# Understanding Symbolic Logic

## byVirginia Klenk

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This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small “bites” that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic.

Title:Understanding Symbolic LogicFormat:PaperbackDimensions:480 pages, 9.15 × 6.95 × 1.3 inPublished:April 19, 2007Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0132051524

ISBN - 13:9780132051521

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## Reviews

I. SENTENTIAL LOGIC

1. Introduction to Logic
Why Study Logic?
Induction and Deduction
Form and Validity
Truth and Validity
The Nature of Symbolic Logic
The Scope of Symbolic Logic
Definitions
Study Questions
Exercises

2. The Structure of Sentential Logic
Simple and Compound Sentences
Sentential Operators
The Structure and Symbolism of Sentential Logic
Definitions
Study Questions
Exercises

3. Computing Truth Values
Truth Tables for the Operators
Computing Truth Values
Truth-functional Operators
Non-truth-functional Operators
Definitions
Study Questions
Exercises

4. Symbolizing English Sentences
Simple Sentences
Truth-functional and Non-truth-functional Compounds
Symbolizing Truth-functional English Operators
Symbolizing Multiply Complex Sentences
Exercises

5. Truth Tables for Testing Validity
Constructing Base Columns for Truth Tables
The Truth Table Test for Validity
Shortcut Validity Tests
Mechanical Decision Procedures
Definitions
Study Questions
Exercises

6. Further Applications of the Truth Table Method
Logical Implication and Logical Equivalence
Rules of Inference, Logical Implication, and Logical Equivalence
Consistency
Four Kinds of Truth Table Problems and the Relations Between Them
Definitions
Study Questions
Exercises

7. The Proof Method: Eight Basic Inference Rules
Form and Substitution Instance
The Proof Process
Eight Basic Inference Rules
Derivations and Proofs
Constructing Simple Proofs
Constructing More Complex Proofs
Summary of Rules of Inference
Definitions
Exercises

8. Replacement Rules
The Structure of Replacement Rules
The Ten Replacement Rules
Constructing Simple Proofs with Replacement Rules
Strategies for More Complex Proofs
Summary of Replacement Rules
Exercises

9. Conditional Proof and Indirect Proof
Conditional Proof
Indirect Proof
Discharging Assumptions; Restrictions on C.P. and I.P.
Using C.P. and I.P.
Proofs of Theorems
Invalidity
Truth and Proof
Summary of Rules of Conditional Proof and Indirect Proof
Definitions
Exercises

10. Singular Sentences
Singular Sentences and Propositional Functions
Symbolizing Singular Sentences
Definitions
Exercises

11. Quantifiers
Universal and Existential Quantifiers
Free and Bound Variables; Scope of a Quantifier
Negated Quantifiers
Definitions
Exercises

12. Categorical Propositions
The Four Categorical Propositions
Individuals, Sets, and Properties
Venn Diagrams
Symbolizing Categorical Propositions
Negated Categorical Propositions
Deriving C.Q.N. Rules from Q.N. Rules
Symbolizing English Categorical Sentences
Summary of Categorical Propositions
Definitions
Exercises

13. Complex Subjects and Predicates
Complex Subjects and Predicates
Equivalent Symbolizations
Exercises

14. Quantifier Form and Truth-Functional Compounds of Quantifier Statements
Quantifier Form
Truth-functional Compounds and Quantifier Form
Symbolizing Truth-functional Compounds
Definitions
Exercises

15. Proofs in Predicate Logic
Preliminary Statement of the Four Quantifier Rules
Instances of Quantified Formulas
The Rules of Universal Instantiation (U.I.) and Existential Generalization (E.G.)
The Rules of Existential Instantiation (E.I.) adn Universal Generalization (U.G.); Flagging Restrictions
Constructing Proofs for "Pure" Quantifier Arguments
Constructing Proofs for Arguments Containing Truth-functional Compounds
Constructing Proofs of Quantifier Theorems
Statement of the Quantifier Rules, with All Necessary Restrictions
Exercises

16. Invalidity in Quantifier Logic
The Natural Interpretation Method
Truth Conditions for Quantifier Statements
The Model Universe Method
Definitions
Exercises

III. RELATIONAL PREDICATE LOGIC

17. Symbolization in Relational Predicate Logic
Relational Predicates and Singular Sentences
Multiple Quantifiers
Quantifier Negation
Categorical Relational Statements; Complex Subjects and Predicates
Symbolizing English Sentences
Exercises

18. Proofs and Invalidity for Relational Predicate Logic
Proofs in Relational Predicate Logic
Invalidity in Relational Predicate Logic
Exercises

19. Identity and Definite Descriptions
Identity Statements and Their Negations
Exceptives and "Only" Statements
Superlatives
Numerical Statements
Definite Descriptions
Exercises

20. Proofs Involving Identity
Rules for Identity
Proofs Containing Identity Statements
Summary of Identity Rules
Exercises

IV. EXTRA CREDIT UNITS

21. Well-Formed Formulas for Sentential Logic
Exercises

22. Proof Trees for Sentential Logic
Exercises

23. Using Venn Diagrams to Prove Validity
Exercises

24. Proof Trees for Predicate Logic
Exercises