This volume has its origins in the ?rst Learning Language in Logic (LLL) wo- shop which took place on 30 June 1999 in Bled, Slovenia immediately after the Ninth International Workshop on Inductive Logic Programming (ILP'99) and the Sixteenth International Conference on Machine Learning (ICML'99). LLL is a research area lying at the intersection of computational linguistics, machine learning, and computational logic. As such it is of interest to all those working in these three ?elds. I am pleased to say that the workshop attracted subm- sions from both the natural language processing (NLP) community and the ILP community, re?ecting the essentially multi-disciplinary nature of LLL. Eric Brill and Ray Mooney were invited speakers at the workshop and their contributions to this volume re?ect the topics of their stimulating invited talks. After the workshop authors were given the opportunity to improve their papers, the results of which are contained here. However, this volume also includes a substantial amount of two sorts of additional material. Firstly, since our central aim is to introduce LLL work to the widest possible audience, two introductory chapters have been written. Dzeroski, ? Cussens and Manandhar provide an - troduction to ILP and LLL and Thompson provides an introduction to NLP.

Thisvolumecontainsoneinvitedand?fteensubmittedpaperspresentedatthe Tenth International Conference on Inductive Logic Programming (ILP2000). The?fteenacceptedpaperswereselectedbytheprogramcommitteefromthe 37paperssubmittedtotheconference. Eachpaperwascarefullyreviewedby threereferees. ILP2000washeldatImperialCollege,London,24-27July2000andwasin- grated with the First International Conference on Computational Logic (CL2000). With ILP's strong roots in computational logic, this was a na- ralmarriage. CL2000wasa?ve-dayextravaganza,incorporatingboththeSixth InternationalConferenceonRulesandObjectsinDatabases(DOOD2000)and theTenthInternationalWorkshoponLogic-basedProgramSynthesisandTra- formation(LOPSTR2000)andfeaturingeightinvitedspeakers,twelvetutorials, andsevena?liatedworkshops. RegistrantsforCL2000andILP2000couldmove freelybetweenthetwoevents,themaindistinctionbetweentheeventsbeings- arateconferenceproceedings. WewishtothankalltheauthorswhosubmittedtheirpaperstoILP2000; theprogramcommitteemembers,andotherreviewerswhodidathoroughjobin spiteofdemandingdeadlines;andourinvitedspeaker,DavidPage. Thanksalso toAlfredHofmann,andeveryoneelseatSpringerfortheirsmoothhandlingof theseproceedings. WewouldalsoliketothanktheorganisersofCL2000,whose cooperation brought the two events together: John Lloyd (Program Chair), Marek Sergot (Conference Chair), Frank Kriwaczek and Francesca Toni (- calOrganisers),FemkevanRaamsdonk(PublicityChair)andSandroEtalle (Workshop Chair). Finally, we are grateful to our sponsors for their ?nancial support. May2000 JamesCussens&AlanFrisch ProgramChairs ILP2000 ILP2000 Program Committee HenrikBostrom(UniversityofStockholm,Sweden) IvanBratko(UniversityofLjubljana,Slovenia) JamesCussens(UniversityofYork,UK) Shan-HweiNienhuys-Cheng(UniversityofRotterdam,Netherlands) WilliamCohen(WhizbangsLabs,USA) LucDeRaedt(UniversityofFreiburg,Germany) Sa?soD?zeroski(Jo?zefStefanInstitute,Ljubljana) PeterFlach(UniversityofBristol,UK) AlanFrisch(UniversityofYork,UK) KoichiFurukawa(UniversityofKeio,Japan) RoniKhardon(UniversityofEdinburgh,UK) Jorg-UweKietz(SwissLife,Switzerland) NadaLavra?c(Jo?zefStefanInstitute,Slovenia) JohnLloyd(AustralianNationalUniversity,Australia) StanMatwin(UniversityofOttawa,Canada) RaymondMooney(UniversityofTexas,USA) StephenMuggleton(UniversityofYork,UK) DavidPage(UniversityofWisconsin,USA) BernhardPfahringer(UniversityofWaikato,NewZealand) C'elineRouveirol(Universit'edeParis-Sud,France) ClaudeSammut(UniversityofNewSouthWales,Australia) ' Mich'eleSebag(EcolePolytechnique,France) AshwinSrinivasan(UniversityofOxford,UK) PrasadTadepalli(OregonStateUniversity,USA) StefanWrobel(UniversityofMagdeburg,Germany) AkihiroYamamoto(UniversityofHokkaido,Japan) Additional Referees ' ErickAlphonse(Universit'edeParis-Sud,France) LiviuBadea(NationalInstituteforResearchandDevelopmentinInformatics, Romania) DamjanDemsar(Jo? zefStefanInstitute,Slovenia) ElisabethGoncalves(Universit'edeParis-Sud,France) MarkoGrobelnik(Jo?zefStefanInstitute,Slovenia) ClaireKennedy(UniversityofBristol,UK) DanielKudenko(UniversityofYork,UK) JohanneMorin(UniversityofOttawa,Canada) TomonobuOzaki(KeioUniversity,Japan) EdwardRoss(UniversityofBristol,UK) LjupcoTodorovski(Jo?zefStefanInstitute,Slovenia) V'eroniqueVentos(Universit'edeParis-Sud,France) VIII ProgramCommitteeandReferees Sponsors of ILP2000 ILPNet2,TheEuropeanNetworkofExcellenceinInductiveLogicProgramming MLNet,TheEuropeanNetworkofExcellenceinMachineLearning CompulogNet,TheEuropeanNetworkofExcellenceinComputationalLogic Table of Contents IInvitedPaper ILP:JustDoIt...3 DavidPage II Contributed Papers ANewAlgorithmforLearningRangeRestrictedHornExpressions...21 MartaArias,RoniKhardon ARe?nementOperatorforDescriptionLogics...40 LiviuBadea,Shan-HweiNienhuys-Cheng ExecutingQueryPacksinILP ...60 HendrikBlockeel,LucDehaspe,BartDemoen,GerdaJanssens, JanRamon,HenkVandecasteele ALogicalDatabaseMiningQueryLanguage ...78 LucDeRaedt Induction of Recursive Theories in the Normal ILP Setting: Issues and Solutions ...93 FlorianaEsposito,DonatoMalerba,FrancescaA. Lisi ExtendingK-MeansClusteringtoFirst-OrderRepresentations...112 MathiasKirsten,StefanWrobel TheoryCompletionUsingInverseEntailment ...130 StephenH. Muggleton,ChristopherH. Bryant SolvingSelectionProblemsUsingPreferenceRelationBasedonBayesian Learning...147 TomofumiNakano,NobuhiroInuzuka ConcurrentExecutionofOptimalHypothesisSearchforInverse Entailment...165 HayatoOhwada,HiroyukiNishiyama,FumioMizoguchi UsingILPtoImprovePlanninginHierarchicalReinforcementLearning...174 MarkReid,MalcolmRyan X TableofContents TowardsLearninginCARIN-ALN...191 C'elineRouveirol,V'eroniqueVentos InverseEntailmentinNonmonotonicLogicPrograms...209 ChiakiSakama ANoteonTwoSimpleTransformationsforImprovingtheE?ciencyofan ILPSystem ...225 V'?torSantosCosta,AshwinSrinivasan,RuiCamacho SearchingtheSubsumptionLatticebyaGeneticAlgorithm ...243 AlirezaTamaddoni-Nezhad,StephenH. Muggleton NewConditionsfortheExistenceofLeastGeneralizationsunderRelative Subsumption...253 AkihiroYamamoto Author Index ...265 ILP:JustDoIt DavidPage Dept. ofBiostatisticsandMedicalInformatics andDept. ofComputerSciences UniversityofWisconsin 1300UniversityAve. ,Rm5795MedicalSciences Madison,WI53706 U. S. A. page@biostat. wisc. edu Abstract. Inductivelogicprogramming(ILP)isbuiltonafoundation laidbyresearchinotherareasofcomputationallogic. Butinspiteofthis strongfoundation,at10yearsofageILPnowfacesanumberofnewch- lengesbroughtonbyexcitingapplicationopportunities.

This book constitutes the thoroughly refereed post-conference proceedings of the 26th International Conference on Inductive Logic Programming, ILP 2016, held in London, UK, in September 2016. The 10 full papers presented were carefully reviewed and selected from 29 submissions. The papers represent well the current breath of ILP research topics such as predicate invention; graph-based learning; spatial learning; logical foundations; statistical relational learning; probabilistic ILP; implementation and scalability; applications in robotics, cyber security and games.