Title:
Logic techniques of formal reasoning
Personal Author:
Edition:
2nd ed
Publication Information:
San Diego, Calif : Harcourt Brace Jovanovich, 1980
ISBN:
9780155511811
Subject Term:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000000489082 | BC135 K26 1980 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarifyprinciples. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered.
Table of Contents
| Chapter I ""Not"" and ""If"" |
| 1 Symbols and sentences |
| 2 From symbols to English and back |
| 3 Derivability and validity of symbolic arguments |
| 4 Validity of English arguments |
| 5 Fallacies |
| 6 Theorems |
| 7 Historical remarks |
| 8 Appendix |
| Chapter II ""And,"" ""Or,"" ""If and Only If"" |
| 1 Symbols and sentences |
| 2 Translation and symbolization |
| 3 Inference rules and derivability |
| 4 Theorems with unabbreviated proofs |
| 5 Abbreviated derivations |
| 6 Theorems with unabbreviated proofs |
| 7 Arguments |
| 8 Truth-value analysis of sentences |
| 9 Truth-value analysis of arguments |
| 10 Historical remarks |
| 11 Appendix: list of theorems of chapters I and II |
| 12 Appendix: solutions to selected exercises |
| Chapter III ""All"" and ""Some"" |
| 1 Variables, quantifiers, formulas |
| 2 Bondage and freedom |
| 3 Informal notational conventions |
| 4 Translation and symbolization |
| 5 Inference rules |
| 6 Derivations |
| 7 Theorems with unabbreviated proofs |
| 8 Abbreviated derivations |
| 9 Fallacies |
| 10 Theorems with abbreviated proofs |
| 11 Arguments |
| 12 Invalidity: truth-functional expansions and models |
| 13 Historical remarks |
| 14 Appendix: list of theorems of chapter III |
| 15 Appendix: solutions to selected exercises |
| 16 Appendix: summary of the system of logic developed in chapters I-III |
| Chapter IV ""All"" and ""Some,"" continued |
| 1 Terms and formulas |
| 2 Bondage and freedom |
| 3 Informal notational conventions |
| 4 Translation and symbolization |
| 5 Revised inference rules |
| 6 Theorems |
| 7 Invalidity: truth-functional expansions and models |
| 8 Invalidity: false arithmetical translations |
| 9 Arguments of English |
| 10 Historical remarks |
| 11 Appendix: list of theorems of chapter IV |
| 12 Appendix: solutions to selected exercises |
| Chapter V ""Is"" (in one sense) |
| 1 Terms and formulas |
| 2 Translation and symbolization |
| 3 Inference rules |
| 4 Theorems |
| 5 Invalidity |
| 6 Historical remarks |
| 7 Appendix: list of theorems of chapter V |
| 8 Appendix: solutions to selected exercises |
| Chapter VI ""The"" |
| 1 Descriptive phrases, terms, formulas |
| 2 Bondage and freedom |
| 3 Informal notational conventions |
| 4 Translation and symbolization |
| 5 Inference rules |
| 6 Theorems |
| 7 Invalidity |
| 8 Arguments of English |
| 9 Historical remarks |
| 10 Appendix: list of theorems of chapter VI |
| 11 Appendix: solutions to selected exercises |
| Chapter VII Additional Derivational Procedures |
| 1 Alphabetic variance |
| 2 Substitution |
| 3 Abbreviated derivations reconsidered |
| biconditional derivations |
| 4 Formulas without overlay and prenex normal form, again |
| 5 Abbreviated derivations justified |
| generalized priciples of interchange |
| 6 Historical remarks |
| 7 Appendix: list of theorems of chapter VII |
| 8 Appendix: solutions to selected exercises |
| 9 Appendix: summary of the system of logic developed in chapters I-VII |
| Chapter VIII ""The"" again: A Russellian Theory of Descriptions |
| 1 The Fregean theory of chapter VI reconsidered |
| 2 A Russellian theory of descriptions |
| 3 Historical remarks |
| 4 Appendix: list of theorems of chapter VIII |
| 5 Appendix: solutions to selected exercises |
| 6 Appendix: summary of the Russellian system of logic developed in chapter VIII |
| Chapter IX Automatic Procedures |
| 1 Introduction |
| 2 Tautologies reconsidered |
| 3 Tautological implication |
| generalized indirect derivation |
| 4 A proof procedure for prenex formulas |
| 5 A derivation procedure for prenex arguments |
| 6 Conversion to prenex form |
| 7 A derivation procedure for arbitrary symbolic arguments |
| 8 A decision procedure for certain prenex formulas |
| 9 A decision procedure for certain prenex arguments |
| 10 Historical remarks |
| Chapter X Definitions: Formal Theories |
| 1 The vocabulary of formal languages |
| 2 Bondage and freedom |
| proper substitution |
| alphabetic varianc |
| 3 Informal notational conventions |
| 4 Derivability |
| 5 Formal theories |
| the theory of commutative ordered fields |
| 6 Extensions of theories |
| the theory of real numbers |
| 7 Definitions |
| Chapter XI Variable-Binding Operators |
| 1 Definitions reconsidered |
| 2 The theory of convergence |
| 3 A sketch of further developments |
| 4 Historical remarks |
| 5 Appendix: list of constants used in chapters X and XI |
| 6 Appendix: list of axioms, definitions, and theorems of chapters X and XI |
| Bibliography |
| Index of Proper Names |
| Index of Subjects |
