Open Research Online The Open University’s repository of research publications and other research outputs Generating Natural Language Explanations For Entailments In Ontologies Thesis How to cite: Nguyen, Tu Anh Thi (2013). Generating Natural Language Explanations For Entailments In Ontologies. PhD thesis The Open University. For guidance on citations see FAQs. c 2013 Tu Nguyen Version: Version of Record Link(s) to article on publisher’s website: http://dx.doi.org/doi:10.21954/ou.ro.000098cc Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online’s data policy on reuse of materials please consult the policies page. oro.open.ac.uk GENERATING NATURAL LANGUAGE EXPLANATIONS FOR ENTAILMENTS IN ONTOLOGIES A THESIS SUBMITTED TO THE OPEN UNIVERSIY (UNITED KINGDOM) FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF MATHEMATICS, COMPUTING & TECHNOLOGY 2013 by Tu Anh T. Nguyen Department of Computing Contents List of Figures vii List of Tables xi Abstract 1 Acknowledgements 3 1 Introduction 5 1.1 Research Problem and Methodological Approach . .7 1.2 Contributions . 10 1.3 Plan of the Thesis . 11 1.4 Published Work . 12 2 Background 13 2.1 OWL Ontology and Description Logics . 13 2.1.1 OWL Ontology . 13 2.1.2 Description Logics . 14 2.1.3 Syntax . 15 i 2.1.4 Formal Semantics . 16 2.2 Reasoning in Description Logics . 18 2.2.1 Reasoning Tasks . 18 2.2.2 Structural Subsumption Algorithms . 20 2.2.3 Tableau-Based Algorithms . 21 2.2.4 Resolution-Based Algorithms . 23 2.3 Justifications for Entailments . 25 2.3.1 Justifications as Explanations . 25 2.3.2 Computing Justifications . 26 2.3.3 Laconic justifications . 28 2.4 Discussion and Conclusions . 30 3 Related Work 33 3.1 Explaining Reasoning in Description Logics . 33 3.1.1 Reasoning-Based Explanations . 33 3.1.2 Justification-Based Explanations . 38 3.2 Explaining Mathematical Theorems . 41 3.3 Discussion and Conclusions . 46 4 Construction of Deduction Rules 49 4.1 Ontology Corpus . 49 4.2 Collecting Justifications for Entailments . 51 4.2.1 Method . 51 4.2.2 Results . 52 4.3 Collecting Deduction Patterns . 53 4.3.1 Structural Equivalence Relation . 54 ii 4.3.2 Method . 55 4.3.3 Results . 57 4.4 Collecting Deduction Rules . 58 4.4.1 Method . 58 4.4.2 Results . 60 4.4.3 Coverage of the Rule Set . 62 4.5 Conclusions and Future Work . 62 5 Construction of Proof Trees 69 5.1 Computing Initial Trees . 70 5.1.1 Method . 70 5.1.2 Exceptions . 71 5.2 Computing Proof Trees . 76 5.3 Feasibility of Computing Proof Trees . 78 5.4 Conclusions and Future Work . 79 6 Verbalisations for Deduction Rules 81 6.1 Diversity of Verbalisations for Deduction Rules . 81 6.2 Verbalisations for OWL Axioms . 83 6.2.1 State of the Art . 83 6.2.2 Selection of Verbalisations . 86 6.3 Verbalisations of Deduction Rules . 87 6.3.1 Selection of Verbalisations . 91 6.3.2 Extra Statements for Implicit Information . 92 6.4 An Empirical Study . 98 6.4.1 Candidate Verbalisations . 99 iii 6.4.2 Materials . 100 6.4.3 Method . 101 6.4.4 Results . 102 6.5 Conclusions and Future Work . 109 7 Understandability of OWL Inferences 111 7.1 Related Work . 111 7.2 Measuring the Understandability of Deduction Rules . 113 7.2.1 Materials . 113 7.2.2 Method . 114 7.2.3 Control Questions and Response Bias . 114 7.2.4 Facility Indexes . 116 7.3 Predicting the Understandability of OWL Inferences . 116 7.4 Evaluation of the Model . 117 7.4.1 Materials . 117 7.4.2 Method . 120 7.4.3 Control Questions and Response Bias . 121 7.4.4 Analysis of Objective Understanding . 122 7.4.5 Analysis of Subjective Understanding . 124 7.5 Discussion and Conclusions . 131 8 Strategy-Based Explanations for Hard Deduction Rules 133 8.1 Identification of Hard Deduction Rules . 133 8.2 Special Strategies for Explanations . 135 8.3 Evaluation of the Strategies . 137 8.3.1 Materials . 137 iv 8.3.2 Method . 139 8.3.3 Control Questions . 140 8.3.4 Response Bias . 140 8.3.5 Results of Study 1 . 142 8.3.6 Results of Study 2 . 143 8.4 Discussion and Conclusions . 145 9 Generation of Explanations 147 9.1 Generation of Axiom Verbalisations . 147 9.1.1 Lexicons for Atomic Entities . 147 9.1.2 Templates for OWL Constructors . 149 9.2 Generation of Explanations for Steps . 150 9.3 Generation of Complete Explanations . 151 9.4 Implementation and User Interface . 152 9.5 Conclusions and Future Work . 153 10 Preliminary Evaluation 155 10.1 Materials . 157 10.2 Method . 164 10.3 Control Questions . 164 10.4 Results . 164 10.5 Subjects' Comments and Lessons Learnt . 167 10.6 Related Work . 168 10.7 Conclusions and Future Work . 169 11 Conclusion 171 11.1 Answers to Research Questions . 172 v 11.2 Other Key Findings . 172 11.3 Limitations of the Research . 173 11.4 Broader Significance of the Work . 174 11.5 Future Work . 175 Bibliography 177 Index 193 A Frequently Occurring Deduction Patterns 193 B Subjects' Comments from the Preliminary Evaluation Study 197 vi List of Figures 1.1 An example of a proof tree generate by the system . .9 1.2 Architecture of the explanation system . 10 2.1 A justification for an entailment of an ontology . 25 2.2 The basic algorithm for computing a single justification . 28 3.1 An example of an explanation generated by Kwong's system . 38 3.2 Schematic of a justification oriented proof . 39 3.3 A example of a justification oriented proof generated by Horridge's system . 40 3.4 An example of a natural deduction proof generated by Lingenfelder's system 42 3.5 An example of a proof generated by Huang's system . 44 3.6 Reconstruction of an assertion level inference rule in Huang's work . 46.