Mathematical aspects of logic programming semantics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2011
|
| Schriftenreihe: | Studies in informatics series
A Chapman & Hall book |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020663111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XXX, 274 S. |
| ISBN: | 9781439829615 9781138114227 |
Internformat
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| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2011 | |
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Datensatz im Suchindex
| _version_ | 1819348825209307136 |
|---|---|
| adam_text | Contents
List of Figures
xi
List of Tables
xiii
Preface
xv
Introduction
xix
About the Authors
xxix
1
Order and Logic
1
1.1
Ordered Sets and Fixed-Point Theorems
........... 1
1.2
First-Order Predicate Logic
................... 7
1.3
Ordered Spaces of Valuations
.................. 12
2
The Semantics of Logic Programs
23
2.1
Logic Programs and Their Models
............... 23
2.2
Supported Models
........................ 28
2.3
Stable Models
.......................... 32
2.4
Fitting Models
.......................... 37
2.5
Perfect Models
.......................... 43
2.6
Well-Founded Models
...................... 56
3
Topology and Logic Programming
65
3.1
Convergence Spaces and Convergence Classes
......... 66
3.2
The Scott Topology on Spaces of Valuations
......... 69
3.3
The Cantor Topology on Spaces of Valuations
........ 76
3.4
Operators on Spaces of Valuations Revisited
......... 83
4
Fixed-Point Theory for Generalized Metric Spaces
87
4.1
Distance Functions in General
................. 88
4.2
Metrics and Their Generalizations
............... 91
4.3
Generalized Ultrametrics
.................... 97
vn
viii Contents
4.4
Dislocated Metrics
........................ 102
4.5
Dislocated Generalized Ultrametrics
.............. 104
4.6
Quasimetrics
........................... 106
4.7
A Hierarchy of Fixed-Point Theorems
............. 112
4.8
Relationships Between the Various Spaces
........... 114
4.9
Fixed-Point Theory for Multivalued Mappings
........ 125
4.10
Partial Orders and Multivalued Mappings
........... 127
4.11
Metrics and Multivalued Mappings
.............. 129
4.12
Generalized Ultrametrics and Multivalued Mappings
..... 129
4.13
Quasimetrics and Multivalued Mappings
........... 132
4.14
An Alternative to Multivalued Mappings
........... 136
5
Supported Model Semantics
139
5.1
Two-Valued Supported Models
................. 140
5.2
Three-Valued Supported Models
................ 151
5.3
A Hierarchy of Logic Programs
................. 159
5.4
Consequence Operators and Fitting-Style Operators
..... 161
.- 5.5
Measurability Considerations
.................. 166
6
Stable and Perfect Model Semantics
169
6.1
The
Fixpoint
Completion
.................... 169
6.2
Stable Model Semantics
..................... 171
6.3
Perfect Model Semantics
.................... 175
7
Logic Programming and Artificial Neural Networks
185
7.1
Introduction
........................... 185
7.2
Basics of Artificial Neural Networks
.............. 188
7.3
The Core Method as a General Approach to Integration
. . . 191
7.4
Propositional Programs
..................... 192
7.5
First-Order Programs
...................... 196
7.6
Some Extensions
-
The Propositional Case
.......... 212
7.7
Some Extensions
-
The First-Order Case
........... 218
8
Final Thoughts
221
8.1
Foundations of Programming Semantics
............ 221
8.2
Quantitative Domain Theory
.................. 222
8.3
Fixed-Point Theorems for Generalized Metric Spaces
.... 223
8.4
The Foundations of Knowledge Representation and Reasoning
223
8.5
Clarifying Logic Programming Semantics
........... 224
8.6
Symbolic and Subsymbolic Representations
.......... 225
8.7
Neural-Symbolic Integration
.................. 225
8.8
Topology, Programming, and Artificial Intelligence
...... 226
Contents ix
Appendix:
Transfinite
Induction
and General Topology
229
A.I The Principle of
Transfinite
Induction
............. 229
A.
2
Basic Concepts from General Topology
............ 234
A.3 Convergence
........................... 237
A.
4
Separation Properties and Compactness
............ 238
A.
5
Subspaces and Products
..................... 239
A.6 The Scott Topology
....................... 240
Bibliography
243
Index
265
|
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| id | DE-604.BV036745745 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T14:41:09Z |
| institution | BVB |
| isbn | 9781439829615 9781138114227 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020663111 |
| oclc_num | 705934363 |
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| owner_facet | DE-473 DE-BY-UBG DE-19 DE-BY-UBM |
| physical | XXX, 274 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Studies in informatics series A Chapman & Hall book |
| spellingShingle | Hitzler, Pascal Seda, Anthony Mathematical aspects of logic programming semantics Logic programming Mathematische Methode (DE-588)4155620-3 gnd Logische Programmierung (DE-588)4195096-3 gnd Semantische Analyse (DE-588)4169748-0 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4195096-3 (DE-588)4169748-0 |
| title | Mathematical aspects of logic programming semantics |
| title_auth | Mathematical aspects of logic programming semantics |
| title_exact_search | Mathematical aspects of logic programming semantics |
| title_full | Mathematical aspects of logic programming semantics Pascal Hitzler, Kno.e.sis Center at Wright State University, Dayton, Ohio, USA ; Anthony Seda, University Colege Cork, Ireland |
| title_fullStr | Mathematical aspects of logic programming semantics Pascal Hitzler, Kno.e.sis Center at Wright State University, Dayton, Ohio, USA ; Anthony Seda, University Colege Cork, Ireland |
| title_full_unstemmed | Mathematical aspects of logic programming semantics Pascal Hitzler, Kno.e.sis Center at Wright State University, Dayton, Ohio, USA ; Anthony Seda, University Colege Cork, Ireland |
| title_short | Mathematical aspects of logic programming semantics |
| title_sort | mathematical aspects of logic programming semantics |
| topic | Logic programming Mathematische Methode (DE-588)4155620-3 gnd Logische Programmierung (DE-588)4195096-3 gnd Semantische Analyse (DE-588)4169748-0 gnd |
| topic_facet | Logic programming Mathematische Methode Logische Programmierung Semantische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020663111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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