Relational and Algebraic Methods in Computer Science: 12th International Conference, RAMICS 2011, Rotterdam, The Netherlands, May 30 – June 3, 2011. Proceedings PDF
Preview Relational and Algebraic Methods in Computer Science: 12th International Conference, RAMICS 2011, Rotterdam, The Netherlands, May 30 – June 3, 2011. Proceedings
Lecture Notes in Computer Science 6663 CommencedPublicationin1973 FoundingandFormerSeriesEditors: GerhardGoos,JurisHartmanis,andJanvanLeeuwen EditorialBoard DavidHutchison LancasterUniversity,UK TakeoKanade CarnegieMellonUniversity,Pittsburgh,PA,USA JosefKittler UniversityofSurrey,Guildford,UK JonM.Kleinberg CornellUniversity,Ithaca,NY,USA AlfredKobsa UniversityofCalifornia,Irvine,CA,USA FriedemannMattern ETHZurich,Switzerland JohnC.Mitchell StanfordUniversity,CA,USA MoniNaor WeizmannInstituteofScience,Rehovot,Israel OscarNierstrasz UniversityofBern,Switzerland C.PanduRangan IndianInstituteofTechnology,Madras,India BernhardSteffen TUDortmundUniversity,Germany MadhuSudan MicrosoftResearch,Cambridge,MA,USA DemetriTerzopoulos UniversityofCalifornia,LosAngeles,CA,USA DougTygar UniversityofCalifornia,Berkeley,CA,USA GerhardWeikum MaxPlanckInstituteforInformatics,Saarbruecken,Germany Harrie de Swart (Ed.) Relational and Algebraic Methods in Computer Science 12th International Conference, RAMICS 2011 Rotterdam, The Netherlands, May 30 – June 3, 2011 Proceedings 1 3 VolumeEditor HarriedeSwart ErasmusUniversityRotterdam FacultyofPhilosophy P.O.Box1738,3000DRRotterdam,TheNetherlands E-mail:[email protected] ISSN0302-9743 e-ISSN1611-3349 ISBN978-3-642-21069-3 e-ISBN978-3-642-21070-9 DOI10.1007/978-3-642-21070-9 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:Appliedfor CRSubjectClassification(1998):F.4,I.1,I.2.3,D.2.4,D.3.4 LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues ©Springer-VerlagBerlinHeidelberg2011 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable toprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:Camera-readybyauthor,dataconversionbyScientificPublishingServices,Chennai,India Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface This volume contains the proceedings of the 12th International Conference on Relationaland Algebraic Methods in Computer Science (RAMiCS 2011)with a special track on Computational Social Choice and Social Software. The confer- ence took place in Rotterdam, The Netherlands, from May 30 to June 3, 2011. Overthepast20years,theRelMiCS(RelationalMethodsinComputerScience) andAKA(Applications ofKleeneAlgebra)conferenceshavebeenamainforum forresearcherswhousethecalculusofrelationsandsimilaralgebraicformalisms as methodological and conceptual tools. At the last of these conferences it was decided that the two series should be united under the new title “Relational and Algebraic Methods in Computer Science” (RAMiCS). This year, special attentionwas paid to the fact that the meetings started 20 yearsagoat the Ba- nach Center in Warsaw.It was commemorated with an invited lecture by Chris Brink, who, together with Ewa Orlowska and Gunther Schmidt, was one of the originators of this series. Relationaland algebraicmethods andsoftware tools likeRelView turn out tobeusefulforsolvingproblemsinsocialchoiceandgametheory.Forthatreason this conference included a special track on Computational Social Choice and Social Software, organized by the CFSC (Computational Foundations of Social Choice)andSSEAC(SocialSoftwareforElections,theAllocationoftendersand Coalition formation) projects of the ESF LogiCCC programme. Each submission was reviewed by three Programme Committee members. The committee decided to accept 18 papers. The programme also included five invited talks, ofwhich three were on relationaland algebraicmethods, by Chris Brink, Bernhard Mo¨ller (included) and Renate Schmidt (included), and two on social choice theory, by Donald Saari and Agnieszka Rusinowska (included). In addition, there were two tutorials on relational and algebraic methods, by GeorgStruth(included)andMichaelWinter(included),andtwoonsocialchoice theory, by Donald Saari (included) and Felix Brandt (included). These tutori- als were part of a special PhD programme, where PhD students also had the opportunity to present their work in progress. I am very grateful to the members of the Programme Committee and the external referees for their care and diligence in reviewing the submitted papers. I would also like to thank the Faculty of Philosophy of the Erasmus University in Rotterdam for having accepted to host this conference, in particular Willy Ophelders, Amanda Koopman, Linda Degener and Lizzy Patilaya for their as- sistance. I also gratefully appreciate the excellent facilities offered by the Easy- Chairconferenceadministrationsystem.LastbutnotleastIwouldliketothank the European Science Foundation (ESF) and the Erasmus Trust Fund for their generous financial support. March 2011 Harrie de Swart Conference Organization Programme Chair Harrie de Swart Rotterdam, The Netherlands Programme Committee Rudolf Berghammer University of Kiel, Germany Felix Brandt Technical University Munich, Germany Jules Desharnais Laval University, Canada Ulle Endriss University of Amsterdam, The Netherlands Marcelo Frias University of Buenos Aires, Argentina Hitoshi Furusawa University of Kagoshima,Japan Peter H¨ofner University of Augsburg, Germany Ali Jaoua University of Qatar, Qatar Peter Jipsen Chapman University, USA Wolfram Kahl McMaster University, Canada Larissa Meinicke Macquarie University, Sydney, Australia Bernhard M¨oller University of Augsburg, Germany Ewa Orlowska National Institute of Telecommunications, Warsaw, Poland Agnieszka Rusinowska University of Paris 1, France Gunther Schmidt UniBw Munich, Germany Renate Schmidt University of Manchester, UK Georg Struth University of Sheffield, UK Michael Winter Brock University, Canada External Reviewers Bernd Brassel Martin Eric Mueller Han-Hing Dang Koki Nishizawa Guillaume Feuillade Ingrid Rewitzky Roland Glu¨ck Patrick Roocks Timothy Griffin Kim Solin Annabelle McIver Toshinori Takai Roger Maddux Dmitry Tishkovsky Sponsors LogiCCC programme of the European Science Foundation (ESF) Erasmus Trust Fund, Rotterdam Faculty of Philosophy, Erasmus University, Rotterdam Table of Contents Building Structured Theories (Invited Paper)........................ 1 Bernhard Mo¨ller Social Networks: Prestige, Centrality, and Influence (Invited Paper) .... 22 Agnieszka Rusinowska, Rudolf Berghammer, Harrie De Swart, and Michel Grabisch Synthesising Terminating Tableau Calculi for Relational Logics (Invited Paper) .................................................. 40 Renate A. Schmidt From Arrow’s Impossibility to Schwartz’s Tournament Equilibrium Set (Invited Tutorial) ................................................ 50 Felix Brandt Automated Engineering of Relational and Algebraic Methods in Isabelle/HOL (Invited Tutorial).................................... 52 Simon Foster, Georg Struth, and Tjark Weber Explaining Voting Paradoxes; Including Arrow’s and Sen’s Theorems (Invited Tutorial) ................................................ 68 Donald G. Saari Relation Algebraic Approaches to Fuzzy Relations (Invited Tutorial) ... 70 Michael Winter A First-Order Calculus for Allegories ............................... 74 Bahar Aameri and Michael Winter Relational Modelling and Solution of Chessboard Problems............ 92 Rudolf Berghammer A Functional, Successor List Based Version of Warshall’s Algorithm with Applications ................................................ 109 Rudolf Berghammer Variable Side Conditions and Greatest Relations in Algebraic Separation Logic................................................. 125 Han-Hing Dang and Peter H¨ofner An Algebraic Approach to Preference Relations...................... 141 Ivo Du¨ntsch and Ewa Or(cid:2)lowska VIII Table of Contents Relational and Multirelational Representation Theorems for Complete Idempotent Left Semirings ........................................ 148 Hitoshi Furusawa and Koki Nishizawa Using Bisimulations for Optimality Problems in Model Refinement ..... 164 Roland Glu¨ck Pathfinding Through Congruences ................................. 180 Alexander J.T. Gurney and Timothy G. Griffin Towards a Typed Omega Algebra .................................. 196 Walter Guttmann Towards an Algebra of Routing Tables.............................. 212 Peter H¨ofner and Annabelle McIver Dependently-Typed Formalisation of Relation-Algebraic Abstractions... 230 Wolfram Kahl Omega Algebras and Regular Equations ............................ 248 Michael R. Laurence and Georg Struth On Probabilistic Kleene Algebras, Automata and Simulations ......... 264 Annabelle McIver, Tahiry M. Rabehaja, and Georg Struth Ampersand: Applying Relation Algebra in Practice................... 280 Gerard Michels, Sebastiaan Joosten, Jaap van der Woude, and Stef Joosten Programming from Galois Connections ............................. 294 Shin-Cheng Mu and Jos´e Nuno Oliveira Constructions around Partialities .................................. 314 Gunther Schmidt Splitting Atoms in Relational Algebras ............................. 331 Prathap Siddavaatam and Michael Winter Relational Heterogeneity Relaxed by Subtyping ...................... 347 Jaap van der Woude and Stef Joosten Author Index.................................................. 363 Building Structured Theories (Invited Paper) Bernhard M¨oller Institut fu¨r Informatik, Universit¨at Augsburg,D-86135 Augsburg, Germany [email protected] Abstract. Weprovideaset of syntactictools for structuringlarge col- lections oflogical theories. Theiruseisdemonstrated byaformalisation of algebras that areused in describing thesemantics ofconcepts in pro- gramming languages, butalso of more general systems. 1 Introduction Within the series of RelMiCS, AKA and now RAMiCS conferences we have seen many algebraic theories, starting with relation and Kleene algebras, which have diversified considerably to cover more and more application areas. Still, many of them share a significant common core, and hence it seems adequate to think about their connections in a systematic way. At the same time, some of the theories are quite complex. This is similar to the situation in programming, where one tries to cope with that using suitable structuring mechanisms, such as inheritance and encapsulation. In the present paper we attempt a similar structured presentation of some essential RAMiCS theories. While there is already some work in that direc- tion in connection with treating these theories with automatic theorem provers [6,15,29,30], we try to modularise further in a number of new and perhaps un- usualwaystopinpointmoreclearlywhichpartsofthetheoriesdependonwhich others. Ofcourse,there is alreadyalotofworkonstructuringlargerformaltheories. Thereisthelongseriesoflanguagesdesignedinthefieldofalgebraicspecification, likeCLEAR[3],CIP-L[2],ASL[67],ACTONE[14]andCASL[4].Theyallcomprise some sort of structuring mechanism, and many show notational similarity to whatwe willuse inthe presentpaper.However,bytheir nature they aremostly restricted to first-order equational logic, whereas we will be more liberal. There is also work on structuring specifications in Edinburgh LCF [40,56]. General structured specification frameworks based on category theory appear in [12,16, 20,58,60,61].Andthereistheinterestingdependentlytypedfunctionallanguage Agda [1] with proof assistant, which also allows expressing structured theories. What we present here deviates from these approaches in that we introduce a numberofadditionalconstructionmechanisms.Moreover,weforegothedefinition of a semantics in terms of operations on model classes or of pushouts/colimits. Rather,weviewourstructuringtoolsassyntacticdevicesthatabbreviatecertain H.deSwart(Ed.): RAMICS2011,LNCS6663,pp. 1–21,2011. Springer-VerlagBerlinHeidelberg2011 (cid:0) 2 B. M¨oller compounds of formulas and can be re-used and instantiated to exhibit common and recurring parts of specifications.For their meaning we rely on the standard semanticsoffirst-orderandhigher-orderlogic. In motivating the particular ingredients of the theories we present we fre- quently resort to their use in specifying the semantics of transition systems and the like. However, as it has been demonstrated in many excellent papers throughoutthisseriesofconferences,thetheorieshavemuchwiderapplicability, andwehopethatourmethodsofstructuringwillhelpinextendingthealgebraic treatment to many further areas. 2 Theories and Definitions A theory has a name and may have an imports clause that specifies on which other theories it depends, a list of sorts (i.e., names for carrier sets), a list of operatorsandalistofpredicates,eachwiththeirtyping,alistofaxioms(which should be independent) and a list of properties, starting with the keyword de- rives, that follow from the axioms. We will only write down the non-empty ones ofthese;listitemsareseparatedbythesymbol|orlinebreaks,sometimesalsoby | a horizontalline.For space limitations we usuallylist only a few ofthe more in- teresting/importantderivedproperties. The operatorsand predicates are called the constituents ofthe theory.Occasionallywe willmarkcertainconstituentsas hidden, since they only have auxiliary character for formulating certain axioms inamoreconvenientandgenericway.Allnon-hiddenconstituentsarevisible to the outside and canbe importedby other theories.A theory may alsocontaina listoftypedvariablesthatareusedintheaxiomsorderivedproperties.Weomit the explicit definition of variables whose type can be inferred from the typing of the operators and predicates that are applied to them. We use the standard convention that all free variables in a logical formula are implicitly universally quantified. Definitions are similar to theories except that they do not contain axioms. Rather they give, following the keywords defined by, definitional equalities or equivalencesforeachoftheirconstituents.Theonlyexceptionarenewconstants that may be added without giving particular properties for them. The distinction between theories and definitions is purely for documentation purposes.Forbrevitywewillrefertothemuniformlyas(building) blocks.Blocks may be freely imported and/or instantiated, possibly under renaming. For the latter we use simple positional notation, listing the new names between paren- theses after the block name. The meaning of an import is simple replacement of the block name by its body (with renaming if specified). If no renaming list is given, the block is imported with its original names. Hence upon import of several blocks into another one, identical names mean identical constituents. An instantiated block may also be used in the axioms, defined by or derives partsofotherblocks;inthis caseitsconstituentinformationisignoredandonly thelogicalformulasinitsbodyarecopiedin(underrenamingifspecified).Inthis case the block serves as a function from constituent names to sets of formulas. Building Structured Theories 3 Bythistwofolduseofblocksweachieveacertainnotationaleconomy,aswillbe seen in the examples. Types may be simple identifiers or Cartesian product, function or power set types. Mostly, however, we will use the higher types only in auxiliary blocks to improve the structuring; they will then disappear again after instantiation of these blocks. Only at the very end of the paper, when we talk about quantales, some higher types persist. A unary predicate is identified with the subset of elements that satisfy it. Use of such a predicate in the position of a type then achievessubsorting.Inparticular,ifvariablesaredeclaredtobeofsuchasubsort type, quantifiers involving them range over the subsort only. As first examples to show our notation at work we specify some aspects of comparison,inparticular,ofpreordersandpartialorders.Firstwejustintroduce the type of the comparison predicate. theory COMPARE sorts S predicates ≤ ⊆ S×S Next, even without any assumptions on the predicate ≤, we define the con- cepts of isotony and antitony. This already involves predicates of higher type that take functions as arguments. definition ISO ANTI imports COMPARE predicates isotone,antitone ⊆ S → S defined by isotone(f) ⇔df ∀x,y.x≤y ⇒ f(x)≤f(y) antitone(f) ⇔df ∀x,y.x≤y ⇒ f(y)≤f(x) Wenowintroduceageneralmechanismforpropagatingpropertieslikeisotony and antitony to binary operators. This again involves higher-order concepts. theory LEFT ARG sorts S operators g:S×S → S predicates P ⊆ S → S hidden right const:S → (S → S) axioms right const(y)(x) = g(x,y) ∀y.P(right const(y)) Now for instance LEFT ARG(T,◦,isotone) expresses that an operator ◦:T × T → T on some set T is isotone in its left argument. A symmetrical theory RIGHT ARG propagates a predicate to the right argumentof a binary operator. Below we will also use this mechanism to express left and right distributivity of a binary operator in terms of distributivity of a unary one. Next, we specify preorders and partial orders.
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