Dynamic tractable reasoning: a modular approach to belief revision
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2020]
|
| Schriftenreihe: | Synthese library
volume 420 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 236 Seiten Diagramm |
| ISBN: | 9783030362324 |
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Datensatz im Suchindex
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| adam_text | Contents 1 Introduction.................................................................................................. 1.1 Apparent Intractability of Belief Changes........................................... 1.2 Computational Theory of Mind........................................................... 1.3 Frame Logic......................................................................................... 1.4 TM Belief Revision.............................................................................. 1.5 Modularity in Cognitive Science........................................................ 1.6 Modularity in Knowledge Representation ......................................... 1.7 Extant Tractable Logics....................................................................... 1.8 Extant Tractable Belief Revision Schemes......................................... 1.9 Overview............................................................................................... Part I 1 2 4 7 9 9 13 14 16 19 Foundations 2 Frames........................................................................................................... 2.1 Minsky-Frames...................................................................................... 2.1.1 The Abstract Theory................................................................ 2.1.2 Examples.................................................................................. 2.1.3 Criticism of the Logistic Approach ....................................... 2.2 Classes in Object-Oriented Programming.......................................... 2.2.1
The Notion of a Class.............................................................. 2.2.2 Composition and Inheritance.................................................. 2.2.3 Philosophical Logic and OOP................................................. 2.3 Theory-Elements in Structuralism....................................................... 2.3.1 Set-Theoretic Structures and Predicates ................................ 2.3.2 Potential and Actual Models.................................................... 2.3.3 Intended Applications.............................................................. 2.3.4 Links and Theory-Nets............................................................. 23 23 23 25 26 28 28 32 35 38 38 40 42 45 3 Belief Revision................................................................................................ 3.1 Classical Belief Revision Theory.......................................................... 3.1.1 Beliefs...................................................................................... 3.1.2 Belief Sets................................................................................ 49 49 49 51 xiii
xiv Contents 3.1.3 AGM Postulates for Belief Changes......... 3.1.4 Constructive Approaches........................... Belief Base Revision............................................... 3.2.1 BeUef Bases................................................. 3.2.2 Belief Bases vs. Belief Sets........................ 3.2.3 The Direct Mode of Belief Base Revision . Some Open Problems in Belief Revision Theory.. 3.3.1 Tractability.................................................. 3.3.2 The Justificatory Structure.......................... 3.3.3 Epistemic Ordering .................................... 52 54 56 56 57 59 61 61 62 63 4 Defeasible Reasoning....................................................... 4.1 The Rationale........................................................... 4.1.1 Common-Sense Reasoning........................ 4.1.2 Scientific Reasoning................................... 4.1.3 Consequence vs. Inference Operations...... 4.2 Preferred Subtheories ............................................. 4.2.1 Basic Ideas................................................... 4.2.2 Inferences from Preferred Subtheories...... 4.2.3 A Simple Example...................................... 4.2.4 Belief Revision with Preferred Subtheories 4.2.5 Reversing the Levi Identity........................ 4.3 Truth Maintenance .................................................. 67 67 67 3.2 3.3 Part II 68 69 70 70 70 72 73 75 76 Belief Revision with Frames 5 Postulates for Structuralism........................... 5.1 Preliminaries........................................... 5.2 Intended
Applications and Theoreticity . 5.3 Intended Applications Liberalised 949201 5.4 The Postulates......................................... 5.5 Semantics of Theoretical Terms............ 5.5.1 Foundations................................. 5.5.2 Defined Terms............................. 5.5.3 The Semantics of AE(T) ........... 6 Structuralist Belief Revision.............................................. 6.1 Toward a Default Theory for Structuralism.............. 6.1.1 Abductive Reasoning in Science.................. 6.1.2 The Belief Base of a Theory-Net N.............. 6.2 A Reliabilist Account of Epistemic Ranking............ 6.2.1 A Simple Case Study.................................... 6.2.2 The Reliability of Expectations..................... 6.2.3 The Epistemic Ranking of Theory-Elements 6.3 The Final Synthesis ................................................... 81 81 83 84 86 91 91 93 95 97 97 97 98 99 99 101 103 107
Contents XV 7 Truth Maintenance...................................................................................... 7.1 Computational Complexity and Cognition......................................... 7.1.1 Tractability............................................................................... 7.1.2 Computation of Revisions...................................................... 7.1.3 Cognitive Aspects.................................................................... 7.2 A Truth Maintenance System for Frames.......................................... 7.2.1 Unique Model Extensions...................................................... 7.2.2 Logical Foundations of the TMS............................................ 7.2.3 Determining Successful Intended Applications .................... 7.2.4 Revision by an Intended Application .................................... 7.2.5 Link Satisfaction...................................................................... 7.2.6 Refinements............................................................................. 7.2.7 The Truth Maintenance Algorithm......................................... 7.3 Tractability............................................................................................ 7.3.1 Operation Tree ......................................................................... 7.3.2 Termination............................................................................... 7.3.3 Computational Complexity..................................................... 7.3.4 Tractability and
Modularity..................................................... 7.4 Issues of Soundness and Completeness............................................. 7.4.1 The Inference Relation of the TMS....................................... 7.4.2 Admissible T-Extensions........................................................ 7.4.3 Division of H(N) .................................................................... 7.4.4 Subsets of Doubted Applications............................................ 7.4.5 Irrelevant Determinations........................................................ 7.4.6 Weak Determinations.............................................................. 7.4.7 Preliminary Evaluation ........................................................... 7.5 Approaching Soundness and Completeness....................................... 7.5.1 Composition............................................................................. 7.5.2 More Defeasible Reasoning.................................................... 109 109 109 113 115 117 117 117 118 119 120 121 128 132 132 134 136 140 143 143 144 145 146 147 148 148 149 149 151 8 Frame Logic.................................................................................................. 8.1 Revising Our Understanding of Links................................................. 8.2 Frame Logic......................................................................................... 8.2.1 Syntax ...................................................................................... 8.2.2 Natural Deduction
Rules......................................................... 8.2.3 Semantics.................................................................................. 8.2.4 Soundness and Completeness................................................. 8.2.5 Tractability............................................................................... 8.2.6 Composition............................................................................. 8.3 Resolution Frame Logic....................................................................... 8.3.1 The Resolution Principle.......................................................... 8.3.2 Frame Logic with Resolution.................................................. 8.3.3 Soundness, Completeness and Tractability........................... 153 153 155 155 156 161 163 164 167 168 168 170 174
xvi Contents 8.4 8.5 9 Tractable Belief Revision.................................................................... 8.4.1 Avoiding Irrelevant Determinations....................................... 8.4.2 Weak Determinations Resolved............................................. 8.4.3 TM Belief Revision................................................................. 8.4.4 Tractability .............................................................................. 8.4.5 Comparison............................................................................... Truth Maintenance by Resolution...................................................... 8.5.1 Resolution-Based Truth Maintenance.................................... 8.5.2 Compositions........................................................................... 8.5.3 Soundness, Completeness and Tractability........................... 174 175 177 177 182 187 187 188 190 191 Conclusions.................................................................................................... 195 A Proofs............................................................................................................... A.l Chapter 5................................................................................................ A.2 Chapter 7................................................................................................ A.3 Chapter 8................................................................................................ 199 199 200 206
Bibliography........................................................................................................ 219 Index of Symbols................................................................................................. 227 Author Index........................................................................................................ 233 Subject Index....................................................................................................... 235
|
| adam_txt |
Contents 1 Introduction. 1.1 Apparent Intractability of Belief Changes. 1.2 Computational Theory of Mind. 1.3 Frame Logic. 1.4 TM Belief Revision. 1.5 Modularity in Cognitive Science. 1.6 Modularity in Knowledge Representation . 1.7 Extant Tractable Logics. 1.8 Extant Tractable Belief Revision Schemes. 1.9 Overview. Part I 1 2 4 7 9 9 13 14 16 19 Foundations 2 Frames. 2.1 Minsky-Frames. 2.1.1 The Abstract Theory. 2.1.2 Examples. 2.1.3 Criticism of the Logistic Approach . 2.2 Classes in Object-Oriented Programming. 2.2.1
The Notion of a Class. 2.2.2 Composition and Inheritance. 2.2.3 Philosophical Logic and OOP. 2.3 Theory-Elements in Structuralism. 2.3.1 Set-Theoretic Structures and Predicates . 2.3.2 Potential and Actual Models. 2.3.3 Intended Applications. 2.3.4 Links and Theory-Nets. 23 23 23 25 26 28 28 32 35 38 38 40 42 45 3 Belief Revision. 3.1 Classical Belief Revision Theory. 3.1.1 Beliefs. 3.1.2 Belief Sets. 49 49 49 51 xiii
xiv Contents 3.1.3 AGM Postulates for Belief Changes. 3.1.4 Constructive Approaches. Belief Base Revision. 3.2.1 BeUef Bases. 3.2.2 Belief Bases vs. Belief Sets. 3.2.3 The Direct Mode of Belief Base Revision . Some Open Problems in Belief Revision Theory. 3.3.1 Tractability. 3.3.2 The Justificatory Structure. 3.3.3 Epistemic Ordering . 52 54 56 56 57 59 61 61 62 63 4 Defeasible Reasoning. 4.1 The Rationale. 4.1.1 Common-Sense Reasoning. 4.1.2 Scientific Reasoning. 4.1.3 Consequence vs. Inference Operations. 4.2 Preferred Subtheories . 4.2.1 Basic Ideas. 4.2.2 Inferences from Preferred Subtheories. 4.2.3 A Simple Example. 4.2.4 Belief Revision with Preferred Subtheories 4.2.5 Reversing the Levi Identity. 4.3 Truth Maintenance . 67 67 67 3.2 3.3 Part II 68 69 70 70 70 72 73 75 76 Belief Revision with Frames 5 Postulates for Structuralism. 5.1 Preliminaries. 5.2 Intended
Applications and Theoreticity . 5.3 Intended Applications Liberalised 949201 5.4 The Postulates. 5.5 Semantics of Theoretical Terms. 5.5.1 Foundations. 5.5.2 Defined Terms. 5.5.3 The Semantics of AE(T) . 6 Structuralist Belief Revision. 6.1 Toward a Default Theory for Structuralism. 6.1.1 Abductive Reasoning in Science. 6.1.2 The Belief Base of a Theory-Net N. 6.2 A Reliabilist Account of Epistemic Ranking. 6.2.1 A Simple Case Study. 6.2.2 The Reliability of Expectations. 6.2.3 The Epistemic Ranking of Theory-Elements 6.3 The Final Synthesis . 81 81 83 84 86 91 91 93 95 97 97 97 98 99 99 101 103 107
Contents XV 7 Truth Maintenance. 7.1 Computational Complexity and Cognition. 7.1.1 Tractability. 7.1.2 Computation of Revisions. 7.1.3 Cognitive Aspects. 7.2 A Truth Maintenance System for Frames. 7.2.1 Unique Model Extensions. 7.2.2 Logical Foundations of the TMS. 7.2.3 Determining Successful Intended Applications . 7.2.4 Revision by an Intended Application . 7.2.5 Link Satisfaction. 7.2.6 Refinements. 7.2.7 The Truth Maintenance Algorithm. 7.3 Tractability. 7.3.1 Operation Tree . 7.3.2 Termination. 7.3.3 Computational Complexity. 7.3.4 Tractability and
Modularity. 7.4 Issues of Soundness and Completeness. 7.4.1 The Inference Relation of the TMS. 7.4.2 Admissible T-Extensions. 7.4.3 Division of H(N) . 7.4.4 Subsets of Doubted Applications. 7.4.5 Irrelevant Determinations. 7.4.6 Weak Determinations. 7.4.7 Preliminary Evaluation . 7.5 Approaching Soundness and Completeness. 7.5.1 Composition. 7.5.2 More Defeasible Reasoning. 109 109 109 113 115 117 117 117 118 119 120 121 128 132 132 134 136 140 143 143 144 145 146 147 148 148 149 149 151 8 Frame Logic. 8.1 Revising Our Understanding of Links. 8.2 Frame Logic. 8.2.1 Syntax . 8.2.2 Natural Deduction
Rules. 8.2.3 Semantics. 8.2.4 Soundness and Completeness. 8.2.5 Tractability. 8.2.6 Composition. 8.3 Resolution Frame Logic. 8.3.1 The Resolution Principle. 8.3.2 Frame Logic with Resolution. 8.3.3 Soundness, Completeness and Tractability. 153 153 155 155 156 161 163 164 167 168 168 170 174
xvi Contents 8.4 8.5 9 Tractable Belief Revision. 8.4.1 Avoiding Irrelevant Determinations. 8.4.2 Weak Determinations Resolved. 8.4.3 TM Belief Revision. 8.4.4 Tractability . 8.4.5 Comparison. Truth Maintenance by Resolution. 8.5.1 Resolution-Based Truth Maintenance. 8.5.2 Compositions. 8.5.3 Soundness, Completeness and Tractability. 174 175 177 177 182 187 187 188 190 191 Conclusions. 195 A Proofs. A.l Chapter 5. A.2 Chapter 7. A.3 Chapter 8. 199 199 200 206
Bibliography. 219 Index of Symbols. 227 Author Index. 233 Subject Index. 235 |
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| index_date | 2024-07-03T14:29:03Z |
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| series | Synthese library |
| series2 | Synthese library |
| spelling | Andreas, Holger 1974- Verfasser (DE-588)13300726X aut Dynamic tractable reasoning a modular approach to belief revision Holger Andreas Cham, Switzerland Springer [2020] © 2020 xvii, 236 Seiten Diagramm txt rdacontent n rdamedia nc rdacarrier Synthese library volume 420 Philosophy of Mind Artificial Intelligence Logic Information and Communication, Circuits Neurosciences Philosophy of mind Artificial intelligence Information theory Glaube (DE-588)4071867-0 gnd rswk-swf Philosophy of Mind (DE-588)4248301-3 gnd rswk-swf Künstliche Intelligenz (DE-588)4033447-8 gnd rswk-swf Neurowissenschaften (DE-588)7555119-6 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Schlussfolgern (DE-588)4251178-1 gnd rswk-swf Glaube (DE-588)4071867-0 s Schlussfolgern (DE-588)4251178-1 s Künstliche Intelligenz (DE-588)4033447-8 s Informationstheorie (DE-588)4026927-9 s Logik (DE-588)4036202-4 s Neurowissenschaften (DE-588)7555119-6 s Philosophy of Mind (DE-588)4248301-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-36233-1 Synthese library volume 420 (DE-604)BV000005044 420 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032114173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andreas, Holger 1974- Dynamic tractable reasoning a modular approach to belief revision Synthese library Philosophy of Mind Artificial Intelligence Logic Information and Communication, Circuits Neurosciences Philosophy of mind Artificial intelligence Information theory Glaube (DE-588)4071867-0 gnd Philosophy of Mind (DE-588)4248301-3 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd Neurowissenschaften (DE-588)7555119-6 gnd Logik (DE-588)4036202-4 gnd Informationstheorie (DE-588)4026927-9 gnd Schlussfolgern (DE-588)4251178-1 gnd |
| subject_GND | (DE-588)4071867-0 (DE-588)4248301-3 (DE-588)4033447-8 (DE-588)7555119-6 (DE-588)4036202-4 (DE-588)4026927-9 (DE-588)4251178-1 |
| title | Dynamic tractable reasoning a modular approach to belief revision |
| title_auth | Dynamic tractable reasoning a modular approach to belief revision |
| title_exact_search | Dynamic tractable reasoning a modular approach to belief revision |
| title_exact_search_txtP | Dynamic tractable reasoning a modular approach to belief revision |
| title_full | Dynamic tractable reasoning a modular approach to belief revision Holger Andreas |
| title_fullStr | Dynamic tractable reasoning a modular approach to belief revision Holger Andreas |
| title_full_unstemmed | Dynamic tractable reasoning a modular approach to belief revision Holger Andreas |
| title_short | Dynamic tractable reasoning |
| title_sort | dynamic tractable reasoning a modular approach to belief revision |
| title_sub | a modular approach to belief revision |
| topic | Philosophy of Mind Artificial Intelligence Logic Information and Communication, Circuits Neurosciences Philosophy of mind Artificial intelligence Information theory Glaube (DE-588)4071867-0 gnd Philosophy of Mind (DE-588)4248301-3 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd Neurowissenschaften (DE-588)7555119-6 gnd Logik (DE-588)4036202-4 gnd Informationstheorie (DE-588)4026927-9 gnd Schlussfolgern (DE-588)4251178-1 gnd |
| topic_facet | Philosophy of Mind Artificial Intelligence Logic Information and Communication, Circuits Neurosciences Philosophy of mind Artificial intelligence Information theory Glaube Künstliche Intelligenz Neurowissenschaften Logik Informationstheorie Schlussfolgern |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032114173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005044 |
| work_keys_str_mv | AT andreasholger dynamictractablereasoningamodularapproachtobeliefrevision |