Logic 2: Modal Logic


These notes are aimed at philosophy students who have taken an introductory course in formal logic. They provide an introduction to modal logic, with may philosophical applications. Along the way, they introduce general ideas that might be taught in an intermediate logic course: different methods of proof, the concept of a model, soundness and completeness, compactness, three-valued logics, free logics, supervaluation, properties of relations and orders, etc.

Chapters 1–3 introduce the standard toolkit of modal propositional logic: Kripke models, frame correspondence, some popular systems, the tableau method and axiomatic calculi. Chapter 4 goes through soundness and completeness. Chapters 5–8 turn to philosophical applications. Each of these chapters also extends the toolkit from chapter 3. Chapter 5 introduces multi-modal logics, chapter 6 ordering models and neighbourhood semantics, chapter 6 two-dimensional semantics and supervaluationism, chapter 7 conditional logics and Lewis-Stalnaker models. Chapters 9 and 10 look at some of the complexities that arise in first-order modal logic.

Apart from chapter 9, which sets the stage for chapter 10, every chapter after chapter 3 can be skipped or skimmed without affecting the accessibility of later chapters.

The best way to learn logic is by solving problems. That’s why the text is frequently interrupted by exercises. As a student, you should try to do the exercises as soon as you reach them, before continuing with the text.

Next chapter: 1 Modal Operators