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Cover

Logic

Techniques of Formal Reasoning

Second Edition

Donald Kalish, Richard Montague, and Gary Mar

Publication Date - April 1980

ISBN: 9780195155044

544 pages
Hardcover
6-3/16 x 9-1/4 inches

In Stock

Retail Price to Students: $92.95

Description

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 clarify principles. 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.

Previous Publication Date(s)

April 1964

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