An introduction to substructural logics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Routledge
2000
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIV, 381 S. |
| ISBN: | 041521534X 9780415215343 |
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| 245 | 1 | 0 | |a An introduction to substructural logics |c Greg Restall |
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Record in the Search Index
| _version_ | 1804127317204664320 |
|---|---|
| adam_text | Contents
List of Figures
ix
List of Tables
xi
Acknowledgements
xiii
1
Introduction
1
1.1
Introducing the Topic
.................... 1
1.2
Introducing the Book
.................... 3
1 Proof Theory
7
2
Ifs,
Ands
and
Ors
9
2.1
Consequences
....................... 9
2.2
Languages and Structures, Consecutions and Proofs
..... 14
2.3
Ifs and
Ands
........................ 22
2.4
Truth
........................... 30
2.5
Ands
and
Ors
....................... 33
2.6
Cutting and Pasting Proofs
................. 37
2.7
Putting Things Together
.................. 39
2.8
History
........................... 41
2.9
Exercises
.......................... 44
3
Modalities
47
3.1
Positive Modalities
..................... 47
3.2
Non-Normal Modalities
................... 54
3.3
Negative Modalities
.................... 59
3.4
History
........................... 69
3.5
Exercises
.......................... 70
vi
Contents
4
Hubert
Systems
73
4.1
Mass-produced Hubert Systems
............... 74
4.2
Hand Tuning
........................ 84
4.3
Consequence and Deduction Theorems
........... 86
4.4
History
........................... 87
4.5
Exercises
.......................... 88
5
Theories
89
5.1
Defining Theories
..................... 89
5.2
Constructing Prime Theories
................ 92
5.3
Metavaluations
....................... 95
5.4
History
........................... 102
5.5
Exercises
.......................... 103
6
Gentzen Systems
105
6.1
An Example System
.................... 105
6.2
The Core Ideas
.......................
Ill
6.3
The Proof
......................... 119
6.4
Examples
......................... 122
6.5
History
........................... 125
6.6
Exercises
.......................... 125
7
Formulae as Types, Proofs as Terms
127
7.1
Defining Terms and Decorating Proofs
........... 129
7.2
Introducing Normalisation
................. 137
7.3
Normalisation and Cut Elimination
............. 142
7.4
History
........................... 150
7.5
Exercises
................... ,...... 151
II Propositional Structures
153
8
Defining Propositional Structures
155
8.1
Definitions
......................... 157
8.2
Example Structures
..................... 170
8.3
Soundness and Completeness
................ 181
8.4
History
........................... 185
8.5
Exercises
........ , . . . . 186
Contents
vii
9
Manipulating Proposirional Structures
189
9.1
Algebra Facts
........................ 190
9.2
Filters, Ideals and Ideal Structures
............. 194
9.3
Negation
.......................... 201
9.4
Normal Modalities
..................... 204
9.5
The
Юеепе
Star in Structures
................ 207
9.6
History
........................... 209
9.7
Exercises
.......................... 209
10
Categories
211
10.1
Categories in a Nutshell
.................. 211
10.2
Extensional Connectives
.................. 215
10.3
Intensional Connectives
.................. 224
10.4
Coherence Spaces
..................... 227
10.5
History
........................... 232
10.6
Exercises
.......................... 232
III Frames
233
11
Frames I: Logics with Distribution
235
11.1
Examples
......................... 236
11.2
Definitions
......................... 239
11.3
Soundness and Completeness
................ 248
11.4
Negation
.......................... 260
11.5
Correspondence
...................... 263
11.6
New Conditions and New Logics
.............. 265
11.7
Conservative Extensions from Frames
............ 269
11.8
History
........................... 269
11.9
Exercises
.......................... 271
12
Frames II: Logics Rejecting Distribution
275
12.1
How to Reject Distribution
................. 275
12.2
Definitions
......................... 279
12.3
Soundness and Completeness
................ 285
12.4
Phase Spaces
........................ 288
12.5
History
........................... 292
12.6
Exercises
.......................... 293
viii Contents
13 Frame
Constructions
295
13.1
Directed
Bisìmulations
................... 295
13.2
Reduced Frames
...................... 304
13.3
Doing Without Inclusion
.................. 306
13.4
Linguistic Frames
...................... 307
13.5
History
........................... 308
13.6
Exercises
.......................... 309
IV Decidability
311
14
Decision Procedures
313
14.1
Proof Search
........................ 313
14.2
Finite Model Property
................... 318
14.3
History
........................... 321
14.4
Exercises
.......................... 322
15
Undecidability
323
15.1
KR and
Projective
Spaces
.................. 324
15.2
The KR Result Generalised
................. 327
15.3
Undecidability via Machines
................ 331
15.4
History
........................... 336
15.5
Exercises
........................... 336
V Coda
337
16
Using
Substructural
Logic
339
16.1
Internal and External Perspectives
............. 339
16.2
Points as States
....................... 341
16.3
Disjunctive Syllogism and Worlds
.............. 344
16.4
Pluralism about Consequence
................ 346
16.5
History
........................... 347
Bibliography
349
Index
365
Restall
has written a powerful book... It is the first book in a
long time that has made me want to teach from it right away.
Nuel Belnap,
ŕ. jh
An Introduction
ta Substructural
Logics represents the first
systematic collection of new results in our approach to and
understanding of logics.
Stechen
R vs
Restall s introduction to
substructural
logics is a tour
de force/
Gral· d
This book introduces an important group of logics that have come to be
known under the umbrella term substructure! . Substruct agics
have independently
¡ed
to Significant developments in philosophy,
computing and linguistics. An introduction to
Substructural
Log
e
ftrst book to systematically survey the new results and the
significant impact that this ctass of logics has had on a wide range of
fields. The following topics are covered:
Both students and professors of philosophy, computing, linguistics
and mathematics will find this book an important addition to
their readtng.
sophy at Macquarie
Univers
Sydney
New Fetter I«». Untea
ŁC4?
4££
29
«lest
354*
Street. New York NT
ЮС
ISBN
Ч7п-а-Ч15-гД.53Ч-Э
90000
,
80415
215343
|
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| callnumber-label | BC135 |
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| classification_rvk | CC 2400 CC 2600 SK 130 |
| ctrlnum | (OCoLC)41482150 (DE-599)BVBBV012659334 |
| dewey-full | 160 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 160 - Philosophical logic |
| dewey-raw | 160 |
| dewey-search | 160 |
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| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| spelling | Restall, Greg Verfasser aut An introduction to substructural logics Greg Restall 1. publ. London [u.a.] Routledge 2000 XIV, 381 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Logica gtt Logique symbolique et mathématique Modaliteit gtt Symbolische logica gtt Logik Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008601336&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008601336&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Restall, Greg An introduction to substructural logics Logica gtt Logique symbolique et mathématique Modaliteit gtt Symbolische logica gtt Logik Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4151278-9 |
| title | An introduction to substructural logics |
| title_auth | An introduction to substructural logics |
| title_exact_search | An introduction to substructural logics |
| title_full | An introduction to substructural logics Greg Restall |
| title_fullStr | An introduction to substructural logics Greg Restall |
| title_full_unstemmed | An introduction to substructural logics Greg Restall |
| title_short | An introduction to substructural logics |
| title_sort | an introduction to substructural logics |
| topic | Logica gtt Logique symbolique et mathématique Modaliteit gtt Symbolische logica gtt Logik Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logica Logique symbolique et mathématique Modaliteit Symbolische logica Logik Logic, Symbolic and mathematical Mathematische Logik Einführung |
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