ISBN: 3-540-64515-2
TITLE: The Automation of Reasoning with Incomplete Information
AUTHOR: Schaub, Torsten
TOC:

Preface V 
Acknowledgments VII 
1. Introduction 1 
1.1 The plan of the book 4 
1.2 The book in context 6 
1.3 Preliminaries 9 
2. The original approach: Classical default logic 11 
2.1 Formal properties 13 
2.2 Restricted default theories 18 
2.3 A semantics for classical default logic 20 
3. An alternative approach: Constrained default logic 23 
3.1 Motivation 23 
3.2 Constrained default logic 24 
3.3 Formal properties 26 
3.4 The focused models semantics 28 
3.5 Variations of constrained default logic 30 
3.6 Conclusion 32 
4. Putting default logics into perspective 33 
4.1 Variants modifying the notion of consistency 33 
4.1.1 A guiding example 33 
4.1.2 Justified default logic 34 
4.1.3 Constrained default logic: Revisited 37 
4.1.4 Rational default logic 40 
4.2 Variants recording consistency assumptions 41 
4.2.1 Cumulative default logic 42 
4.2.2 Variants of cumulative default logic 47 
4.3 Other Variants 50 
4.4 Conclusion 51 
5. A context-based framework for default logics 53 
5.1 Motivation 53 
5.2 Contextual default logic 55 
5.3 Embedding existing default logics 58 
5.4 Formal properties 61 
5.5 Conclusion 62 
6. Possible worlds semantics for default logics 63 
6.1 Motivation 63 
6.2 Possible worlds semantics for constrained default logic 65 
6.3 Possible worlds semantics for classical default logic 67 
6.4 Possible worlds semantics for justified default logic 69 
6.5 Possible worlds semantics for contextual default logic 72 
6.6 Conclusion 74 
7. Adding specificity to default logics 75 
7.1 Motivation 75 
7.2 Determination of specificity information 76 
7.3 Compiling specificity into default theories 80 
7.4 Conclusion 82 
8. Adding lemma handling to default logics 85 
8.1 Motivation 85 
8.2 Lemma handling in constrained default logic 86 
8.3 Lemma handling in classical default logic 90 
8.4 Conclusion 90 
9. Query-answering in default logics 93 
9.1 Motivation 93 
9.2 Computational characterizations 96 
9.3 A method for query-answering in default logics 98 
9.3.1 The connection method 99 
9.3.2 Complementarity 100 
9.3.3 Admissibility 102 
9.3.4 Compatibility 103 
9.3.5 Characterizing default proofs 105 
9.4 Implementing the approach 106 
9.4.1 An algorithm 107 
9.4.2 A preliminary case-study 111 
9.5 An incremental approach 112 
9.5.1 An alternative characterization of extensions 113 
9.5.2 Incremental compatibility 114 
9.5.3 An incremental algorithm 116 
9.6 Discussion 119 
9.7 Experiments 121 
9.7.1 A straightforward implementation 121 
9.7.2 Implementations separating compatibility 123 
9.7.3 Implementations integrating compatibility 125 
9.8 Extensions 127 
9.8.1 Integration of lemma handling 128 
9.8.2 Model-based consistency-checking 129 
9.8.3 Skeptical query-answering 131 
9.9 Conclusion 132 
10. A Prolog-technology compiler for query-answering 135 
10.1 Motivation 135 
10.2 Implementing query-answering 136 
10.3 Extensions and implementation 140 
10.4 Conclusion 141 
11. Conclusions and perspectives 143 
A. Appendix 147 
A.1 Original definition of rational extensions 147 
A.2 Modal logic 148 
References 149 
END
