Belief revision in non-classical logics

✍ Scribed by Márcio Moretto Ribeiro

• Publisher: Springer
• Year: 2013
• Tongue: English
• Leaves: 127
• Series: SpringerBriefs in computer science
• Category: Library

✦ Synopsis

Since the advent of the Semantic Web, interest in the dynamics of ontologies (ontology evolution) has grown significantly. Belief revision presents a good theoretical framework for dealing with this problem; however, classical belief revision is not well suited for logics such as Description Logics.Belief Revision in Non-Classical Logics presents a framework which can be applied to a wide class of logics that include - besides most Description Logics such as the ones behind OWL - Horn Logic and Intuitionistic logic, amongst others. The author also presents algorithms for the most important constructions in belief bases. Researchers and practitioners in theoretical computing will find this an invaluable resource. Read more... Consequence -- Logics -- Classical Belief Revision -- AGM Contraction in Non-Classical Logics -- AGM Revision in Logics Without Negation -- Base Revision in Logics Without Negation -- Algorithms for Belief Bases -- Conclusion

✦ Table of Contents

Cover......Page 1
Belief Revision in Non-Classical Logics......Page 3
Preface......Page 6
Contents......Page 8
9 Conclusion......Page 11
1.1 Belief Revision......Page 12
1.3 Postulates and Constructions......Page 13
1.4 Non-Classical Logics......Page 14
1.6 Organization of the Book......Page 15
References......Page 16
2.1 Tarskian Consequence Operator......Page 18
2.2.1 Properties of the Consequence Operator......Page 20
2.3 Standard Languages......Page 24
References......Page 27
3 Logics......Page 28
3.1.2 Semantic......Page 29
3.1.3 Axiomatic System......Page 30
3.1.4 Properties......Page 34
3.2.1 Semantics......Page 35
3.2.2 Axiomatic System......Page 36
3.2.3 Properties......Page 38
3.3 Horn Logic (Horn)......Page 39
3.3.1 Properties......Page 40
3.4 Description Logics......Page 41
3.4.1 Language......Page 42
3.4.2 Semantics......Page 43
3.4.3 Extensions of ALC......Page 44
3.4.4 OWL......Page 46
3.4.5 Properties......Page 47
3.5 Conclusion......Page 51
References......Page 52
4.1 Belief Systems......Page 54
4.2 AGM Theory......Page 56
4.2.1 AGM Contraction......Page 57
4.2.2 AGM Revision......Page 62
4.3 Belief Base Theory......Page 65
4.3.1 Base Contraction......Page 66
4.3.2 Belief Base Revision......Page 71
4.3.3 Belief Base Semi-Revision......Page 75
4.4 Conclusion......Page 78
References......Page 79
5.1 Generalized AGM Postulates......Page 81
5.2 AGM Compliance......Page 82
5.3 Relevance Compliance......Page 84
5.4 Relevance and Partial Meet Contraction......Page 85
5.5 Rationality......Page 88
5.6 Conclusion......Page 90
References......Page 91
6.2 Construction......Page 93
6.3 Representation Theorems......Page 95
References......Page 98
7.1 External Revision Without Negation......Page 101
7.1.1 External Kernel Revision With Strong Success......Page 102
7.1.2 External Kernel Revision with Strong Consistency......Page 104
7.1.3 External Partial Meet Revision with Strong Success......Page 105
7.1.4 External Partial Meet Revision with Strong Consistency......Page 107
7.2 Internal Revision Without Negation......Page 108
7.2.1 Internal Partial Meet Revision......Page 109
7.2.2 Internal Kernel Revision......Page 110
7.3 Conclusion......Page 112
References......Page 113
8.1 Computing One α-Kernel......Page 114
8.2 Minimal Cuts......Page 116
8.3 Computing the Kernel......Page 117
8.4 Computing the Remainder Set......Page 118
8.5 Kernel and Remainder Sets......Page 119
8.6 Conclusion......Page 121
References......Page 122
References......Page 125
Index......Page 126