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Introduction to Logic

Author Eric Kao , Michael Genesereth
Release Date: 2012/11/01
ISBN: 9781627050050
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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. The primary content difference concerns the semantics of the logic that is taught. 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. Copyright
  3. Title Page
  4. Contents
  5. Preface
  6. 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
  7. 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
  8. 3 Propositional Proofs
    1. 3.1 Introduction
    2. 3.2 Linear Proofs
    3. 3.3 Structured Proofs
    4. 3.4 Fitch
    5. 3.5 Soundness and Completeness
  9. 4 Propositional Resolution
    1. 4.1 Introduction
    2. 4.2 Clausal Form
    3. 4.3 Resolution Principle
    4. 4.4 Resolution Reasoning
  10. 5 Satisfiability
    1. 5.1 Introduction
    2. 5.2 Truth Table Method
    3. 5.3 Basic Backtracking Search
    4. 5.4 Simplification and Unit Propagation
    5. 5.5 DPLL
    6. 5.6 GSAT
  11. 6 Herbrand 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 Herbrand Logic
    12. 6.12 Logical Entailment
    13. 6.13 Finite Herbrand Logic
    14. 6.14 Omega Herbrand Logic
    15. 6.15 General Herbrand Logic
  12. 7 Herbrand Logic Proofs
    1. 7.1 Introduction
    2. 7.2 Proofs
    3. 7.3 Example
    4. 7.4 Example
    5. 7.5 Example
  13. 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
  14. 9 Induction
    1. 9.1 Introduction
    2. 9.2 Finite Induction
    3. 9.3 Linear Induction
    4. 9.4 Tree Induction
    5. 9.5 Structural Induction
  15. 10 First Order Logic
    1. 10.1 Introduction
    2. 10.2 Conceptualization
    3. 10.3 Syntax and Semantics
    4. 10.4 Blocks World
    5. 10.5 Arithmetic
    6. 10.6 Properties of Sentences
    7. 10.7 Logical Entailment
    8. 10.8 Proofs
    9. 10.9 Examples: Equality
    10. 10.10 Example: Blocks World
    11. 10.11 Example: Arithmetic
    12. 10.12 Soundness and Completeness
    13. 10.13 Herbrand Logic Versus First Order Logic
  16. A: Summary of Fitch Rules
  17. Bibliography
  18. Authors’ Biographies
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