Nonmonotonic Reasoning: A Unifying FrameworkThe capability to reason in a world full of uncertainties, vagueness and ignorance is what distinguishes humans. This ability to argument in a partially known world is the informal definition of common-sense reasoning. The question how common-sense reasoning is performed occupied humanity since we can think of. Last century this issue reached an immense importance. Especially during the last three decades the study of common-sense reasoning became one of the major research topics in Artificial Intelligence (AI). Several formalisms to capture the mechanism of common-sense reasoning have been proposed so far. This book concentrates on presenting the most important formalisms for common-sense reasoning, and, showing that one of the discussed formalisms serves perfectly to capture the mechanism of common-sense reasoning, since this formalism subsumes all other in this book introduced formalisms dealing with common-sense reasoning. |
Contents
| 1 | |
| 2 | |
113 Relations | 4 |
114 Ordinals | 5 |
115 Fixpoints | 6 |
121 Syntax of Propositional Logic | 7 |
122 Semantics of Propositional Logic | 8 |
123 Theories and Inference Systems | 10 |
514 Restrictions on Autoepistemic Expansions | 87 |
52 Embedding | 88 |
521 Translation | 89 |
523 Minimal Expansions | 94 |
525 Super Strongly Grounded Expansions | 95 |
53 Relations To Default Logic | 96 |
532 Remarks | 97 |
54 Inverse Transformation | 98 |
13 Consequences of a Theory | 12 |
132 Marginalization | 14 |
133 Quantifier Elimination | 17 |
Nonmonotonic Reasoning | 21 |
22 Nonmonotonic Systems | 23 |
222 Autoepistemic Logic | 26 |
223 Default Logic | 28 |
224 Circumscription and Closed World Assumption | 29 |
225 Truth Maintenance Systems | 31 |
23 Objections | 33 |
Argumentation Systems | 37 |
311 Introductory Example | 38 |
312 Scenarios | 39 |
313 Arguments | 41 |
314 Extending The Basic Framework | 43 |
32 Basic Properties | 45 |
322 Skeptical and Credulous Reasoning | 47 |
323 Nonmonotonicity | 48 |
33 Separable Argumentation Systems | 49 |
34 Remarks | 52 |
Reiters Default Logic | 55 |
42 Semantics of Default Logic | 60 |
43 Translation | 63 |
432 ConsequenceJustification Pairs | 66 |
433 Computing Default Terms | 73 |
434 Query Answering | 76 |
Autoepistemic Logic | 79 |
511 Semantic Characterization of Expansions | 80 |
512 Syntactic Characterization of Expansions | 82 |
513 Autoepistemic Reduction Theorem | 85 |
543 Conclusion | 100 |
Modified Default Logic | 101 |
62 Semantics for Modified Default Logic | 104 |
63 Characterization of Modified Extensions | 105 |
632 Computing Modified Default Terms | 111 |
633 Query Answering | 113 |
Alternative Formalizations | 115 |
712 Singular Embedding | 117 |
713 Constrained Default Terms | 121 |
72 Hypothetical Default Logic | 123 |
722 Relations to Argumentation Systems | 125 |
73 Constrained vs Hypothetical Default Reasoning | 127 |
74 Supernormal Default Theories | 130 |
Minimization and Falsification | 133 |
811 Circumscribing one Proposition | 135 |
812 Circumscribing Several Propositions | 138 |
813 Semantics of Circumscription | 142 |
82 Negation as Failure | 143 |
822 Generalized Closed World Assumption | 144 |
823 Extended Generalized Closed World Assumption | 145 |
824 Careful Closed World Assumption | 146 |
825 Extended Closed World Assumption | 147 |
826 Iterated Closed World Assumption | 148 |
83 Argumentation Systems and Minimization | 149 |
832 Variants of the General Case | 153 |
833 The Basic Cases | 155 |
References | 157 |
| 167 | |
Common terms and phrases
a₁ allows already applicable approachable argumentation system associated assume autoepistemic expansion autoepistemic theory belief set called chapter characterization circumscription closed world assumption complete compute conclude conjunction consequence Consider consistent constrained default constrained extension construct contains contradictions corollary default assumption default logic default term default theory default theory E,A defined definition denoted discuss disjunction equivalent exactly Example extension fact Finally fixpoint formalisms formula framework Furthermore given hence hypothesis identify implies inconsistent inference interpretation introduced justifications language lemma Let E,A literals means minimal modal modified default modified extension Moreover nonmonotonic normal form Note notion objective operator possible present PROOF propositional logic prove reasoning relation respect result rule satisfies scenarios semantics sequence skeptical specified stable term strongly grounded structure subset supporting theorem tion true usual µI(E
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