Trends in Logic 38 Christian Straßer Adaptive Logics for Defeasible Reasoning Applications in Argumentation, Normative Reasoning and Default Reasoning Trends in Logic Volume 38 For furthervolumes: http://www.springer.com/series/6645 TRENDS IN LOGIC Studia Logica Library VOLUME 38 Managing Editor Ryszard Wójcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland Editors Wieslaw Dziobiak, University of Puerto Rico at Mayagüez, Mayagüez, USA Melvin Fitting, City University of New York, New York, USA Vincent F. Hendricks, Department of Philosophy and Science Studies, Roskilde University, Roskilde, Denmark Daniele Mundici, Department of Mathematics ‘‘Ulisse Dini’’, University of Florence, Florence, Italy Ewa Orłowska, National Institute of Telecommunications, Warsaw, Poland Krister Segerberg, Department of Philosophy, Uppsala University, Uppsala, Sweden Heinrich Wansing, Institute of Philosophy, Dresden University of Technology, Dresden, Germany SCOPE OF THE SERIES Trends in Logic is a book series covering essentially the same area as the journal Studia Logica—that is, contemporary formal logic and its applications and rela- tions to other disciplines. These include artificial intelligence, informatics, cog- nitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time. Volume Editor Heinrich Wansing Christian Straßer Adaptive Logics for Defeasible Reasoning Applications in Argumentation, Normative Reasoning and Default Reasoning 123 Christian Straßer Ghent University Ghent Belgium ISSN 1572-6126 ISSN 2212-7313 (electronic) ISBN 978-3-319-00791-5 ISBN 978-3-319-00792-2 (eBook) DOI 10.1007/978-3-319-00792-2 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013940955 (cid:2)SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. 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While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Dedicated to all the birds who cannot fly Especially to Kiwis. . . Sorry, Tweety, next time! Preface In this book I will study defeasible reasoning. There are many facts of reasoning that are captured under the term defeasible. Sometimes we argue on the basis of typicality, normality, sometimes we make inductive generalizations, etc. We ‘‘jump to conclusions’’ in different ways. It is not my intention to give an exhaustive characterization of all possible forms of defeasible reasoning. Hence I will paradigmatically examine various contexts in which defeasible reasoning is useful, such as default reasoning (Part II), reasoning in the context of argumen- tation (Part III), and normative reasoning (Part IV). Still,myperspectiveisaunificatoryone.Itisgainedbythechoiceofaspecific formal logical framework. With the help of this framework I will develop logical modelsofformsofdefeasiblereasoning.Theframeworkisthatofadaptivelogics which originates in the work of Diderik Batens. The standard format of adaptive logics provides a unified characterization of a class of logics that, as will be demonstratedandarguedforinthismanuscript,aredecenttoolsinordertomodel defeasible reasoning. The merits of the study offered in this book are two-fold. First,itoffersadeeperunderstandingof(formsof)defeasiblereasoning.Onthe one hand, the logics that are introduced in this manuscript deepen our under- standing of the formal properties (particular forms) of defeasible inferences, of retracting inferences, etc. On the other hand, formulating them in a unificatory framework offers possibilities to compare them and to identify formal properties they have in common. Second, the book affirms and substantiates the status of adaptive logics as a generic formal framework for defeasible reasoning. It does so by offering case studies stemming from various contexts of defeasible reasoning. In addition, as will be shown, there are various metatheoretic advantages of adaptive logics compared to many other logics or logical frameworks that model defeasible reasoning. vii viii Preface The Structure of the Book This book is structured as follows: InPartIwebeginwithageneralintroductionintodefeasiblereasoning(Chap.1). After that, adaptive logics (in short, ALs) are introduced (Chap. 2). It is demon- strated that they offer an intuitive and powerful framework to model defeasible reasoning.ALsarediscussedintheirstandardformat.Itisarguedthatthestandard formatcomeswithanattractivemeta-theory.InChap.3,itisshownhowALscanbe combined.Chapter4containsjointworkwithDiderikBatensandPeterVerdée.We arguethatALsofferatransparentmodelfordefeasiblereasoningsinceelegantand intuitive criteria are available to decide whether (extensions of) premise sets are equivalent.Finally,inChap.5,itisdemonstrated howthestandardformatcanbe generalized while keeping its metatheoretic merits intact. This is joint work with FrederikVanDePutte. PartIIcontainstwoapplicationsofALsinthecontextofdefaultreasoning.Let A B express that from A normally/usually/typically/etc. (depending on the application)followsB.NotethatModusPonensisnotunrestrictedlyvalidinsuch acontext.Thisisduetocasesofspecificity.Wherebstandsfor‘‘beingabird’’and ffor ‘‘flying’’, we have b [ f (‘‘Birds usually fly’’). However, where p stands for ‘‘being a penguin’’, we also have (p^b) : f. Now suppose we have both premises, p and b. If Modus Ponens would be valid we would be able to derive bothfand:f.Obviouslythisisnotdesired.InChap.6,Iwillproposeadefeasible handling of Modus Ponens by means of ALs. In [1] Lehmann, Magidor and Kraus tackle the question ‘‘What does a condi- tional knowledge base entail?’’ by means of a sophisticated semantic selection procedure,theso-calledRationalClosureofaknowledgebase.Chapter7offersan AL interpretation of Rational Closure. This way we gain a full logic for Rational Closure, one that is equipped with a (dynamic) proof theory. The semantic selection of [1] is very much in the spirit of Shoham’s semantic selections (see e.g., [2]). Hence, the logic developed in Chap. 7 offers a paradigmatic demon- strationthatALsareabletorepresentlogicsdefinedbysemanticselectionsinthe styleofShoham.ThisinturnsubstantiatestheclaimthatALsofferaverygeneric and unifying framework for defeasible reasoning. InPartIII,ALsareusedforthemodelingofargumentations.Dungpresentedin [3] a highly influential account of abstract argumentation. Arguments are repre- sentedasabstractentitiesandtherelationshipsbetweenargumentsaremodeledby anattackrelation.Thetwoelementsdefineabstractargumentationsystems.Dung offered a number of clear and intuitive semantics for selecting arguments from argumentationsystems.Chapter8presentsjointworkwithDunjaŠešeljainwhich we develop a unifying AL framework for abstract argumentation. Our family of logics models all the semantics proposed by Dung and moreover provides a dynamic proof-theory for each. In Chap. 9 I generalize the AL framework in accordance with Nielsen and Parsons’ generalization of Dung’s framework [4] in such away thatjointattacksare possible,i.e.,attacksinwhich several arguments Preface ix attack several arguments. This paradigmatically presents one of many possible enhancements to the systems introduced in Chap. 8. Part IV features various applications of ALs in the context of deontic logics. Most of the systems presented in this part are heavily influenced by the work of LouGoble.Oneofthemainchallengesfordeonticlogiciansistodevelopsystems that are conflict-tolerant. That is to say, logics that do not exhibit explosive behaviorwhenconfrontedwithconflictingnormssuchas‘‘You’reobligedtobring about A’’ and ‘‘You’re obliged to bring about not-A’’. Goble suggested an attractive way of tackling this problem, namely by restricting the so-called inheritance rule that allows to derive from the obligation to bring about A the obligation to bring about B in the case in which A necessitates B. Chapter 10 presentsjointworkwithJokeMeheusandMathieuBeirlaeninwhichwepointout certain problems with Goble’s systems and improve on them by strengthening them by means of ALs. The remaining sections in Part IV feature applications in the context of con- ditional deontic logics. Chapter 11 generalizes and enhances the results of Chap. 10 for the conditional setting. In Chap. 12, I tackle a similar problem as in Chap. 6. The majority of conditional deontic logics does not allow for the factual detachment of conditional obligations. That is to say, given the commitment AundertheconditionBandthefactualinformationB,inmanycircumstancesitis desired that we derive the ‘actual’ and unconditional obligation to bring about A. However, similar as in the context of default reasoning, here we have to deal withcasesofspecificityaswell.Moreover,wealsohavetotakeintoconsideration contrary-to-duty obligations. This motivates a defeasible handling of detachment. It is realized by means of ALs. Ghent, March 2013 Christian Straßer References 1.Lehmann, D.J., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1),1–60(1992) 2.Shoham, Y.: A semantical approach to nonmonotonic logics. In: Ginsberg, M.L. (ed.) ReadingsinNon-MonotonicReasoning,pp.227–249.MorganKaufmann,LosAltos(1987) 3.Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning,logicprogrammingandn-persongames.Artif.Intell.77,321–358(1995) 4.Nielsen,S.H.,Parsons,S.:AgeneralizationofDung’sabstractframeworkforargumentation: Arguing with sets of attacking arguments. In: Maudet, N., Parsons, S., Rahwan, I. (eds.) Argumentation in Multi-Agent Systems, Lecture Notes in Computer Science, vol. 4766, pp.54–73.Springer,Heidelberg(2006) Acknowledgments I wish to thank the following persons: • FirstandforemostmyPh.D.-supervisorsJokeMeheusandDiderikBatens:Iwas abletolearnalotfromthemsinceIbeganworkingattheCLPS.Theirworkon adaptive logics has been deeply inspiring andforms the very foundation ofthis book.Iamthankfulforalltheeffortandtimetheyhaveinvestedinguidingand assisting my research. • Lou Goble for his fascinating and inspiring work on deontic logics on which a part of this book is based. • Leon Van Der Torre, Lou Goble, Peter Verdée, and Erik Weber for their excellent feedback on my Ph.D.-thesis which was very useful for this manuscript. • Myco-authorsandcollaboratorsMathieuBeirlaen,DunjaŠešelja,FrederikVan DePutte,andPeterVerdée:Ithasbeenandisagreatpleasuretoworkwithyou. I couldn’t wish for better collaborators. • My great professors of philosophy Wilhelm Lütterfelds and Thomas Mohrs for evoking my fascination and sharpening my thinking in the subject, and for keeping me deeply inspired while struggling with philosophical problems. I couldn’t have wished for better teachers. • Two most remarkable professors of mathematics and computer sciences to whose teaching I was addicted since its crystal clearness shines like an arche- typeofformalthinking:VolkerWeispfennig,forevokingmyfascinationforthe beauty of algebra, mathematical logic, and model theory. Klaus Donner, for teaching me that the choice of the right formal mathematical tools can enable one to master even the most difficult problems with ease. The razor-sharp and perfectly ordered thinking of the both of them will keep on being an inspira- tional source and force to me. • Thomas Sturm, from whom I learned a lot about writing a thesis properly. He would have been my Ph.D.-supervisor if I had stayed inComputer Science. If a day would have 48 hours I wouldn’t have hesitated a second. • My family for all the support they have given me when and since I moved to Belgium. xi