Relational and Kleene-Algebraic Methods in Computer Science: 7th International Seminar on Relational Methods in Computer Science and 2nd International Workshop on Applications of Kleene Algebra, Bad Malente, Germany, May 12-17, 2003, Revised Selected Pape PDF
Preview Relational and Kleene-Algebraic Methods in Computer Science: 7th International Seminar on Relational Methods in Computer Science and 2nd International Workshop on Applications of Kleene Algebra, Bad Malente, Germany, May 12-17, 2003, Revised Selected Pape
Lecture Notes in Computer Science 3051 CommencedPublicationin1973 FoundingandFormerSeriesEditors: GerhardGoos,JurisHartmanis,andJanvanLeeuwen EditorialBoard TakeoKanade CarnegieMellonUniversity,Pittsburgh,PA,USA JosefKittler UniversityofSurrey,Guildford,UK JonM.Kleinberg CornellUniversity,Ithaca,NY,USA FriedemannMattern ETHZurich,Switzerland JohnC.Mitchell StanfordUniversity,CA,USA MoniNaor WeizmannInstituteofScience,Rehovot,Israel OscarNierstrasz UniversityofBern,Switzerland C.PanduRangan IndianInstituteofTechnology,Madras,India BernhardSteffen UniversityofDortmund,Germany MadhuSudan MassachusettsInstituteofTechnology,MA,USA DemetriTerzopoulos NewYorkUniversity,NY,USA DougTygar UniversityofCalifornia,Berkeley,CA,USA MosheY.Vardi RiceUniversity,Houston,TX,USA GerhardWeikum Max-PlanckInstituteofComputerScience,Saarbruecken,Germany 3 Berlin Heidelberg NewYork HongKong London Milan Paris Tokyo Rudolf Berghammer Bernhard Mo¨ller Georg Struth (Eds.) Relational and Kleene-Algebraic Methods in Computer Science 7thInternationalSeminaronRelationalMethodsinComputerScience and2ndInternationalWorkshoponApplicationsofKleeneAlgebra BadMalente,Germany,May12-17,2003 RevisedSelectedPapers 1 3 VolumeEditors RudolfBerghammer Christian-Albrechts-Universita¨tzuKiel Institutfu¨rInformatikundPraktischeMathematik Olshausenstr.40,24098Kiel,Germany E-mail:[email protected] BernhardMo¨ller GeorgStruth Universita¨tAugsburg,Institutfu¨rInformatik Universita¨tsstr.14,86135Augsburg,Germany E-mail:{bernhard.moeller,georg.struth}@informatik.uni-augsburg.de LibraryofCongressControlNumber:2004106383 CRSubjectClassification(1998):F.4,D.2.4,F.3,I.1,I.2.3,G.2 ISSN0302-9743 ISBN3-540-22145-XSpringer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsare liabletoprosecutionundertheGermanCopyrightLaw. Springer-VerlagisapartofSpringerScience+BusinessMedia springeronline.com (cid:2)c Springer-VerlagBerlinHeidelberg2004 PrintedinGermany Typesetting:Camera-readybyauthor,dataconversionbyDA-TeXGerdBlumenstein Printedonacid-freepaper SPIN:11011163 06/3142 543210 Preface This volume contains the proceedings of the 7th International Seminar on Re- lational Methods in Computer Science (RelMiCS 7) and the 2nd International WorkshoponApplicationsofKleeneAlgebra.Thecommonmeetingtookplacein BadMalente(nearKiel),Germany,fromMayMay12–17,2003.Itspurposewas to bring together researchers from various subdisciplines of Computer Science, Mathematics and related fields who use the calculi of relations and/or Kleene algebra as methodological and conceptual tools in their work. This meeting is the joint continuation of two different series of meetings. Previous RelMiCS seminars were held in Schloss Dagstuhl (Germany) in Jan- uary 1994, Parati (Brazil) in July 1995, Hammamet (Tunisia) in January 1997, Warsaw (Poland) in September 1998, Quebec (Canada) in January 2000, and Oisterwijk (The Netherlands) in October 2001. The first workshop on applica- tions of Kleene algebra was also held in Schloss Dagstuhl in February 2001. To join these two events in a common meeting was mainly motivated by the sub- stantialcommoninterestsandoverlapofthetwocommunities.Wehopethatthis leads to fruitful interactions and opens new and interesting research directions. Thisvolumecontains23contributionsbyresearchersfromallovertheworld: 21 regular papers and two invited papers Choice Procedures in Pairwise Com- parison of Multiple-Attribute Decision Making Methods by Raymond Bisdorff andMarcRoubensandKleene Algebra with Relations byJulesDesharnais.The papers show that relational algebra and Kleene algebra have wide-ranging di- versity and applicability in theory and practice. Just to give an (incomplete) overview, the papers deal with problems appearing in software technology and program verification and analysis, the formal treatment of pointer algorithms andofalgorithmsformanyproblemsondiscretestructures,applicationsofrela- tions in combinationwith fixed points to investigate games,questions arising in the context of databases and data mining, the relational modeling of real-world situations,manytopicsfromartificialintelligencesuchasknowledgerepresenta- tion and acquisition, preference modeling and scaling methods, and, finally, the use of tools for prototyping and programming with relations and for relational reasoning. We are very grateful to the members of the program committee and the external referees for their care and diligence in reviewing the submitted papers. We also want to thank Ulrike Pollakowski-Geuther, Ulf Milanese, and Frank Neumann for their assistance; they made organizing this meeting a pleasant experience.Finally,wewanttothankGu¨ntherGedigaandGuntherSchmidtfor their help. March 2004 Rudolf Berghammer Bernhard Mo¨ller Georg Struth VIII Preface Program Committee Roland Backhouse (U. Nottingham, UK) Rudolf Berghammer (U. Kiel, Germany) Richard Bird (Oxford U., UK) Jules Desharnais (U. Laval, Canada) Ivo Du¨ntsch (Brock U., Canada) Marcelo Fr´ıas (U. Buenos Aires, Argentina) Ali Jaoua (U. Qatar, Qatar) Dexter Kozen (Cornell U., USA) Bernhard Mo¨ller (U. Augsburg, Germany) Oege de Moor (Oxford U., UK) Ewa Orl(cid:3)owska (U. Warsaw, Poland) Gunther Schmidt (U. Armed Forces, Munich, Germany) Harrie de Swart (U. Tilburg, The Netherlands) Joakim von Wright (˚Abo Akademi U., Finland) External Referees Hans Bherer Claude Bolduc Ernst-ErichDoberkat Woitek Dzik Thorsten Ehm Alexander Fronk Ali Jaoua Wolfram Kahl Michiel van Lambalgen Vincent Mathieu Damian Niwinski Eric Offermann Dominik Slezak Andrzej Slezak Georg Struth Michael Winter Sponsoring Institutions The generous support of the following institutions and companies is gratefully acknowledged: Deutsche Forschungsgemeinschaft EU COST Action 274 TARSKI Faculty of Engineering of Kiel University CrossSoft (Kiel) Lufthansa Revenue Services (Hamburg) Choice Procedures in Pairwise Comparison Multiple-Attribute Decision Making Methods Raymond Bisdorff1 and Marc Roubens2 1 Department of Management and Informatics UniversityCenter of Luxembourg [email protected] 2 Department of Mathematics University of Liege [email protected] Abstract. Weconsider extensionsof someclassical rational axioms in- troduced in conventional choice theory to valued preference relations. Theconceptofkernelisrevisitedusingtwoways:oneproposestodeter- minekernelswithadegreeofqualificationandtheotherpresentsafuzzy kernelwhereeveryelementofthesupportbelongstotherationalchoice setwithamembershipdegree.Linksbetweenthetwoapproachesisem- phasized. We exploit these results in Multiple-attribute Decision Aid to determinethegoodandbadchoices.Alltheresultsarevalidifthevalued preference relations are evaluated on a finiteordinal scale. 1 Introduction We consider a pair wise comparison multiple-attribute decision making proce- dure that assigns to each ordered pair (x,y),x,y ∈ A (the set of alternatives) a globaldegreeofpreferenceR(x,y).R(x,y) representsthe degreeto which xis weakly preferred to y. We suppose that R(x,y) belongs to a finite set L : {c ,c ,...,c ,...,c } 0 1 m 2m that constitutes a (2m+1)-element chain {c ,c ,...,c }. R(x,y) may be un- 0 1 2m derstoodas the level of credibility that “a is at least as good as b”.The set L is built using the values of R taking into consideration an antitone unary contra- diction operator ¬ such that ¬c =c for i=0,...,2m. i (2m−i) If R(x,y) is one of the elements of L, then automatically ¬R(x,y) belongs to L. We call such a relation an L-valued binary relation. We denote L(cid:2)m :{cm+1,...,c2m} and L≺m :{c0,...,cm−1}. If R(x,y) ∈ L(cid:2)m, we say that the proposition “(x,y) ∈ R” is L-true. If however R(x,y)∈L≺m, we say that the proposition is L-false. If R(x,y)=c , m the median level (a fix point of the negation operator) then the proposition “(x,y) ∈ R” is L-undetermined. If R(a,b) = c and R(c,d) = c ,c < c , it r s r s means that the proposition“a is at leastas goodas b” is less credible than“c is at least as good as d”. In the classical case where R is a crisp binary relation (m = 2, and R(x,y) is never rated c ; R(x,y) = c = 1 is denoted xRy and R(x,y) = c = 0 1 2 0 R.Berghammeretal.(Eds.):RelMiCS/Kleene-AlgebraWs2003,LNCS3051,pp.1–7,2004. (cid:4)c Springer-VerlagBerlinHeidelberg2004
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