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Deductive logic:

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Bibliographic Details
Main Authors:	Leblanc, Hugues (Author), Wisdom, William A. (Author)
Format:	Book
Language:	English
Published:	Boston Allyn and Bacon 1976
Edition:	2. ed.
Subjects:	Logique Logic Logik Mathematische Logik
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 443 S. graph. Darst.
ISBN:	020505496X

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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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isbn	020505496X
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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
work_keys_str_mv	AT leblanchugues deductivelogic AT wisdomwilliama deductivelogic

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