Graph-based knowledge representation: computational foundations of conceptual graphs:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Guildford, Surrey
Springer London
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 427 S. Ill. |
| ISBN: | 9781848002852 1848002858 |
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MARC
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| 100 | 1 | |a Chein, Michel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Graph-based knowledge representation: computational foundations of conceptual graphs |c Michel Chein ; Marie L. Mugnier |
| 264 | 1 | |a Guildford, Surrey |b Springer London |c 2009 | |
| 300 | |a XIV, 427 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804138912169328640 |
|---|---|
| adam_text | Contents
1
Introduction
................................................... 1
1.1 Knowledge
Representation and Reasoning
..................... 1
1.1.1
Knowledge-Based Systems
............................ 2
1.1.2
Requirements for a Knowledge Representation Formalism
.. 3
1.2
Conceptual Graphs
......................................... 8
1.2.1
Basic Notions
....................................... 8
1.2.2
Subsumption and Homomorphism
...................... 9
1.2.3
Formal Semantics
.................................... 11
1.2.4
Full CGs
........................................... 12
1.3
A Graph-Based Approach to KR
.............................. 13
1.3.1
Motivations
......................................... 13
1.3.2
Extensions of the Basic Formalism
..................... 14
1.3.3
Several Approaches to CGs
............................ 16
Part I Foundations: Basic and Simple Conceptual Graphs
2
Basic Conceptual Graphs
....................................... 21
2.1
Definition of Basic Conceptual Graphs (BGs)
................... 22
2.1.1
Vocabulary
......................................... 22
2.1.2
Basic Conceptual Graphs
.............................. 25
2.1.3
SubBGs and PseudoBGs
.............................. 29
2.2
BG Homomorphism
........................................ 30
2.2.1
Subsumption and Homomorphism
...................... 30
2.2.2
Bijective Homomorphisms and Isomorphisms
............ 33
2.2.3
BG Queries and Answers
............................. 34
2.3
BG Subsumption Properties
................................. 35
2.3.1
Subsumption Preorder
................................ 35
2.3.2 Irredundant
BGs
..................................... 37
2.4
Generalization and Specialization Operations
................... 40
2.4.1
Elementary Generalization Operations for BGs
........... 40
2.4.2
Generalization and Homomorphism
..................... 42
2.4.3
Elementary Specialization Operations
................... 45
2.4.4
Specialization and Homomorphism
..................... 48
2.5
Normal BGs
............................................... 49
2.5.1
Definition of Normal BGs
............................. 49
2.5.2
Elementary Operations for Normal BGs
................. 52
2.6
Complexity of Basic Problems
............................... 54
2.7
Bibliographic Notes
........................................ 56
Simple Conceptual Graphs
...................................... 59
3.1
Introduction
............................................... 60
3.2
Vocabulary
................................................ 62
3.3
Simple Conceptual Graphs (SGs)
............................. 66
3.4
Generalization and Specialization Operations
................... 69
3.5
Standard and Normal SGs
................................... 71
3.6
Coref-Homomorphism
...................................... 72
3.7 Antinormal Form
and Homomorphism
......................... 76
3.8
Bibliographic Notes
........................................ 80
Formal Semantics of SGs
....................................... 83
4.1
Model Semantic
........................................... 84
4.1.1
Models of SGs
...................................... 84
4.1.2
Soundness and Completeness of (coref) Homomorphism
... 87
4.2
Logical Semantic
........................................... 89
4.2.1
The
FOL
Semantic
Φ
................................ 89
4.2.2
Model Semantic and
Φ
............................... 91
4.3
Positive, Conjunctive, and Existential Fragment of
FOL
.......... 92
4.3.1
Ordered Language and
/ľ-Substitution
................... 93
4.3.2
Soundness and Completeness Revisited
.................. 94
4.3.3
Relationships Between SGs and
FOLCA,
3) .............. 95
4.3.4
Another
FOL
Semantic:
Ψ
............................ 98
4.4
Note on the Relationships Between Description Logics
and Conceptual Graphs
...................................... 100
4.5
Bibliographic Notes
........................................ 104
BG Homomorphism and Equivalent Notions
...................... 105
5.1
Conceptual Graphs and Conceptual Hypergraphs
................ 107
5.1.1
Conceptual Hypergraphs
.............................. 107
5.1.2
Different Kinds of Vocabularies
5.2
Graphs
5.2.1
From Graphs to BGs
5.2.2
From BGs to Graphs
5.3
Relational Structures and Databases
5.3.1
Relational Structures and BGs
10
13
14
17
19
19
5.3.2
Conjunctive Queries and BGs
..........................120
5.4
Constraint Satisfaction Problem
..............................124
Contents xi
5.4.1 Definition
of
CSP....................................124
5.4.2
From CSP to BGs
....................................127
5.4.3
From BGs to CSP
....................................128
5.5
Bibliographic Notes
........................................132
Part II Computational Aspects of Basic Conceptual Graphs
6
Basic Algorithms for BG Homoniorphisin
.........................135
6.1
Algorithms for BG Homomorphisms
..........................135
6.1.1
Basic Backtrack Algorithms
...........................136
6.1.2
Backtrack Improvements
..............................141
6.2
Constraint Processing
.......................................151
6.2.1
A Panorama of Constraint Processing Techniques
.........151
6.2.2
Arc-Consistency
.....................................154
6.2.3
Forward Checking
...................................159
6.3
Label Comparison
..........................................161
6.3.1
Basic Data Structures and Algorithms
...................163
6.3.2
Related Problems
....................................164
6.3.3
Tree Orders
.........................................166
6.3.4
Partition in Chains
...................................167
6.3.5
Lattices
............................................168
6.4
Bibliographic Notes
........................................169
7
Tractable Cases
................................................171
7.1
Introduction
...............................................171
7.1.1
About Tractability
...................................172
7.1.2
The Structure of the Target BG is of No Help
.............172
7.2
Tractability Based on the Multigraph-Acyclicity of the Source BG
. 174
7.2.1
Acyclic Multigraphs and Trees
.........................174
7.2.2
BGs Trivially Logically Equivalent to Acyclic BGs
........184
7.3
Tractability Based on the Hypergraph-Acyclicity of the Source BG
. 185
7.3.1
Use of a Join Tree
....................................187
7.3.2
Construction of a Join Tree
............................191
7.3.3
Equivalence with the Existential Conjunctive Guarded
Fragment
...........................................193
7.4
Generalizations of Graph-Acyclicity and Hypergraph-Acyclicity
... 198
7.4.1
Graphs and Treewidth
................................198
7.4.2
Hypergraphs and Hypertreewidth
.......................200
7.4.3
Expressivity Results
..................................201
7.5
What About Labels?
........................................202
7.6
Complementary Notes
......................................204
8
Other Specialization/Generalization Operations
...................207
8.1
The Least Generalization and Greatest Specialization of Two BGs
.. 208
8.2
Basic Compatibility Notions and Maximal Joins
.................212
8.2.1
Compatible Node Set
.................................212
8.2.2
Maximal Join
.......................................215
8.3
Compatible Partitions and Extended Join
.......................222
8.3.1
Compatible C-Partition and R-Partition
..................222
8.3.2
Extended Join
.......................................226
8.3.3
Join According to a Compatible Pair of
С
-Partitions.......
226
8.4
^-Specializations
...........................................228
8.4.1
Surjective Homomorphism
............................228
8.4.2
Union
..............................................229
8.4.3
Inductive Definition of BGs
...........................231
8.4.4
^/-Specializations
....................................232
8.5
Type Expansion and Contraction
..............................235
8.6
Bibliographic Notes
........................................242
Partili
Extensions
9
Nested Conceptual Graphs
......................................247
9.1
Introduction
...............................................248
9.2
Nested Basic Graphs (NBGs)
.................................249
9.3
Nested Graphs (NGs)
.......................................256
9.4
Nested Typed Graphs
.......................................258
9.5
The Semantics
Φν
..........................................262
9.5.1
Definition of
Φ/ν
.....................................263
9.5.2
Soundness and Completeness
..........................265
9.6
Representation of Nested Typed Graphs by BGs
.................267
9.7
Bibliographic Notes
........................................270
10
Rules
.........................................................273
10.1
Definition and Logical Semantics of a Rule
.....................273
10.1.1
Logical Semantics of a Rule
...........................276
10.1.2
Rule as a Bicolored Graph
.............................277
10.2
Forward Chaining
..........................................278
10.2.1
Rule Application
.....................................279
10.2.2
Derivation and Deduction
.............................281
10.2.3
Non-Redundant Rule Application
......................284
10.2.4
Soundness and Completeness of Forward Chaining
........286
10.3
Backward Chaining
.........................................291
10.3.1
Outline of the Backward Chaining Mechanism
...........292
10.3.2
Piece Resolution
.....................................294
10.3.3
Soundness and Completeness of Backward Chaining
......298
10.4
Computational Complexity of .FTC-deduction with Rules
.......301
10.4.1
Semi-Decidability of .FTC-deduction with Rules
........301
10.4.2
Decidable Cases
.....................................303
10.5
Bibliographic Notes
........................................307
11
The BG Family: Facts, Rules and Constraints
.....................311
11.1
Overview of the BG Family
..................................311
11.2
TC: Facts and Constraints
...................................313
11.2.1
Positive and Negative Constraints
......................313
11.2.2
Translation to
FOL
...................................316
11.2.3
Complexity of Consistency and Deduction
...............318
11.3
Combining Rules and Constraints
.............................321
11.3.1
TTIC: Constraints and Inference Rules
..................321
11.3.2
TEC: Constraints and Evolution Rules
..................325
11.3.3
TTZEC: Constraints, Inference and Evolution Rules
.......326
11.3.4
Complexity of Combining Rules and Constraints
..........326
11.4
Complexity in TTZC/TEC/TTZEC for Particular Cases of Rules
and Constraints
............................................327
11.4.1
Particular Cases of Rules
..............................327
11.4.2
Particular Cases of Constraints
.........................330
11.5
Bibliographic Notes
........................................334
12
Conceptual Graphs with Negation
...............................337
12.1
Full Conceptual Graphs
.....................................338
12.1.1
Existential Graphs: a Diagrammatical System for Logics
... 338
12.1.2
Full Conceptual Graphs (FCGs)
........................340
12.1.3
Logical Semantics of FCGs
............................342
12.1.4
Equivalence of CGs and
FOL
..........................344
12.1.5
FCG Calculus
.......................................346
12.1.6
Dau s FCGs
.........................................347
12.1.7
Kerdiles FCGs
......................................348
12.2
Conceptual Graphs with Atomic Negation
......................350
12.2.1
Polarized Graphs
....................................350
12.2.2
Handling Coreference and Difference
...................355
12.2.3
pg-deduction and Equivalent Problems
...............359
12.2.4
Complexity of pg-deduction
........................360
12.2.5
Special Cases with Lower Complexity for PG-DEDUCTION
. 362
12.2.6
Algorithmic Improvements
............................367
12.2.7
Querying Polarized Graphs
............................371
12.2.8
Note on Negation and Rules
...........................374
12.3
Bibliographic Notes
........................................375
13
An Application of Nested Typed Graphs: Semantic Annotation Bases
377
13.1
Annotation
................................................377
13.1.1
Annotations, Metadata and Resources
...................377
13.1.2
Examples of Annotation Base Uses
.....................378
13.1.3
Components of an Annotation System
...................380
xiv Contents
13.2 Annotation Base...........................................381
13.2.1
Exact
Knowledge....................................382
13.2.2 Modules............................................383
13.2.3 Plausible Knowledge.................................384
13.3
Querying
an Annotation Base................................385
13.3.1
Exact Search........................................
386
13.3.2
Approximate Search
..................................386
13.4
Annotation and the Semantic Web
............................388
13.5
Conclusion
................................................390
A Mathematical Background
......................................393
A.
1
Sets and Relations
..........................................394
АЛЛ
Sets and Elements
....................................394
A.
1.2
Relations and Mappings
..............................395
A.2 Graphs
...................................................397
A.2.1 Directed Graphs
.....................................397
A.2.2 Homomorphism
.....................................399
A.2.3 Different Sorts of Graphs
..............................400
A.2.4 Hypergraphs
........................................403
A.3 Ordered Sets
...............................................403
A.3.
1
Basic Notions
.......................................403
A.3.2 Lattices
............................................405
A.4 First Order Logic
(FOL)
.....................................406
A.4.
1
Syntax
.............................................406
A.4.
2
Semantics and Models
................................408
A.4.3 Clausal Form
........................................409
A.4.4 Resolution and SLD-Resolution
........................409
A.5 Algorithm and Problem Complexity
...........................410
References
.........................................................413
Index
.............................................................423
|
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| id | DE-604.BV035458226 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:43Z |
| institution | BVB |
| isbn | 9781848002852 1848002858 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017378133 |
| oclc_num | 633991112 |
| open_access_boolean | |
| owner | DE-739 DE-11 |
| owner_facet | DE-739 DE-11 |
| physical | XIV, 427 S. Ill. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer London |
| record_format | marc |
| spelling | Chein, Michel Verfasser aut Graph-based knowledge representation: computational foundations of conceptual graphs Michel Chein ; Marie L. Mugnier Guildford, Surrey Springer London 2009 XIV, 427 S. Ill. txt rdacontent n rdamedia nc rdacarrier Begriffsgraph (DE-588)4314945-5 gnd rswk-swf Wissensrepräsentation (DE-588)4049534-6 gnd rswk-swf Wissensrepräsentation (DE-588)4049534-6 s Begriffsgraph (DE-588)4314945-5 s DE-604 Mugnier, Marie-Laure Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017378133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chein, Michel Mugnier, Marie-Laure Graph-based knowledge representation: computational foundations of conceptual graphs Begriffsgraph (DE-588)4314945-5 gnd Wissensrepräsentation (DE-588)4049534-6 gnd |
| subject_GND | (DE-588)4314945-5 (DE-588)4049534-6 |
| title | Graph-based knowledge representation: computational foundations of conceptual graphs |
| title_auth | Graph-based knowledge representation: computational foundations of conceptual graphs |
| title_exact_search | Graph-based knowledge representation: computational foundations of conceptual graphs |
| title_full | Graph-based knowledge representation: computational foundations of conceptual graphs Michel Chein ; Marie L. Mugnier |
| title_fullStr | Graph-based knowledge representation: computational foundations of conceptual graphs Michel Chein ; Marie L. Mugnier |
| title_full_unstemmed | Graph-based knowledge representation: computational foundations of conceptual graphs Michel Chein ; Marie L. Mugnier |
| title_short | Graph-based knowledge representation: computational foundations of conceptual graphs |
| title_sort | graph based knowledge representation computational foundations of conceptual graphs |
| topic | Begriffsgraph (DE-588)4314945-5 gnd Wissensrepräsentation (DE-588)4049534-6 gnd |
| topic_facet | Begriffsgraph Wissensrepräsentation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017378133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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