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Knowledge representation research is not only formal, it is also descriptiveand normative. Its aim is to implement a formal system which captures a practically relevant body of cognitive faculties employed by humans and capitalizes on its technical strength to extend human knowledge representation and reasoning capabilities. In this monograph, the author develops formalisms for his own notion of a vivid knowledge representation and reasoning system, characterized by the presence of two kinds of negation (weak and strong) and the requirements of restricted reflexivity, constructivity, and non-explosiveness. The book is based on work carried out within an interdisciplinary research project at the Free University of Berlin.

Knowledge representation research is not only formal, it is also descriptiveand normative. Its aim is to implement a formal system which captures a practically relevant body of cognitive faculties employed by humans and capitalizes on its technical strength to extend human knowledge representation and reasoning capabilities. In this monograph, the author develops formalisms for his own notion of a vivid knowledge representation and reasoning system, characterized by the presence of two kinds of negation (weak and strong) and the requirements of restricted reflexivity, constructivity, and non-explosiveness. The book is based on work carried out within an interdisciplinary research project at the Free University of Berlin.

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CONTENTS
1 General Introduction = 1
 1.1 Overview = 3
 1.2 Vivid Knowledge Representation and Logic Programming = 5
2 Vivid Knowledge Representation and Reasoning = 7
 2.1 Principles of Vividness = 7
 2.2 Vivid Logic versus Standard Logic = 11
  2.2.1 Inferences and Answers = 13
  2.2.2 Updates = 14
  2.2.3 Knowledge Representation Systems = 15
  2.2.4 Examples = 15
 2.3 Different Types of Inference = 17
  2.3.1 Constructivity = 18
  2.3.2 Non-Explosiveness = 19
 2.4 Different Types of  Knowledge Bases = 20
  2.4.1 Unique Representation = 22
  2.4.2 Definite information = 22
  2.4.3 Negation-as-Failure and Indefinite Information = 23
 2.5 Different Types of Queries = 24
  2.5.1 Intensional Queries = 25
  2.5.2 Non-ground Queries and the Problem of Definiteness = 25
  2.5.3 Existential Queries and the Generation of Answers = 26
 2.6 Different Types of Updates = 27
 2.7 Rule Knowledge Representation Systems = 30
 2.8 Equivalence between KBs and KRSs = 32
 2.9 Levesque's Concept of a Vivid Knowledge Base = 34
 2.10 On the Concept of a VKRS = 36
  2.10.1 Simplification of Compound Formulas = 37
  2.10.2 How to Construct a Definite VKRS = 38
3 Partiality, Paraconsistency and Constructivity = 41
 3.1 Partial Logic = 41
  3.1.1 Partial Models = 42
  3.1.2 Four-Valued Truth Tables = 45
  3.1.3 Some Remarks on Implication = 46
  3.1.4 Natural Deduction = 46
  3.1.5 Disjunctive Normal Form = 48
  3.1.6 Partial Logic and Classical Logic = 49
 3.2 Belnap's Concept of an Information State = 51
  3.2.1 Definite Epistemic States = 52
  3.2.2 General Epistemic States = 53
  3.2.3 Information States = 57
  3.2.4 Rule-Based Systems as Information States = 58
 3.3 Paraconsistent Constructive Logic = 58
  3.3.1 Partial Kripke Models for Constructive Logic = 59
  3.3.2 Natural Deduction = 60
  3.3.3 Definite Information = 61
  3.3.4 Disjunctive Normal Form = 62
4 Vivid Reasoning on the Basis of Facts = 63
 4.1 Fact Bases = 63
 4.2 Inherent Consistency in Fact Bases = 65
  4.2.1 Deleting Contradictory Information = 66
  4.2.2 Keeping Contradictory Information = 67
 4.3 Partial and Total Representation of Predicates = 68
 4.4 Example = 69
 4.5 Exact Predicates and Indefinite Answers = 69
 4.6 Epistemic States and Weak Negation = 71
5 Lindenbaum-Algebraic Semantics of Logic Programs = 75
 5.1 Introduction = 75
 5.2 Positive Logic Programs = 76
  5.2.1 The Atom Hierarchy of a Program = 77
  5.2.2 Valuations in Distributive Lattices as Models = 78
  5.2.3 Construction of an Adequate Model = 79
  5.2.4 Example = 81
  5.2.5 Possible Applications = 81
 5.3 Logic Programs with strong Negation = 81
  5.3.1 The Literal Hierarchy of a Program = 82
  5.3.2 Valuations in DeMorgan Algebras = 83
  5.3.3 Construction of an Adequate Model = 84
  5.3.4 Example = 86
 5.4 Conclusion = 86
6 Logic Programming with Strong Negation and Inexact Predictes = 89
 6.1 Introduction = 89
 6.2 Logic Programs with Strong Negation = 92
 6.3 Model Theory = 93
 6.4 Proof Theory = 93
  6.4.1 Partial and Total Predicates = 95
 6.5 Wellfounded Programs = 97
 6.6 Non-Wellfounded Programs = 98
  6.6.1 Top-Down Derivation = 98
  6.6.2 Bottom-Up Derivation = 99
 6.7 Logic Programs with Strong Negation as Vivid Rule Knowledge Bases = 100
 6.8 Relation to other Logics = 101
  6.8.1 Reducibility to Positive Logic = 101
  6.8.2 Relation to Classical Logic = 103
  6.8.3 Relation to Forward Chaining = 104
  6.8.4 Relation to Constructive Logic = 104
 6.9 Inconsistency Handling = 106
 6.10 Related work = 108
 6.11 Conclusion = 110
7 Vivid Reasoning on the Basis of Rules = 111
 7.1 Introduction = 111
 7.2 Vivid Knowledge Bases = 112
 7.3 Model Theory = 114
 7.4 Wellfounded VKBs = 116
 7.5 weakly wellfounded VKBs = 120
  7.5.1 The Induced Model Mv Is Perfect = 120
  7.5.2 Loop-Tolerant Top-Down Derivation = 121
  7.5.3 Bottom-Up Derivation = 121
 7.6 VKBs as Rule Knowledge Bases = 122
 7.7 Related Work = 123
  7.7.1 The 'Answer Set Semantics' of Gelfond and Lifschitz = 123
  7.7.2 The 'wellfounded Semantics with Explicit Negation' of Pereira and Alferes = 124
  7.7.3 Other Work on the Use of two Kinds of Negation = 125
 7.8 Weak Negation and Indefinite Knowledge = 127
 7.9 Conclusion = 128
8 Further Topics, Open Problems = 131
 8.1 Disjunctive Information = 131
 8.2 Conditional Queries = 132
 8.3 Active Knowledge Bases = 133
Bibliography = 137
An Interpreter for VL in Prolog = 145
Index = 147