbyanyrevisionfunction which is defined from a contraction function satisfying the postulates above (and conversely,ifacontractionfunctiongivesrisetoarevisionfunctionthatsatisfiesthe AGMpostulatesforrevision,thenthisfunctionmustsatisfytheabovepostulatesfor contraction). Theconstructiveapproachconsistsindevisingexplicitconstructionsofcontrac- tion functions. Apart from the socalled partial meet contractions, the construction mostfrequentlydiscussedthesedaysisprobablythemethodofentrenchmentbased contraction.Thismethodusesanauxiliaryconceptcalledanentrenchmentrelation, which is a binary relation over the language associated with a given belief set K, satisfyingthefollowingpostulates: (transitivity)α ≤β andβ ≤ χ impliesα ≤ χ (dominance)β ∈Cn(α)impliesα ≤β (conjunctiveness)eitherα ≤(α∧β)orβ ≤(α∧β) (minimality)if⊥ ∈/ K thenα ∈/ K iffα ≤β forallβ ∈L (maximality)β ≤α forallβ onlyifα ∈ Cn(Ø) Given a belief set K with an associated entrenchment order ≤, we can define a correspondingentrenchmentbasedcontractionfunction÷bysetting,forallα: K÷α = {β ∈K |α <α∨β orα ∈Cn(Ø)} df. The intuition here is that the entrenchment order encodes how entrenched the various beliefs in K are in comparison to each other, or which beliefs the agent would prefer to give up if a choice has to be made. Entrenchment based contrac- tionsarethendesignedsoastoremovelessentrenchedbeliefsinfavorofthemore entrenchedones. How are the axiomatic approach and the constructive approach related to each other?Itturnsoutthattheyareverycloselyrelated:everyentrenchmentbasedcon- tractionsatisfiestheAGMpostulatesforcontraction(includingthesupplementary postulates), and vice versa, if a contraction function satisfies the AGM postulates, then there exists an entrenchment order which defines it. In a sense, the AGM postulates are sound and complete with respect to entrenchment based contractions. This result is one of the celebrated representation theorems of the AGM framework. Draftsofmostofthepapersthatappearinthisvolumewereoriginallypresented at the first Science in Flux conference, organized by Olsson, at Lund University in 2007. (A follow-up conference was organized by Pierre Wagner in 2008 at the CNRSinParis.)Beforetheyweresubmittedintheirfinalversions,thepaperswere revised, often substantially, in order to accommodate various critical points that emerged in the (very lively) discussion at the conference. It has been pointed out to us that there is already a book called “Science in Flux”, by J. Agassi, which Editor’sIntroduction ix appearsintheBostonStudiesinthe1970s.Asfaraswecansee,thereislittleover- lap between the books, and little risk for conflating one with the other, and so we hopeweareexcusedforreusingthetitle. Weshallbrieflypresenteachoftheindividualcontributions: RaúlCarnotaandRicardoRodríguez Intheircontribution,RaúlCarnotaochRicardoRodrígueztakeacloserlookat thehistorybehindtheinfluentialAGMmodelofbeliefrevisionduetoAlchourron, Gärdenfors and Makinson. The AGM theory, as described in the seminal 1985 paper “On The Logic of Theory Change: Partial Meet Contractions and Revision Functions”, had a major influence in most subsequent work on belief change. In particular,theconstructiveapproachspelledoutinthepaperwasadoptedinAIas a paradigm for how to specify updates of knowledge bases. Throughout the years there has been a steady stream of references to that original AGM paper. Going onestepfurther,CarnotaandRodréguezaskthemselveswhytheAGMtheorywas so readily accepted within the AI community, their answer being partly that the theorywasputforwardatacriticaltimeinthehistoryofAIatwhichtheproblem of how to update knowledge bases in the face of input possibly inconsistent with thepreviouscorpuswastakentobeofutmostimportance.Thepaperalsocontains a qualitative and quantitative evaluation of the impact of the AGM theory in AI researchaswellasanaccountofhowthetheoryhassubsequentlybeendeveloped indifferentdirections. SvenOveHansson Thereisaclearconnectionbetweenbeliefrevisiontheoryandoneofthemajor problems within the philosophy of science, the problem of modelling and under- standingthedynamicsofempiricaltheories;boththesefieldsofresearchdealwith thewaytheoriesareupdatedinthelightofincomingdata.Infact,severalofthemost influential ideas in 20th century philosophy of science, e.g. Popper’s hypothetico- deductive method, Kuhn’s theory of paradigm shifts, Lakatos’s ideas concerning the “hard core” and the “protective belt” etc. seem to be in essence theories about thedynamicsoftheories.Thatis,thesetheoriesapparentlyaddresstheverysubject matterofbeliefrevisiontheory.Giventhisconnection,itissomewhatstrikingthat there has been so little contact between the two fields. Hansson draws the conclu- sion that belief revision theory as it stands is unsuitable for modelling changes in empiricaltheories,andsetsouttodevelopaframeworkwhichisbettersuitedforthis task.Hedrawssomefirstcontoursofamodelwherescientificchangeistreatedas apartlyaccumulativeprocess,throughwhichobservationaldataisaddedpiecewise andtheoreticalhypothesesareaddedbyaclosureoperatorrepresenting“inference tothebestexplanation”.Asetofpostulatesforthisoperatorisprovided,andthree versionsofamodeloftheorychangeareintroducedanddiscussedinthetext. HansRott ScientificchangeisalsothemainissueaddressedbyHansRott.Inhispaper,Rott posestheproblemofhow,exactly,toexplicatetheLakatosiannotionofa“progres- sive problem shift” that plays a crucial role in the understanding of how research