Intro
Preface
What's in This Book
How to Read This Book
Differences from the First Edition
Acknowledgments
Contents
Part I Background: Propositional Classical Logic
1 Background: Propositional Language
1.1 Introduction
1.2 The Propositional Language
1.3 Using Induction
Exercises
2 Background: Propositional Axiomatics
2.1 Truth Tables
Exercises
2.2 Axiom Systems
2.3 The Goal and General Outline
Exercises
2.4 Consistency and Lindenbaum's Lemma
Exercises
2.5 Implication and the Deduction Theorem
Exercises

2.6 The Other Connectives
2.6.1 Conjunction
2.6.2 Disjunction
2.6.3 Negation
2.6.4 Implication
Exercises
2.7 Summary of Our Classical Axiom System
Exercises
2.8 Completeness At Last
2.9 Redefining Consistency
3 Background: Propositional Tableaus
3.1 Tableaus
Exercises
3.2 Logical Consequence Using Tableaus
Exercises
3.3 Tableau Soundness
Exercises
3.4 Tableau Completeness
3.4.1 Hintikka Sets
3.4.2 Completeness, Constructively
3.4.3 Tableau Completeness, Non-constructively
3.4.4 Coda
Exercises

3.5 Strong Completeness and Compactness
Exercises
References
Part II Propositional Modal Logic
4 Modal Logic, an Introduction
4.1 What Is a Modal?
Exercises
4.2 Can There Be a Modal Logic?
4.3 Aristotle's Modal Square
4.4 Informal Interpretations
Exercises
4.5 Temporal Interpretations
Exercises
4.6 Historical Highlights
4.6.1 Aristotle's Development of the Square
Exercises
4.6.2 Aristotle's Future Sea Battle
Exercises
4.6.3 The Master Argument of Diodorus Cronus
4.6.4 The Once and Future Conditional
4.6.5 The Reality of Necessity

References
5 Propositional Modal Logic
5.1 What Are the Formulas?
Exercises
5.2 What Are the Models?
Exercises
5.3 Examples
Exercises
5.4 Modal Logics, Semantically Defined
Exercises
5.5 The Modal Cube
Exercises
5.6 Semantic Consequence
Exercises
References
6 Propositional Modal Axiom Systems
6.1 The Logic K Axiomatically
Exercises
6.2 More Axiom Systems
Exercises
6.3 Logical Consequence, Axiomatically
Exercises
6.4 Axiom Systems Work
6.4.1 Soundness
6.4.2 Completeness
Exercises
6.5 Informal Notes

6.5.1 Gödel's Intuitionistic Logic Interpretation
6.5.2 Epistemic Logic
6.5.3 The Knowability Paradox
6.6 Justification Logic
Exercises
References
7 Propositional Modal Tableaus
7.1 Tableaus
Exercises
7.2 More Tableau Systems
Exercises
7.3 Logical Consequence and Tableaus
Exercises
7.4 Modal Tableau Soundness
Exercises
7.5 Modal Hintikka Sets
7.6 Propositional Modal Tableau Completeness
7.6.1 Modal Tableau Completeness, Constructively
7.6.2 Logical Consequence
7.6.3 Modal Completeness, Non-constructively
Exercises