Deductive logic:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
Allyn and Bacon
1976
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 443 S. graph. Darst. |
| ISBN: | 020505496X |
Internformat
MARC
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| 100 | 1 | |a Leblanc, Hugues |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Deductive logic |c Hugues Leblanc ; William A. Wisdom |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston |b Allyn and Bacon |c 1976 | |
| 300 | |a XIV, 443 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804131059504250880 |
|---|---|
| adam_text | CONTENTS
Preface xi
Preface to the First Edition xiii
INTRODUCTION 1
1 • THE LOGIC OF CONNECTIVES 7
1.1 Truth Functional Composition 7
Truth Functionally Compound Statements 8;
Truth Functional Connectives 10; Abbreviation,
Punctuation, and Translation 18; Statements and
Components 20; Truth Value Assignments 22;
Truth Tables 24; Truth Table Tests for Logical
Properties and Relations 27; Truth Functional
Modes of (Statement) Composition 38;
Exercises 42.
1.2 Consistency Trees (1) 47
Trees 48; The Rules 54; The Tree
Method 55; On Making Trees 57; On Using
Trees 63; Exercises 68.
1.3 Derivations (1) 72
Arguments and Derivations 73; The Rules 74;
Strategy Hints 90; Illustrations 93;
Theorems and Proofs 98; Other Uses of
Derivations 100; Exercises 103.
2 • THE LOGIC OF QUANTIFIERS 109
2.1 Quantification 109
PART ONE: Predicates, Individual Terms, and
Atomic Statements 110; Universal
Quantification, and Term Variables 114;
viii Contents
Existential and Mixed Quantification 117;
Translation 121; Instances, Statements, and
Subformulas 134; Quantification as a Mode
of Statement Composition 140.
PART TWO: Truth 144; Truth Tables for the
Quantifiers 151; Logical Properties and
Relations 154; Infinite Sets of Statements 165;
Quantificational Modes of (Statement)
Composition 166; Exercises 167.
2.2 Consistency Trees (2) 174
The New Rules 176; Examples and
Strategies 180; The Routine 187; Further
Examples 191; Exercises 197.
2.3 Derivations (2) 201
The Rules VE and 31 202; The Rule VI 204;
The Rule 3E 207; A Word on Restrictions 211;
Uses of Derivations 213; Strategy Hints 213;
Illustrations 216; The Rules VI* and 3E* 227;
The Rule 3E** 232; Exercises 234.
3 • METALOGIC 239
3.1 Modes of Statement Composition 241
Truth Functional Modes of (Statement)
Composition 241; Quantificational Modes of
(Statement) Composition 249; , D , and V
as Primitive Operators 253; Exercises 256.
3.2 Auxiliary Material 257
Mathematical Induction 257; Strong
Mathematical Induction 259; Derivability From
Infinite Sets of Statements 265; Syntactic
Consistency and Inconsistency 268; Alphabetic
Ordering of Statements 270; Exercises 273.
3.3 The Soundness Theorem 275
Entailment Lemmas 275; Proof of the Soundness
Theorem 279; Corollaries 283; Exercises 284.
3.4 The Completeness Theorem 285
The Two Sets S* and S** 286; The Set S. 287;
The Truth Value Assignment a 290; Corollaries
292; Exercises 293.
3.5 Trees: Some Metalogical Results 294
Closed Trees 294; Hintikka Sets 297; The
First Consistency Theorem 299; The Second
Consistency Theorem 300; Exercises 304.
Contents ix
3.6 Standard Semantics 305
Domains, Interpretations, and the Like 305;
Soundness Revisited 312; Completeness
Revisited 316; Further Results 319; The
Skolem and the Henkin Beth Theorems 321;
Henkin Models and Truth Value Assignments 322;
Addenda to Section 2.1 324; Exercises 325.
3.7 Axioms for Elementary Logic 327
Axioms and Sample a Derivations 328;
Converting a Derivations into Derivations 331;
Converting Derivations into a Derivations 333;
Alternative Axiomatizations 339; Exercises 341.
APPENDIX I ¦ SET THEORETIC MATTERS 345
APPENDIX II ¦ SUMMARY OF RULES 353
A. Rules for Making Trees 353; B. Rules for Making
Derivations 354.
ANSWERS TO SELECTED EXERCISES 359
INDEX OF SYMBOLS, ABBREVIATIONS, AND TABLES 435
INDEX OF NAMES 437
INDEX OF SUBJECTS 439
|
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| id | DE-604.BV018444793 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:30:54Z |
| institution | BVB |
| isbn | 020505496X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-011215536 |
| oclc_num | 2235733 |
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| owner_facet | DE-12 DE-M468 DE-29 |
| physical | XIV, 443 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Allyn and Bacon |
| record_format | marc |
| spelling | Leblanc, Hugues Verfasser aut Deductive logic Hugues Leblanc ; William A. Wisdom 2. ed. Boston Allyn and Bacon 1976 XIV, 443 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Logique Logic Logik (DE-588)4036202-4 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Logik (DE-588)4036202-4 s DE-604 Mathematische Logik (DE-588)4037951-6 s Wisdom, William A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=011215536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leblanc, Hugues Wisdom, William A. Deductive logic Logique Logic Logik (DE-588)4036202-4 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4036202-4 (DE-588)4037951-6 |
| title | Deductive logic |
| title_auth | Deductive logic |
| title_exact_search | Deductive logic |
| title_full | Deductive logic Hugues Leblanc ; William A. Wisdom |
| title_fullStr | Deductive logic Hugues Leblanc ; William A. Wisdom |
| title_full_unstemmed | Deductive logic Hugues Leblanc ; William A. Wisdom |
| title_short | Deductive logic |
| title_sort | deductive logic |
| topic | Logique Logic Logik (DE-588)4036202-4 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logique Logic Logik Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=011215536&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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