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

290 Pages·2004·2.441 MB·English

by  Raymond Bisdorff, Marc Roubens (auth.), Rudolf Berghammer, Bernhard Möller, Georg Struth (eds.)

Lecture Notes in Computer Science 3051
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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
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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