You are previewing Introduction to Logic, 2nd Edition.
O'Reilly logo
Introduction to Logic, 2nd Edition

Book Description

This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material. The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form. Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about. In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at logic.stanford.edu/intrologic/

Table of Contents

  1. Cover
  2. Half title
  3. Copyright
  4. Title
  5. Abstract
  6. Contents
  7. Preface
  8. 1 Introduction
    1. 1.1 Logic
    2. 1.2 Elements of Logic
    3. 1.3 Formalization
    4. 1.4 Automation
    5. 1.5 Reading Guide
  9. 2 Propositional Logic
    1. 2.1 Introduction
    2. 2.2 Syntax
    3. 2.3 Semantics
    4. 2.4 Satisfaction
    5. 2.5 Logical Properties of Propositional Sentences
    6. 2.6 Propositional Entailment
  10. 3 Satisfiability
    1. 3.1 Introduction
    2. 3.2 Truth Table Method
    3. 3.3 Basic Backtracking Search
    4. 3.4 Simplification and Unit Propagation
    5. 3.5 DPLL
    6. 3.6 GSAT
  11. 4 Propositional Proofs
    1. 4.1 Introduction
    2. 4.2 Linear Proofs
    3. 4.3 Structured Proofs
    4. 4.4 Fitch
    5. 4.5 Soundness and Completeness
  12. 5 Propositional Resolution
    1. 5.1 Introduction
    2. 5.2 Clausal Form
    3. 5.3 Resolution Principle
    4. 5.4 Resolution Reasoning
  13. 6 Relational Logic
    1. 6.1 Introduction
    2. 6.2 Syntax
    3. 6.3 Semantics
    4. 6.4 Example: Sorority World
    5. 6.5 Example: Blocks World
    6. 6.6 Example: Modular Arithmetic
    7. 6.7 Example: Peano Arithmetic
    8. 6.8 Example: Linked Lists
    9. 6.9 Example: Pseudo English
    10. 6.10 Example: Metalevel Logic
    11. 6.11 Properties of Sentences in Relational Logic
    12. 6.12 Logical Entailment
    13. 6.13 Finite Relational Logic
    14. 6.14 Omega Relational Logic
    15. 6.15 General Relational Logic
  14. 7 Relational Logic Proofs
    1. 7.1 Introduction
    2. 7.2 Proofs
    3. 7.3 Example
    4. 7.4 Example
    5. 7.5 Example
  15. 8 Resolution
    1. 8.1 Introduction
    2. 8.2 Clausal Form
    3. 8.3 Unification
    4. 8.4 Resolution Principle
    5. 8.5 Resolution Reasoning
    6. 8.6 Unsatisfiability
    7. 8.7 Logical Entailment
    8. 8.8 Answer Extraction
    9. 8.9 Strategies
  16. 9 Induction
    1. 9.1 Introduction
    2. 9.2 Domain Closure
    3. 9.3 Linear Induction
    4. 9.4 Tree Induction
    5. 9.5 Structural Induction
    6. 9.6 Multidimensional Induction
    7. 9.7 Embedded Induction
    8. 9.8 Recap
  17. 10 Equality
    1. 10.1 Introduction
    2. 10.2 Properties of Equality
    3. 10.3 Substitution
    4. 10.4 Fitch With Equality
    5. 10.5 Example – Group Theory
    6. 10.6 Recap
  18. A Summary of Fitch Rules
  19. Bibliography
  20. Authors’ Biographies