Lecture Notes in Computer Science 6663 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen
Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, 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
13 Volume Editor
Harrie de Swart Erasmus University Rotterdam Faculty of Philosophy P.O. Box 1738, 3000 DR Rotterdam, The Netherlands E-mail: [email protected]
ISSN 0302-9743 e-ISSN 1611-3349 ISBN 978-3-642-21069-3 e-ISBN 978-3-642-21070-9 DOI 10.1007/978-3-642-21070-9 Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: Applied for
CR Subject Classification (1998): F.4, I.1, I.2.3, D.2.4, D.3.4
LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues
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This volume contains the proceedings of the 12th International Conference on Relational and 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. Over the past 20 years, the RelMiCS (Relational Methods in Computer Science) and AKA (Applications of Kleene Algebra) conferences have been a main forum for researchers who use the calculus of relations and similar algebraic formalisms 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 attention was paid to the fact that the meetings started 20 years ago at 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. Relational and algebraic methods and software tools like RelView turn out to be useful for solving problems in social choice and game theory. For that reason this conference included a special track on Computational Social Choice and Social Software, organized by the CFSC (Computational Foundations of Social Choice) and SSEAC (Social Software for Elections, the Allocation of tenders and 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, of which three were on relational and algebraic methods, by Chris Brink, Bernhard M¨oller (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 Georg Struth (included) and Michael Winter (included), and two on social choice 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- Chair conference administration system. Last but not least I would like to thank 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 Gl¨uck 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 M¨oller
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 D¨untsch and Ewa Or 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 Gl¨uck
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 f¨ur Informatik, Universit¨at Augsburg, D-86135 Augsburg, Germany [email protected]
Abstract. We provide a set of syntactic tools for structuring large col- lections of logical theories. Their use is demonstrated by a formalisation of algebras that are used in describing the semantics of concepts in pro- gramming languages, but also 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- usual ways to pinpoint more clearly which parts of the theories depend on which others. Of course, there is already a lot of work on structuring larger formal theories. There is the long series of languages designed in the field of algebraic specification, like CLEAR [3], CIP-L [2], ASL [67], ACT ONE [14] and CASL [4]. They all comprise some sort of structuring mechanism, and many show notational similarity to what we will use in the present paper. However, by their nature they are mostly 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]. And there is the interesting dependently typed functional language Agda [1] with proof assistant, which also allows expressing structured theories. What we present here deviates from these approaches in that we introduce a number of additional construction mechanisms. Moreover, we forego the definition of a semantics in terms of operations on model classes or of pushouts/colimits. Rather, we view our structuring tools as syntactic devices that abbreviate certain
H. de Swart (Ed.): RAMICS 2011, LNCS 6663, pp. 1–21, 2011.