Knowledge Representation for Agents and Multi-Agent Systems

167 Pages·2009·2.33 MB·English

by  John-Jules (eds)

Lecture Notes in Artificial Intelligence 5605
EditedbyR.Goebel,J.Siekmann,andW.Wahlster
Subseries of Lecture Notes in Computer Science
John-Jules Ch. Meyer Jan Broersen (Eds.)
Knowledge Representation
for Agents
and Multi-Agent Systems
First International Workshop, KRAMAS 2008
Sydney, Australia, September 17, 2008
Revised Selected Papers
1 3
SeriesEditors
RandyGoebel,UniversityofAlberta,Edmonton,Canada
JörgSiekmann,UniversityofSaarland,Saarbrücken,Germany
WolfgangWahlster,DFKIandUniversityofSaarland,Saarbrücken,Germany
VolumeEditors
John-JulesCh.Meyer
JanBroersen
UniversiteitUtrecht,DepartmentofInformationandComputingSciences
Padualaan14,DeUithof,3584CHUtrecht,TheNetherlands
E-mail:{jj,broersen}@cs.uu.nl
LibraryofCongressControlNumber:2009937292
CRSubjectClassification(1998):I.2.4-6,I.2,F.4.1,H.3,H.2.8,F.1
LNCSSublibrary:SL7–ArtificialIntelligence
ISSN 0302-9743
ISBN-10 3-642-05300-9SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-642-05300-9SpringerBerlinHeidelbergNewYork
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,
reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,
initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable
toprosecutionundertheGermanCopyrightLaw.
springer.com
©Springer-VerlagBerlinHeidelberg2009
PrintedinGermany
Typesetting:Camera-readybyauthor,dataconversionbyScientificPublishingServices,Chennai,India
Printedonacid-freepaper SPIN:12780396 06/3180 543210
Preface
This book comprises the formal proceedings of KRAMAS 2008, a workshop on
Knowledge Representation for Agents and Multi-Agent Systems, held at KR
2008,Sydney, Australia, September 17, 2008. The initiative for KRAMAS 2008
wastakenbylastyear’sKRChairstoenhancecross-fertilizationbetweentheKR
(KnowledgeRepresentationandReasoning)andagentcommunities.Topromote
participation in the KR schedule, the workshop was conveniently ‘sandwiched’
between days with regular KR sessions. The topics solicited included:
– Knowledge representation and reasoning aspects of agent systems (langua-
ges, ontologies, techniques)
– Reasoning about (actions of) agents
– Reasoningmethods(suchasnon-monotonicreasoning,abduction,argumen-
tation, diagnosis, planning, decision making under uncertainty, reasoning
about preference, ...) applied to agents and multi-agent systems (MAS)
– Theory ofnegotiation,communication,cooperation,groupdecisionmaking,
game theory for MAS
– Cognitive robotics
– Representations of other agents / opponent models
– Logics for intelligent agents and MAS
– Specification and verification techniques for agents
– Automated reasoning techniques for agent-based systems
– Logicalfoundationsofagent-basedsystems,normativeMASande-institutions
– Formal semantics of agent programming languages
– Formal techniques for agent-oriented programming and agent-oriented soft-
ware engineering
We originally received 14 papers. There were two review rounds: the first
one deciding on acceptance for presentation at the workshop, and the second
one deciding on inclusion of revised, extended and resubmitted versions of the
presentedpapersintheseproceedings.Oftheoriginal14,10papersmadeitinto
these proceedings. The workshop was a success and proved that there is indeed
muchinterestintheproblemsandissuesarisingatthejunctionofKRandMAS.
WearegratefultotheparticipantsofKRAMAS2008andtotheauthorswho
submitted papers, to the members of the Program Committee for their service
in reviewing papers (twice) and to the KR organizationfor taking the initiative
tohaveKRAMASandtheirsupportinitsorganization.Thanks,too,toRichard
vandeStadtwhoseCyberChairPROsystemwasaverygreathelptous.Finally
weareindebtedtoSpringer,andAlfredHofmanninparticular,fortheirsupport
in getting these proceedings published.
April 2009 John-Jules Ch. Meyer
Jan Broersen
Workshop Organization
Program Chair
John-Jules Meyer
Workshop Chairs
John-Jules Meyer Utrecht University, The Netherlands
Jan Broersen Utrecht University, The Netherlands
Program Committee
Thomas Agotnes Bergen, Norway
Natasha Alechina Nottingham, UK
Jamal Bentahar Montreal, Canada
Rafael Bordini Durham, UK
Jan Broersen Utrecht, The Netherlands
Mehdi Dastani Utrecht, The Netherlands
Giuseppe De Giacomo Rome, Italy
Hans van Ditmarsch Otago, New Zealand
Jurgen Dix Clausthal, Germany
Andreas Herzig Toulouse, France
Wiebe van der Hoek Liverpool, UK
Wojciech Jamroga Clausthal, Germany
Catholijn Jonker Delft, The Netherlands
Yves Lesperance Toronto, Canada
Alessio Lomuscio London, UK
Timothy Norman Aberdeen, UK
Henry Prakken Utrecht, The Netherlands
Alessandro Ricci Cesena, Italy
Renate Schmidt Manchester, UK
Carles Sierra Barcelona, Spain
Francesca Toni London, UK
Rineke Verbrugge Groningen, The Netherlands
Table of Contents
Reasoning about Other Agents’ Beliefs under Bounded Resources ...... 1
Natasha Alechina, Brian Logan, Hoang Nga Nguyen, and
Abdur Rakib
Normative Multi-agent Programs and Their Logics................... 16
Mehdi Dastani, Davide Grossi, John-Jules Ch. Meyer, and
Nick Tinnemeier
Modal Logics for Preferences and Cooperation: Expressivity and
Complexity ..................................................... 32
C´edric D´egremont and Lena Kurzen
Simulation and Information: Quantifying over Epistemic Events........ 51
Hans van Ditmarsch and Tim French
On the Dynamics of Institutional Agreements ....................... 66
Andreas Herzig, Tiago de Lima, and Emiliano Lorini
From Trust in Information Sources to Trust in Communication
Systems: An Analysis in Modal Logic .............................. 81
Emiliano Lorini and Robert Demolombe
Pre-processing Techniques for Anytime Coalition Structure Generation
Algorithms...................................................... 99
Tomasz Michalak, Andrew Dowell, Peter McBurney, and
Michael Wooldridge
Cognitive Use of Artifacts: Exploiting Relevant Information Residing
in MAS Environments ............................................ 114
Michele Piunti and Alessandro Ricci
Information-BasedArgumentation ................................. 130
Carles Sierra and John Debenham
Mediation = Information Revelation + Analogical Reasoning.......... 145
Simeon Simoff, Carles Sierra, and Ramon Lo´pez de Ma`ntaras
Author Index.................................................. 161
Reasoning about Other Agents’ Beliefs under
Bounded Resources
NatashaAlechina,BrianLogan,HoangNgaNguyen,andAbdurRakib(cid:2)
SchoolofComputerScience
UniversityofNottingham
NottinghamNG81BB,UK
{nza,bsl,hnn,rza}@cs.nott.ac.uk
Abstract. There exists a considerable body of work on epistemic logics for
boundedreasonerswheretheboundcanbetime,memory,ortheamountofin-
formationthereasonerscanexchange.Inmuchofthisworktheepistemiclogic
is used as a meta-logic to reason about beliefs of the bounded reasoners from
anexternalperspective.Inthispaper,wepresentaformalmodelofasystemof
boundedreasonerswhichreasonabouteachother’sbeliefs,andproposeasound
andcompletelogicinwhichsuchreasoningcanbeexpressed.Ourformalisation
highlightsaproblemofincorrectbeliefascriptioninresource-boundedreasoning
aboutbeliefs,andweproposeapossiblesolutiontothisproblem,namelyadding
reasoningstrategiestothelogic.
1 Introduction
Thepurposeofthispaperistoinvestigateamulti-agentepistemiclogicwhichresults
fromtakingseriouslytheideathatagentshaveboundedtime,memoryandcommuni-
cation resources, and are reasoning abouteach other’s beliefs. The main contribution
ofthepaperistogeneraliseseveralexistingepistemiclogicsforresource-boundedrea-
sonersbyaddinganabilityforreasonerstoreasonabouteachother’sbeliefs.Weshow
that a problemof incorrectbelief ascription arises as a result, and proposea possible
solutiontothisproblem.
To give the reader an idea where the current proposal fits into the existing body
of research on epistemic logics for bounded reasoners, we include a brief survey of
existingapproaches,concentratingmostlyontheapproacheswhichhaveinfluencedthe
workpresentedhere.
Instandardepistemiclogic(seee.g.[1,2]forasurvey)anagent’s(implicit)knowl-
edgeismodelledasclosedunderlogicalconsequence.Thiscanclearlyposeaproblem
whenusinganepistemiclogictomodelresource-boundedreasoners,whosesetofbe-
liefsisnotgenerallyclosedwithrespecttotheirreasoningrules.Variousproposalsto
modifypossibleworldssemanticsinordertosolvethisproblemoflogicalomniscience
(e.g.,introducingimpossibleworldsasin [3,4],ornon-classicalassignmentasin[5])
resultinagent’sbeliefsstillbeinglogicallyclosed,butwithrespecttoaweakerlogic.
(cid:2)This work was supported by the UK Engineering and Physical Sciences Research Council
[grantnumberEP/E031226].
J.-J.Ch.MeyerandJ.M.Broersen(Eds.):KRAMAS2008,LNAI5605,pp.1–15,2009.
(cid:2)c Springer-VerlagBerlinHeidelberg2009
2 N.Alechinaetal.
Our work builds on another approachto solving this problem,namely treating be-
liefsassyntacticobjectsratherthanpropositions(setsofpossibleworlds).In[6],Fagin
andHalpernproposedamodeloflimitedreasoningusingthenotionofawareness:an
agentexplicitlybelievesonlytheformulaswhichareinasyntacticallydefinedaware-
nessset(aswellasinthesetofitsimplicitbeliefs).Implicitbeliefsarestillclosedunder
consequence,butexplicitbeliefsarenot,sinceaconsequenceofexplicitbeliefsisnot
guaranteedtobelongtotheawarenessset.However,theawarenessmodeldoesnotgive
any insight into the connectionbetween the agent’s awarenessset and the agent’s re-
sourcelimitations,whichiswhatwetrytodointhispaper.1 Konolige[7]proposeda
differentmodelofnon-omniscientreasoners,thedeductionmodelofbelief.Reasoners
wereparameterisedwithsetsofruleswhichcould,forexample,beincomplete.However,
thedeductionmodelofbeliefstillmodelsbeliefsofareasonerasclosedwithrespectto
reasoner’sdeductionrules;itdoesnottakeintoaccountthetimeittakestoproducethis
closure,oranylimitationsontheagent’smemory.Steplogic,introducedin[8],givesa
syntacticaccountofbeliefsastheoriesindexedbytimepoints;eachapplicationofin-
ferencerulestakesaunitoftime.Nofixedboundonmemorywasconsidered,butthe
issueofboundedmemorywastakenintoaccount.Anaccountofepistemiclogiccalled
algorithmicknowledge,whichtreatsexplicitknowledgeassomethingwhichhastobe
computedbyanagent,wasintroducedin[9],andfurtherdevelopedine.g.[1,10].Inthe
algorithmicknowledgeapproach,agentsareassumedtopossessaprocedurewhichthey
usetoproduceknowledge.Inlaterwork[10]thisprocedureisassumedtobegivenasa
setofrewriteruleswhichareappliedtotheagent’sknowledgetoproduceaclosedset,so,
likeKonolige’sapproach,algorithmicknowledgeisconcernedwiththeresultratherthan
theprocessofproducingknowledge.In[11,12]Ducproposedlogicsfornon-omniscient
epistemicreasonerswhichwillbelieveallconsequencesoftheirbeliefseventually,after
someintervaloftime.Itwasshownin[13]thatDuc’ssystemiscompletewithrespect
to semanticsin which the set of agent’sbeliefsis always finite. Duc’s system did not
modeltheagents’reasoningabouteachothers’beliefs.Otherrelevantapproacheswhere
epistemiclogicsweregivenatemporaldimensionandeachreasoningsteptookaunit
oftimeare,forexample,[14],whereeachinferencestepismodelledasanactioninthe
styleofdynamiclogic,and[15]whichproposesalogicforverificationofresponse-time
propertiesofasystemofcommunicatingrule-basedagents(eachrulefiringorcommu-
nicationtakesaunitoftime).Inasomewhatdifferentdirection,[16]proposedalogic
whereagentsreasonabouteachothersbeliefs,buthavenoexplicittimeormemorylimit;
howeverthereisarestrictiononthedepthofbeliefnestings(contextswitchingbythe
agents).Epistemiclogicsforbounded-memoryagentswereinvestigatedin,forexample,
[17,18,19,20],andtheinterplaybetweenboundedrecallandboundedmemory(ability
tostorestrategiesofonlyboundedsize)wasstudiedin[21].
AnepistemiclogicBMCLforcommunicatingagentswithcommunicationlimitson
thenumberofexchangedmessages(andconnectionstospacecomplexityofproofsand
communicationcomplexity)wasinvestigatedin [20]. InthispaperweexpandBMCL
by adding rules for reasoning about other agents’ beliefs, demonstrate that epistemic
reasoningdoneinresource-boundedfashionhasaninherentproblemofincorrectbelief
ascription,andproposetheuseofreasoningstrategiesasasolutiontothisproblem.
1 Wealsocompletelydispensewiththenotionofimplicitbeliefs.
ReasoningaboutOtherAgents’BeliefsunderBoundedResources 3
2 Model ofReasoning Agents
ThelogicBMCLpresentedin[20]formalisesreasoningaboutthebeliefsofasystemof
reasonerswhoreasonusing propositionalresolutionandcan exchangeinformationto
solveaproblemtogether.Thesetupissimilarto,forexample,[22].BMCLmodelseach
inferenceruleapplicationastakingasingletimestep,introducesanexplicitboundon
thesetofbeliefsofeachreasoner,andaboundonthenumberofmessagesthereasoners
can exchange.In this paper,we generalise thisapproachby assumingthat agentscan
also reason about each other’s beliefs. Namely, they assume that other agents use a
certainsetofinferencerules,andtheyreasonaboutwhatanotheragentmaybelieveat
thenextstep.Forexample,ifagentAbelievesthatagentBbelievestwoclausesc1and
c2andthesetwoclausesareresolvabletoaclausec,andagentAassumesthatagentB
reasonsusingresolution,thenitisreasonableforagentAtobelievethatagentB may
believecatthenextstep.
We assume a set of n agents. Each agent i has a set of inference rules, a set of
premisesKBi,andaworkingmemory.ToinferfromthepremisesinKBi,therelevant
formulasmustfirstbereadintoworkingmemory.Weassumethateachagent’sworking
memory is bounded by nM, which is the maximal number of formulas an agent can
believeatthesametime.Wealsosetalimitonthepossiblesizeofaformula,orrather
onthedepthofnestingofbeliefoperators,nB,andalimit,nC,onthemaximalnumber
ofcommunicationsanagentcanmake.Forsimplicity,weassumethattheseboundsare
thesameforallagents,butthiscanbeeasilyrelaxedbyintroducingfunctionsnM(i),
nB(i)andnC(i)whichassignadifferentlimittoeachagenti.
Thesetofreasoningactionsisasfollows:
ReadKB: an agent can retrieve information from its KB and put it into its working
memoryusingtheRead action.Sinceanagenthasa fixedsize memory,addinga
formulatoitsmemorymayrequireerasingsomebeliefalreadyinmemory(ifthe
limitnM wouldotherwisebeexceed).Thesameappliestootherreasoningactions
whichaddanewformula,inthataddinganewformulamayinvolveoverwritinga
formulacurrentlyinworkingmemory.
Resolution: an agent can derive a new clause if it has two resolvable clauses in its
memory.
Copy: anagentcancommunicatewithanotheragenttorequestaclausefromthemem-
oryoftheotheragent.We assumethatcommunicationisalwayssuccessfulifthe
otheragenthastherequestedclause.IfagentAhasclausecinmemory,thenacopy
byBwillresultinagentB believingthatAbelievesc.Copyisonlyenabledifthe
agenthasperformedfewer thannC copyactionsin the past andthe prefixof the
resultingbeliefhasnestingofatmostnB.
Idle: anagentmayidle(donothing)atanytimestep.Thismeansthatatthenexttime
pointofthesystem,theagentdoesnotchangeitsstateofmemory.
Erase: anagentmayremoveaformulafromitsworkingmemory.Thisactionisintro-
ducedfortechnicalreasonstosimplifytheproofs.
Inadditiontotheactionslistedabove,weintroduceactionsthatenableagentstorea-
sonaboutotheragents’beliefs,essentiallyepistemicaxiomsK(ascribingpropositional
4 N.Alechinaetal.
reasoningtotheotheragent)and4(positiveintrospectionabouttheagent’sownbeliefs,
andascribingpositiveintrospectiontootheragents).Thereasonswe donotadoptfor
exampleKD45are as follows.Ifthe agent’sknowledgebase isinconsistent,we want
ittobeabletoderiveB⊥(orB[]where[]istheemptyclause).Negativeintrospection
is also problematic in a resource-boundedsetting, in that the agent may derive ¬Bα
ifαisnotinitscurrentsetofbeliefs,andthenderiveαfromitsotherbeliefs,ending
upwithaninconsistentsetofbeliefs(¬BαandBαbypositiveintrospectionfromα),
evenifitsknowledgebaseisconsistent.Wecouldhaveadoptedarestrictedversionof
negativeintrospection(see,e.g.,[12])butinthispaperweomititforsimplicity.
In addition to the reasoning actions listed above, we therefore add the following
actions:
Other’sResolution: anagentAcanperformthisactionifitbelievesthatanotheragent
B believes two resolvable clauses c1 and c2. Then A can conclude that B will
believein the resolventclause c of c1 andc2 in the nexttime point.As a general
case, we can extend the chain agent-believes ... agent-believes. For example, if
agentAbelievesthatagentBbelievesthatagentCbelievestworesolvableclauses
c1 andc2,thenitispossibleinthenexttimepointthatagentAbelievesthatagent
BbelievesthatagentC believescwhichistheresolventofc1andc2.
PositiveIntrospection: ifanagentAbelievesaclausec,itcanperformthisactionto
reachastatewhereitbelievesthatitbelievesc.
Other’sPositiveIntrospection: ifanagentAbelievesthatanotheragentBbelievesa
clausec,itcanperformthisactiontoreachastatewhereitbelievesthatBbelieves
thatBbelievesc.
The reasoningactionsPositive IntrospectionandOther’sPositive Introspectionare
onlyenabledifthederivedformulahasadepthofnestingofatmostnB.
Note that the assumption that the agents reason using resolution and positive in-
trospectionis not essential for the main argumentof this paper. This particular set of
inferenceruleshasbeenchosentomakethelogicconcrete;wecouldhave,forexam-
ple,assumedthattheagentsreasonusingmodusponensandconjunctionintroduction
insteadofresolution.Inwhatfollows,wegiveaformaldefinitionofanepistemiclogic
forcommunicatingagentswhichreasoninastep-wise,memory-boundedfashionusing
somewell-definedsetofinferencerules.
3 Syntax andSemantics ofERBL
Inthissection,wegivethesyntaxandsemanticsofthelogicERBLwhichformalises
theideassketchedintheprevioussection.ERBL(EpistemicResourceBoundedLogic)
is an epistemic and temporal meta-language in which we can talk about beliefs ex-
pressedintheagents’internallanguage.
Letthe setofagentsbeA = {1,2,...,nA}.We assumethatallagentsagreeona
finitesetPROP ofpropositionalvariables,andthatallbeliefformulasoftheinternal
language of the agents are in the form of clauses or clauses preceded by a prefix of
beliefoperatorsoffixedlength.