Wright State University CORE Scholar Browse all Theses and Dissertations Theses and Dissertations 2015 A Language for Inconsistency-Tolerant Ontology Mapping Kunal Sengupta Wright State University Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all Part of the Computer Engineering Commons, and the Computer Sciences Commons Repository Citation Sengupta, Kunal, "A Language for Inconsistency-Tolerant Ontology Mapping" (2015). Browse all Theses and Dissertations. 1412. https://corescholar.libraries.wright.edu/etd_all/1412 This Dissertation is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. A Language for Inconsistency-Tolerant Ontology Mapping A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Kunal Sengupta B.Tech, DA-IICT, 2006 2015 Wright State University WRIGHT STATE UNIVERSITY GRADUATE SCHOOL August 13, 2015 I HEREBY RECOMMEND THAT THE DISSERTATION PREPARED UNDER MY SUPERVISION BY Kunal Sengupta ENTITLED A Language for Inconsistency-Tolerant Ontology Mapping BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIRE- MENTS FOR THE DEGREE OF Doctor of Philosophy. Pascal Hitzler, Ph.D. Dissertation Director Arthur Goshtasby, Ph.D. Director, Computer Science and Engi- neering Ph.D. Program Robert E.W. Fyffe, Ph.D. Vice President for Research and Dean of the Graduate School Committee on Final Examination Pascal Hitzler, Ph.D. Krzysztof Janowicz, Ph.D. Krishnaprasad Thirunarayan, Ph.D. Prabhaker Mateti, Ph.D. ABSTRACT Sengupta, Kunal. Ph.D., Department of Computer Science and Engineering, Wright State University, 2015. A Language for Inconsistency-Tolerant Ontology Mapping. Ontology alignment plays a key role in enabling interoperability among various data sources present in the web. The nature of the world is such, that the same concepts differ in meaning, often so slightly, which makes it difficult to relate these concepts. It is the omni-present heterogeneity that is at the core of the web. The research work presented in this dissertation, is driven by the goal of providing a robust ontology alignment language for the semantic web, as we show that description logics based alignment languages are not suitable for aligning ontologies. The adoption of the semantic web technologies has been consistently on the rise over the past decade, and it continues to show promise. The core component of the semantic web is the set of knowledge representation languages – mainly the W3C 1 standards Web On- tology Language (OWL), Resource Description Framework (RDF), and Rule Interchange Format (RIF). While these languages have been designed in order to be suitable for the openness and extensibility of the web, they lack certain features which we try to address in this dissertation. One such missing component is the lack of non-monotonic features, in the knowledge representation languages, that enable us to perform common sense reasoning. For example, OWL supports the open world assumption (OWA), which means that knowledge about everything is assumed to be possibly incomplete at any point of time. However, experience has shown that there are situations that require us to assume that 1World Wide Web Consortium - http://w3c.org ii certain parts of the knowledge base are complete. Employing the Closed World Assumption (CWA) helps us achieve this. Circumscription is a very well-known approach towards CWA, which provides closed world semantics by employing the idea of minimal models with respect to certain predicates which are closed. We provide the formal semantics of the notion of Grounded Circumscription, which is an extension of circumscription with desirable properties like decidability. We also provide a tableaux calculus to reason over knowledge bases under the notion of grounded circumscription. Another form of common sense logic, is default logic. Default logic provides a way to specify rules that, by default, hold in most cases but not necessarily in all cases. The classic example of such a rule is: If something is a bird then it flies. The power of defaults comes from the ability of the logic to handle exceptions to the default rules. For example, a bird will be assumed to fly by default unless it is an exception, i.e. it belongs to a class of birds that do not fly, like penguins. Interestingly, this property of defaults can be utilized to create mappings between concepts of different ontologies (knowledge bases). We provide a new semantics for the integration of defaults in description logics and show that it improves upon previously known results in literature. In this study, we give various examples to show the utility and the advantages of using a default logic based ontology alignment language. We provide the semantics and decid- ability results of a default based mapping language for tractable fragments of description logics (or OWL). Furthermore, we provide a proof of concept system and present a qualita- tive analysis of the results obtained from the system, and compare it to the results obtained by applying ontology mapping repair techniques. iii Contents 1 Introduction1 1.1 Problem Statement..............................2 1.2 Approach...................................3 1.2.1 Exploring Non-monotonic Extensions of Description Logics....3 1.2.2 Mapping Language for Tractable Description Logics........5 1.3 Structure....................................6 2 Background and Preliminaries7 2.1 Semantic Web and Ontologies........................7 2.2 Description Logics.............................. 10 2.2.1 Building Blocks (Syntax)....................... 11 2.2.2 Semantics............................... 12 2.3 Ontology Alignment............................. 16 2.4 Non-monotonic Logics............................ 18 2.4.1 Default Logic............................. 18 2.4.2 Integration with Description Logics................. 21 2.4.3 Circumscription........................... 21 3 Grounded Circumscription 26 3.1 Introduction.................................. 26 3.2 Local Closed World Reasoning with Grounded Circumscription...... 28 3.2.1 Grounded Circumscription...................... 28 3.3 Decidability of Grounded Circumscription.................. 32 3.4 Algorithms for Grounded Circumscriptive Reasoning............ 34 3.4.1 Decision Procedure for GC-Satisfiability in ALC .......... 35 3.4.2 Inference Problems beyond GC-Satisfiability............ 40 3.5 Conclusion.................................. 44 4 Free Defaults 47 4.1 Introduction and Motivation......................... 47 4.2 Semantics of Free Defaults.......................... 50 4.3 Decidability.................................. 53 4.4 Default Role Inclusion Axioms........................ 57 4.5 Application of Defaults in Ontology Alignment............... 60 4.6 Conclusion.................................. 64 iv 5 Default Logic Based Ontology Alignment for Tractable DLs 66 5.1 Introduction.................................. 66 5.2 The Description Logic ER?;O ........................ 69 5.3 Mapping Ontologies with ER?;O-Defaults.................. 77 5.3.1 Semantics and Decidability...................... 79 5.3.2 Applying Defeasible Mappings to Unknowns............ 82 5.4 Relationship with Answer sets........................ 86 5.5 Conclusion.................................. 92 6 Implementation and Evaluation 94 6.1 Implementation................................ 94 6.2 Experiments.................................. 98 6.2.1 Mapping Marriage Ontologies.................... 98 6.2.2 Mapping Biomedical Ontologies................... 103 7 Related Work 109 7.1 Non-monotonic Description Logics..................... 109 7.2 Ontology Alignment Repair......................... 111 8 Conclusion 113 8.1 Summary................................... 113 8.1.1 Grounded Circumscription (GC)................... 113 8.1.2 Free Defaults............................. 114 8.1.3 Mapping Language For ER?;O ................... 115 8.2 Future Work.................................. 116 Bibliography 120 A Appendix 136 v List of Figures 2.1 The semantic web layer cake diagram.....................8 2.2 An interpretation I of a knowledge base KB ................. 14 2.3 Interpretations I and J of the knowledge base from Example5...... 24 4.1 Running example with selected axioms.................... 48 4.2 Fragments of two ontologies, (4.17)-(4.21), respectively (4.22)-(4.24), to be aligned.................................... 61 5.1 Example mapping with selected axioms.................... 68 5.2 ER?;O completion rules. New axioms resulting from the rules are added to the existing axioms in KB. Symbols of the form A¯ can be either a class name or a nominal class. We initialize comp(KB) with KB and C v C, ? v C, ? v ? for all named classes C 2 NC ................ 71 5.3 Example mapping............................... 88 6.1 Proteg´ e´ explanation window for the inconsistency in the merged ontology.. 100 6.2 Proteg´ e´ explanation window with explanations # 1, 2 for biomedical on- tologies..................................... 104 6.3 Proteg´ e´ explanation window with explanations # 3, 4 for biomedical on- tologies..................................... 105 6.4 Proteg´ e´ explanation window with explanations # 5, 6 for biomedical on- tologies..................................... 106 vi List of Tables 2.1 Semantics of