## Probabilistic Inductive Logic ProgrammingLuc De Raedt, Paolo Frasconi, Kristian Kersting, Stephen H. Muggleton One of the key open questions within arti?cial intelligence is how to combine probability and logic with learning. This question is getting an increased - tentioninseveraldisciplinessuchasknowledgerepresentation, reasoningabout uncertainty, data mining, and machine learning simulateously, resulting in the newlyemergingsub?eldknownasstatisticalrelationallearningandprobabil- ticinductivelogicprogramming.Amajordriving forceisthe explosivegrowth in the amount of heterogeneous data that is being collected in the business and scienti?c world. Example domains include bioinformatics, chemoinform- ics, transportation systems, communication networks, social network analysis, linkanalysis, robotics, amongothers.Thestructuresencounteredcanbeass- pleassequencesandtrees(suchasthosearisinginproteinsecondarystructure predictionandnaturallanguageparsing)orascomplexascitationgraphs, the WorldWideWeb, andrelationaldatabases. This book providesan introduction to this ?eld with an emphasison those methods based on logic programming principles. The book is also the main resultofthesuccessfulEuropeanISTFETprojectno.FP6-508861onAppli- tionofProbabilisticInductiveLogicProgramming(APRILII,2004-2007).This projectwascoordinatedbytheAlbertLudwigsUniversityofFreiburg(Germany, Luc De Raedt) and the partners were Imperial College London (UK, Stephen MuggletonandMichaelSternberg), theHelsinkiInstituteofInformationTe- nology(Finland, HeikkiMannila), theUniversit` adegliStudidiFlorence(Italy, PaoloFrasconi), andtheInstitutNationaldeRechercheenInformatiqueet- tomatiqueRocquencourt(France, FrancoisFages).Itwasconcernedwiththeory, implementationsandapplicationsofprobabilisticinductivelogicprogramming. Thisstructureisalsore?ectedinthebook. The book starts with an introductory chapter to "Probabilistic Inductive LogicProgramming"byDeRaedtandKersting.Inasecondpart, itprovidesa detailedoverviewofthemostimportantprobabilisticlogiclearningformalisms and systems. We are very pleased and proud that the scientists behind the key probabilistic inductive logic programming systems (also those developed outside the APRIL project) have kindly contributed a chapter providing an overviewoftheircontributions.Thisincludes: relationalsequencelearningte- niques (Kersting et al.), using kernels with logical representations (Frasconi andPasserini), MarkovLogic(Domingosetal.), the PRISMsystem (Satoand Kameya), CLP(BN)(SantosCostaetal.), BayesianLogicPrograms(Kersting andDeRaedt), andtheIndependentChoiceLogic(Poole).Thethirdpartthen provides a detailed account of some show-caseapplications of probabilistic - ductive logic programming, more speci?cally: in protein fold discovery (Chen et al.), haplotyping (Landwehr and Mielik] ainen) and systems biology (Fages andSoliman). The ?nal parttouchesupon sometheoreticalinvestigationsand VI Preface includes chaptersonbehavioralcomparisonof probabilisticlogicprogramming representations(MuggletonandChen)andamodel-theoreticexpressivityan- ysis(Jaeger). |

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### Contents

Probabilistic Inductive Logic Programming | 1 |

Relational Sequence Learning | 28 |

Learning with Kernels and Logical Representations | 56 |

Markov Logic | 92 |

New Advances in LogicBased Probabilistic Modeling by PRISM | 118 |

Constraint Logic Programming for Probabilistic Knowledge | 156 |

Basic Principles of Learning Bayesian Logic Programs | 189 |

The Independent Choice Logic and Beyond | 222 |

Protein Fold Discovery Using Stochastic Logic Programs | 244 |

Probabilistic Logic Learning from Haplotype Data | 263 |

Model Revision from Temporal Logic Properties in Computational Systems Biology | 287 |

A Behavioral Comparison of Some Probabilistic Logic Models | 305 |

ModelTheoretic Expressivity Analysis | 325 |

340 | |

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### Common terms and phrases

abstract acyclic alignment approach Artiﬁcial Intelligence background knowledge Bayes Bayesian clause Bayesian logic programs Bayesian networks BLPs classiﬁcation CLP(BN Conference on Artiﬁcial constraints corresponding database datasets deﬁned denote diﬀerent domain eﬃcient encode estimation example ﬁeld ﬁnd ﬁnite ﬁrst ﬁrst-order logic formulas framework function functor genotype given gradient graph ground atoms haplotype haplotype pair Heidelberg Herbrand Herbrand base hidden Markov models HMMs inductive logic programming inference inﬁnite intensional interpretations kernel Kersting kFOIL language learning algorithm Machine Learning markers Markov logic Markov logic networks Markov networks methods Muggleton multi-class node parameters PCFGs possible worlds predicate PRISM PRMs probabilistic ILP probabilistic logic probabilistic models problem Proceedings Prolog proof trees propositional protein fold query Raedt random variables reﬁnement represent representation sample satisﬁed semantics Skolem terms SLPs speciﬁc Springer statistical stochastic logic programs structure symbols true values WEE1