Logic 2: Modal Logic (Autumn 2019)

This is a follow-on course to Logic 1, focusing on modal extensions of classical propositional and predicate logic. Modal logic is used to reason about possibility and necessity, knowledge and belief, permission and obligation, past and future, and a variety of other topics. The first part of the course will introduce standard models and proofs for propositional modal logic, with a brief look at the meta-logical properties of soundness and completeness. We will then go through a range of philosophical applications, studying the logic of knowledge, the logic of obligation, the logic of time, and logical properties of "if-then" constructions. Finally, we will turn to quantified modal logic. We will look at the choices between constant and variable domains, rigid and non-rigid names, and discuss whether standard predicate logic should be weakened to a "free" logic.

Course organiser

Dr Wolfgang Schwarz (wolfgang.schwarz@ed.ac.uk)

Office hour: Thursday 15:00-16:00 and by appointment

My office is room 6.02, Dugald Stewart Building.

Course administrator

Ann-Marie Cowe (philinfo@ed.ac.uk)


Lecture notes with exercises will be made available each week, and are the only required reading. (See the syllabus below.)

If you want to look ahead, here are the notes from last year (PDF). The content will change for this year, however, so pay attention to what I upload to the syllabus below!

You are encouraged (but not required) to work through the following textbook alongside the classes:

  • Rod Girle, Modal Logics and Philosophy, 2nd edition, 2009

If you want to know even more, get one (or both) of these:

  • Graham Priest, An Introduction to Non-Classical Logic, 2nd edition, 2008
  • G.E. Hughes and Max Cresswell, A New Introduction to Modal Logic, 1996


  • Lecture 1: Monday 10:00-10:50, Room G.06, 50 George Square
  • Lecture 2: Wednesday 10:00-10:50, Room S.1, 7 George Square
  • Tutorial Group 1: Tuesday 11:10-13:00, Room LG.06, David Hume Tower
  • Tutorial Group 2: Monday 14:10-16:00, Room 4.2, Lister Learning and Teaching Centre, 5 Roxburgh Place

Only the first hour of tutorials is compulsory.

If you'd like to change your tutorial group, please use the "Group Change Request form" on the timetabling website.


In addition to the final exam, which accounts for 50% of the grade, there will be two take-home tests, the first counting 20%, the second 30%.

The first take-home test will be released on Monday 7th October, and is due by Thursday 10th October.

The second take-home test will be released on Monday 4th November, and is due by Thursday 7th November.

The final exam will take place in December. The precise date and location are not yet known.

Provisional Syllabus

Week 1: Modal Operators

Lecture notes for week 1 (PDF)

Slides for lecture 1 (PDF)

Slides for lecture 2 (PDF)

New: Answers to selected exercises, weeks 1-3 (PDF)

The language of modal propositional logic. Reasoning about necessity and possibility. Flavours of modality. Some branches of modal logic.

Week 2: Possible Worlds

Lecture notes for week 2 (PDF)

Slides for lecture 3 (PDF)

Slides for lecture 4 (PDF)

New: Answers to selected exercises, weeks 1-3 (PDF)

Basic possible-worlds semantics for modal propositional logic. Tree rules to establish validity and find counterexamples.

Week 3: Accessibility

Lecture notes for week 3 (PDF)

Slides for lecture 5 (PDF)

Slides for lecture 6 (PDF)

New: Answers to selected exercises, weeks 1-3 (PDF)

Adding an accessibility relation to possible-worlds models. Properties of the accessibility relation and corresponding logical systems.

Week 4: Models and Proofs

Lecture notes for week 4 (PDF)

Natural deduction proofs for modal logic (PDF)

Slides for lecture 7 (PDF)

Slides for lecture 8 (PDF)

Soundness and completeness for trees and the axiomatic method. A brief look at the logic of provability.

Week 5: Epistemic Logic

Lecture notes for week 5 (PDF)

Slides for lecture 9 (PDF)

Slides for lecture 10 (PDF)

New: Answers to selected exercises, weeks 1-3 (PDF)

The logics of knowledge and belief. Gaining information as excluding possibilities. Modal logics with multiple modalities. Interaction principles.

Week 6: Deontic Logic

The logic of obligation and permission. Ideal-worlds models. Some puzzles and paradoxes. Neighbourhood models. The concept of conditional obligation.

Week 7: Temporal Logic

The logic of past, present, and future. Worlds and times. Branching time. `Now'. Two-dimensional modal logics.

Week 8: Conditionals

The ``paradoxes of material implication''. Strict implication. Lewis-Stalnaker conditionals. If-clauses as restrictors.

Week 9: Modal Predicate Logic

Modality de dicto and de re. Predicate logic recap. Predicate logic as a modal logic. Challenges for a modal predicate logic.

Week 10: Existence

The connection between quantification and existence. Constant domain models and variable domain models. Free logics.

Week 11: Trans-World Identity

Rigid and non-rigid designators. Contingent identity. Counterpart models.