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Inconsistency and Uncertainty Handling in Lightweight Description Logics

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Inconsistency and Uncertainty Handling in Lightweight Description Logics Inconsistency and uncertainty handling in lightweight description logics THÈSE présentée et soutenue publiquement le 5 juin 2015 en vue de l’obtention du Doctorat de l’Université d’Artois (Spécialité Informatique) par : Zied Bouraoui devant le jury composé de Anthony HUNTER Professor - University College London, United Kingdom (Rapporteur) Henri PRADE Directeur de recherche CNRS - IRIT Toulouse (Rapporteur) Salem BENFERHAT Professeur des universités - Université d’Artois (Directeur de Thèse) Sylvain LAGRUE Maître de conférences (HDR) - Université d’Artois (Examinateur) Marie-Laure MUGNIER Professeur des universités- Université de Montpellier II (Examinatrice) Odile PAPINI Professeur des universités - Université d’Aix Marseille (Examinatrice) Ramón PINO PÉREZ Professor - University of the Andes, Venezuela (Examinateur) Karim TABIA Maître de conférences - Université d’Artois (Examinateur) CENTRE DE RECHERCHE EN INFORMATIQUE DE LENS – CNRS UMR-8188 UNIVERSITÉ D’ARTOIS, RUE JEAN SOUVRAZ, S.P. 18 F-62307, LENS CEDEX FRANCE SECRÉTARIAT :TÉL.: +33(0)321791723–FAX : +33(0)321791770 http://www.cril.univ-artois.fr ABSTRACT Abstract This thesis investigates the dynamics of beliefs and uncertainty management in DL-Lite, one of the most important lightweight description logics. The first part of the thesis concerns the problem of han- dling uncertainty in DL-Lite. First, we propose an extension of the main fragments of DL-Lite to deal with the uncertainty associated with axioms using a possibility theory framework without additional ex- tra computational costs. We then study the revision of possibilistic DL-Lite bases when a new piece of information is available. Lastly, we propose a min-based assertional merging operator when assertions of ABox are provided by several sources of information having different levels of priority. The second part of the thesis concerns the problem of inconsistency handling in flat and prioritized DL-Lite knowledge bases. We first propose how to reason from a flat DL-Lite knowledge base, with a multiple ABox, which can be either issued from multiple information sources or resulted from revising DL-Lite knowledge bases. This is done by introducing the notions of modifiers and inference strategies. The combination of modifiers plus inference strategies can be mapped out in order to provide a principled and exhaustive list of techniques for inconsistency management. We then give an approach based on selecting multiple repairs using a cardinality-based criterion, and we identified suitable strategies for handling inconsistency in the prioritized case. Lastly, we perform a comparative analysis, followed by experimental studies, of the proposed inconsistency handling techniques. A tool for representing and reasoning in possibilistic DL-Lite framework is implemented. Résumé Cette thèse étudie la dynamique des croyances et la gestion de l’incertitude dans DL-Lite, une des plus importantes familles des logiques de description légères. La première partie de la thèse porte sur la gestion de l’incertitude dans DL-Lite. En premier lieu, nous avons proposé une extension des prin- cipaux fragments de DL-Lite pour faire face à l’incertitude associée aux axiomes en utilisant le cadre de la théorie des possibilités. Cette extension est réalisée sans engendrer des coûts calculatoires sup- plémentaires. Nous avons étudié ensuite la révision des bases DL-Lite possibilistes en présence d’une nouvelle information. Enfin, nous avons proposé un opérateur de fusion lorsque les assertions de ABox sont fournies par plusieurs sources d’information ayant différents niveaux de priorité. La deuxième partie de la thèse traite le problème de la gestion d’incohérence dans les bases de connaissances DL-Lite. Nous avons étudié, tout d’abord, comment raisonner à partir d’une base DL-Lite standard avec des ABox mul- tiples en introduisant les notions de modificateurs et de stratégies d’inférence. La combinaison des mod- ificateurs et de stratégies d’inférence fournit une liste exhaustive des principales techniques de gestion de l’incohérence. Nous avons proposé ensuite une approche, basée sur un critère de cardinalité, de sélection des réparations, et nous avons identifié les stratégies appropriées pour la gestion de l’incohérence pour les bases DL-Lite stratifiées. Enfin, nous avons effectué une analyse comparative, suivie par des études expérimentales, des différentes techniques de gestion d’incohérence proposées. Finalement, un outil de représentation et de raisonnement à partir des bases DL-Lite possibiliste est réalisé. CONTENTS Introduction 1 Context and motivations.....................................1 Contributions...........................................3 Organization of the thesis.....................................5 I Preliminaries7 1 Knowledge representation and ontologies9 1.1 Introduction.........................................9 1.2 Ontology languages..................................... 10 1.3 Logic-based languages................................... 13 1.3.1 Propositional logic................................. 13 1.3.2 First order logic................................... 15 1.3.3 Description logics................................. 16 1.4 The DL-Lite family..................................... 22 1.4.1 The DL-Lite family and OWL2-QL ......................... 22 1.4.2 The extended DL-Lite family............................ 29 1.5 Conclusion......................................... 31 2 Belief change and uncertainty management 33 2.1 Introduction......................................... 33 2.2 Uncertainty management.................................. 34 2.2.1 Probability theory................................. 36 2.2.2 Possibility theory.................................. 37 2.2.3 Uncertainly management in description logics................... 45 2.3 Belief change........................................ 47 2.3.1 Belief revision................................... 47 2.3.2 Belief merging................................... 50 2.3.3 Inconsistency handling............................... 55 2.4 Conclusion......................................... 56 II On the possibilistic extension of DL-Lite 57 3 Min-based possibilistic DL-Lite 59 3.1 Introduction......................................... 59 3.2 Possibility distribution over DL-Lite interpretations.................... 60 3.2.1 Possibility distribution............................... 60 5 6 CONTENTS 3.2.2 Possibility and necessity measures......................... 60 3.3 Possibilistic DL-Litecore .................................. 62 3.3.1 Syntax of π-DL-Litecore ............................. 62 3.3.2 From a π-DL-Litecore knowledge base to a π-DL-Litecore possibility distribution 63 3.3.3 Logical properties of π-DL-Litecore ....................... 64 3.4 Possibilistic negated closure in π-DL-Litecore ...................... 65 3.4.1 Rules used to obtain π-negated closure...................... 65 3.4.2 Properties of π-negated closure.......................... 67 3.5 Checking inconsistency degrees.............................. 68 3.5.1 Additional properties of π-neg(T ) ........................ 68 3.5.2 Computing inconsistency degrees in π-DL-Litecore ............... 69 3.5.3 An algorithm for computing inconsistency degrees................ 73 3.6 Possibilistic DL-LiteF and possibilistic DL-LiteR .................... 74 3.6.1 π-DL-LiteF negated closure........................... 75 3.6.2 π-DL-LiteR negated closure........................... 76 3.7 Basic inferences in π-DL-Litecore ............................. 77 3.8 Query answering in possibilistic DL-Lite.......................... 81 3.9 Discussions and related works............................... 85 3.10 Conclusion......................................... 86 4 Min-based conditioning and merging approach of DL-Lite knowledge bases 87 4.1 Introduction......................................... 87 4.2 Min-based merging of π-DL-Lite knowledge bases.................... 88 4.2.1 Merging of π-DL-Lite possibility distributions.................. 88 4.2.2 Syntactical merging of π-DL-Lite knowledge bases............... 90 4.3 Min-based assertional merging approach for π-DL-Lite knowledge bases........ 91 4.3.1 Syntactic merging of π-DL-Lite assertional bases................ 91 4.3.2 Semantic counterpart................................ 95 4.3.3 Logical properties................................. 97 4.4 Conditioning of possibilistic DL-Lite knowledge bases: Preliminary results....... 98 4.4.1 Conditioning of DL-Lite possibility distributions................. 99 4.4.2 Syntactic revision.................................. 102 4.5 Conclusion......................................... 108 III Inconsistency handling in flat DL-Lite knowledge bases 109 5 Non-merge inconsistency management roadmap in flat DL-Lite knowledge bases 111 5.1 Introduction......................................... 111 5.2 Reasoning from MBox knowledge bases.......................... 112 5.2.1 MBox: Multiple ABox............................... 112 5.2.2 Elementary modifiers on MBox.......................... 112 5.2.3 Composite modifiers on MBox........................... 115 5.3 Inference-based strategies from MBox........................... 117 CONTENTS 7 5.3.1 Universal inference................................. 117 5.3.2 Existential inference................................ 118 5.3.3 Safe inference.................................... 119 5.3.4 Other inferences.................................. 119 5.3.5 Comparing inference-based strategies from a fixed MBox............ 120 5.4 Handling inconsistency=Composite
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