The Logic Book

Description

Cover Page Title Page Copyright Page About the Author Table of Content Preface CHAPTER 1 INTRODUCTION TO DEDUCTIVE LOGIC 1.1 Introduction 1.2 Core Concepts of Deductive Logic 1.3 Special Cases of Logical Concepts 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 Using Truth-Trees To Test for Other Truth-Functional Properties 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 (Predicate Logic Extended) CHAPTER 8 PREDICATE LOGIC: SEMANTICS 8.1 Interpretations 8.2 Quantifi cational Truth, Falsehood, and Indeterminacy 8.3 Quantifi cational Equivalence and Consistency 8.4 Quantifi cational 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 Quantifi cational Consistency 9.3 Truth-Trees and Other Semantic Properties 9.4 Fine-Tuning the Tree Method for PL 9.5 Truth-Trees for PLE 9.6 Fine-Tuning the Tree Method 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 PL 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 Appendix 1 Selected Bibliography Index Index of Symbols Back Cover