A structuralist theory of logic:
Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that is does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1992
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| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that is does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part III defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is followed by a substantial treatment of the extensionality of each of the operators, as well as the relation of negation and its dual, because of the novel results they yield. Part IV considers modal operators and examines their interactions with logical operators. By obtaining the usual results without the usual assumptions, this new approach allows one to give a very simple account of modal logic, minus the excess baggage of possible world semantics. The book is aimed at philosophers, logicians, mathematicians, linguists, and computer scientists. It will be accessible to advanced undergraduates and graduates in those fields. |
| Beschreibung: | XI, 418 S. graph. Darst. |
| ISBN: | 0521412676 |
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| 520 | 3 | |a Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that is does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part III defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is followed by a substantial treatment of the extensionality of each of the operators, as well as the relation of negation and its dual, because of the novel results they yield. Part IV considers modal operators and examines their interactions with logical operators. By obtaining the usual results without the usual assumptions, this new approach allows one to give a very simple account of modal logic, minus the excess baggage of possible world semantics. The book is aimed at philosophers, logicians, mathematicians, linguists, and computer scientists. It will be accessible to advanced undergraduates and graduates in those fields. | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: A structuralist theory of logic
Autor: Koslow, Arnold
Jahr: 1992
Contents
Preface page ix
Part I Background
1 Introduction 3
2 The program and its roots 12
3 Introduction and Elimination conditions in a
general setting 19
4 The Belnap program 26
Part II Implication relations
5 The theory of implication relations 35
6 Implications: Variations and emendations 39
7 Familiar implication relations: Deducibility and
logical consequence 42
8 Implication relations: Direct and derived 45
9 Implications from implications 53
10 Implication relations and the a priori: A further
condition? 70
Partni The logical operators
11 Hypotheticals 77
12 Negations 91
13 Conjunctions 108
14 The disjunction operator 117
15 The logical operators parameterized 127
16 Further features of the operators 134
17 The dual of negation: Classical and nonclassical
implication structures 142
18 The distinctness and relative power of the
logical operators 151
19 Extensionality 158
20 Quantification 181
21 Identity 202
viii CONTENTS
22 Special structures I: Logical operators on
individuals: Mereology reconstituted 209
23 Special structures II: Interrogatives and
implication relations 218
24 Completeness 229
Part IV The modal operators
25 Introduction 239
26 Modality 246
27 Modals: Existence and nonextensionality 254
28 Special modals 265
29 The possibility of necessity-style modals 290
30 Modals revisited I 301
31 Quantification and modality 312
32 Modals revisited II 318
33 Knowledge, truth, and modality 327
34 The comparative strength of modals 340
35 Kripke-style systematization of the modals
without possible worlds 345
36 Model functions, accessibility relations, and
theories 360
37 Migrant modals 368
Appendix A An implication relation for the integers in the
programming language BASIC 375
Appendix B Symmetric sequents as products of implication
relations and their duals 378
Appendix C Component-style logical operators and
relevance 382
Notes 388
Bibliography 410
Index 415
|
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| discipline | Philosophie |
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| indexdate | 2024-07-09T16:29:49Z |
| institution | BVB |
| isbn | 0521412676 |
| language | English |
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| spelling | Koslow, Arnold Verfasser aut A structuralist theory of logic Arnold Koslow 1. publ. Cambridge u.a. Cambridge Univ. Press 1992 XI, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that is does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part III defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is followed by a substantial treatment of the extensionality of each of the operators, as well as the relation of negation and its dual, because of the novel results they yield. Part IV considers modal operators and examines their interactions with logical operators. By obtaining the usual results without the usual assumptions, this new approach allows one to give a very simple account of modal logic, minus the excess baggage of possible world semantics. The book is aimed at philosophers, logicians, mathematicians, linguists, and computer scientists. It will be accessible to advanced undergraduates and graduates in those fields. Implication (Logique) Logica gtt Logique symbolique et mathématique Modale logica gtt Operatoren gtt Structuralisme Logik Implication (Logic) Logic, Symbolic and mathematical Structuralism Belnap-Programm rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Strukturalismus (DE-588)4058129-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Strukturalismus (DE-588)4058129-9 s Logik (DE-588)4036202-4 s Belnap-Programm s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003413130&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koslow, Arnold A structuralist theory of logic Implication (Logique) Logica gtt Logique symbolique et mathématique Modale logica gtt Operatoren gtt Structuralisme Logik Implication (Logic) Logic, Symbolic and mathematical Structuralism Belnap-Programm Logik (DE-588)4036202-4 gnd Strukturalismus (DE-588)4058129-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4058129-9 (DE-588)4037951-6 |
| title | A structuralist theory of logic |
| title_auth | A structuralist theory of logic |
| title_exact_search | A structuralist theory of logic |
| title_full | A structuralist theory of logic Arnold Koslow |
| title_fullStr | A structuralist theory of logic Arnold Koslow |
| title_full_unstemmed | A structuralist theory of logic Arnold Koslow |
| title_short | A structuralist theory of logic |
| title_sort | a structuralist theory of logic |
| topic | Implication (Logique) Logica gtt Logique symbolique et mathématique Modale logica gtt Operatoren gtt Structuralisme Logik Implication (Logic) Logic, Symbolic and mathematical Structuralism Belnap-Programm Logik (DE-588)4036202-4 gnd Strukturalismus (DE-588)4058129-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Implication (Logique) Logica Logique symbolique et mathématique Modale logica Operatoren Structuralisme Logik Implication (Logic) Logic, Symbolic and mathematical Structuralism Belnap-Programm Strukturalismus Mathematische Logik |
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