The Logic Book

Chapter 1: INTRODUCTION TO DEDUCTIVE LOGIC

1.1 Introduction

1.2 Core Concepts of Deductive Logic

1.3 Special Cases of Logical Concepts

1.4 Deductive Validity and Soundness

1.5 Inductive Arguments

1.6 Logical Consistency, Truth, Falsity, and Equivalence

1.7 Special Cases of Validity

Chapter 2: SYNTAX AND SYMBOLIZATION

2.1 The Syntax of SL

2.2 Introduction to Symbolization

2.3 More Complex Symbolizations

2.4 Non-Truth-Functional Uses of Connectives

Chapter 3: Sentential Logic: Semantics

3.1 Truth-Value Assignments and Truth-Tables for Sentences

3.2 Truth-Functional Truth, Falsity, and Indeterminacy

3.3 Truth-Functional Equivalence

3.4 Truth-Functional Consistency

3.5 Truth-Functional Entailment and Truth-Functional Validity

3.6 Truth-Functional Properties and Truth-Functional Consistency

Chapter 4: Sentential Logic: Truth-Trees

4.1 The Truth-Tree Method

4.2 Truth-Tree Rules

4.3 Using Truth-Trees to test for other Truths

Chapter 5: Sentential Logic: Derivations

5.1 The Derivation System SD

5.2 Basic Concepts of SD

5.3 Strategies for Constructing Derivations in SD

5.4 The Derivation System SD+

Chapter 6: Sentential Logic: Metatheory

6.1 Mathematical Induction

6.2 Truth-Functional Completeness

6.3 The Soundness of SD and SD+

6.4 The Completeness of SD and SD+

Chapter 7: Predicate Logic: Syntax and Symbolization

7.1 Predicates, Singular Terms, and Quantity Expressions of English

7.2 The Formal Syntax of PL

7.3 Introduction to Symbolization

7.4 Symbolization Fine-Tuned

7.5 The Language PLE (Predicte Logic Extended)

Chapter 8: Predicate Logic: Semantics

8.1 Interpretations

8.2 Quantificational Truth, Falsehood, and Indeterminacy

8.3 Quantificational Equivalence and Consistency

8.4 Quantification Entailment and Validity

8.5 Truth-Functional Expansions

8.6 Semantics for Predicate Logic with Identity and Functors

Chapter 9: Predicate Logic: Truth-Trees

9.1 Truth-Tree RUles for PL

9.2 Truth-Trees and Quantificational Consistency

9.3 Truth-Trees and Other Semantic Properties

9.4 Fine-Tuning the Tree Method

9.5 Trees for PLE

Chapter 10: Predicate Logic: Derivations

10.1 The Derivation System PD

10.2 Using Derivations to Establish Syntactic Properties of PD

10.3 The Derivation System PD+

10.4 The Derivation System PDE

Chapter 11: Predicate Logic: Metatheory

11.1 Semantic Preliminaries for PD

11.2 Semantic Preliminaries for PLE

11.3 The Soundness of PD, PD+, and PDE

11.4 The Completeness of PD, PD+, and PDE

11.5 The Soundness of the Tree Method

11.6 The Completeness of the Tree Method

Selected Bibliography

Index

Index of Symbols

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