9780195155044

Logic Techniques of Formal Reasoning

by ; ;
  • ISBN13:

    9780195155044

  • ISBN10:

    0195155041

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 4/16/1980
  • Publisher: Oxford University Press

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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

""Not"" and ""If""
Symbols and sentences
From symbols to English and back
Derivability and validity of symbolic arguments
Validity of English arguments
Fallacies
Theorems
Historical remarks
Appendix
""And,"" ""Or,"" ""If and Only If""
Symbols and sentences
Translation and symbolization
Inference rules and derivability
Theorems with unabbreviated proofs
Abbreviated derivations
Theorems with unabbreviated proofs
Arguments
Truth-value analysis of sentences
Truth-value analysis of arguments
Historical remarks
Appendix: list of theorems of chapters I and II
Appendix: solutions to selected exercises
""All"" and ""Some""
Variables, quantifiers, formulas
Bondage and freedom
Informal notational conventions
Translation and symbolization
Inference rules
Derivations
Theorems with unabbreviated proofs
Abbreviated derivations
Fallacies
Theorems with abbreviated proofs
Arguments
Invalidity: truth-functional expansions and models
Historical remarks
Appendix: list of theorems of chapter III
Appendix: solutions to selected exercises
Appendix: summary of the system of logic developed in chapters I-III
""All"" and ""Some,"" continued
Terms and formulas
Bondage and freedom
Informal notational conventions
Translation and symbolization
Revised inference rules
Theorems
Invalidity: truth-functional expansions and models
Invalidity: false arithmetical translations
Arguments of English
Historical remarks
Appendix: list of theorems of chapter IV
Appendix: solutions to selected exercises
""Is"" (in one sense)
Terms and formulas
Translation and symbolization
Inference rules
Theorems
Invalidity
Historical remarks
Appendix: list of theorems of chapter V
Appendix: solutions to selected exercises
""The""
Descriptive phrases, terms, formulas
Bondage and freedom
Informal notational conventions
Translation and symbolization
Inference rules
Theorems
Invalidity
Arguments of English
Historical remarks
Appendix: list of theorems of chapter VI
Appendix: solutions to selected exercises
Additional Derivational Procedures
Alphabetic variance
Substitution
Abbreviated derivations reconsidered
biconditional derivations
Formulas without overlay and prenex normal form, again
Abbreviated derivations justified
generalized priciples of interchange
Historical remarks
Appendix: list of theorems of chapter VII
Appendix: solutions to selected exercises
Appendix: summary of the system of logic developed in chapters I-VII
""The"" again: A Russellian Theory of Descriptions
The Fregean theory of chapter VI reconsidered
A Russellian theory of descriptions
Historical remarks
Appendix: list of theorems of chapter VIII
Appendix: solutions to selected exercises
Appendix: summary of the Russellian system of logic developed in chapter VIII
Automatic Procedures
Introduction
Tautologies reconsidered
Tautological implication
generalized indirect derivation
A proof procedure for prenex formulas
A derivation procedure for prenex arguments
Conversion to prenex form
A derivation procedure for arbitrary symbolic arguments
A decision procedure for certain prenex formulas
A decision procedure for certain prenex arguments
Historical remarks
Definitions: Formal Theories
The vocabulary of formal languages
Bondage and freedom
proper substitution
alphabetic varianc
Informal notational conventions
Derivability
Formal theories
the theory of commutative ordered fields
Extensions of theories
the theory of real numbers
Definitions
Variable-Binding Operators
Definitions reconsidered
The theory of convergence
A sketch of further developments
Historical remarks
Appendix: list of constants used in chapters X and XI
Appendix: list of axioms, definitions, and theorems of chapters X and XI
Bibliography
Index of Proper Names
Index of Subjects
Table of Contents provided by Publisher. All Rights Reserved.

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