Logic 2: Modal Logic (Spring 2023)

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 hours: Friday 13:00-14:00 and by appointment

My office is room 8.06, 40 George Square.

Course Secretary

Peter Cruickshank (philinfo@ed.ac.uk)



  • Monday 13:10-14:00, 7 George Square, room S.1
  • Tuesday 13:10-14:00, Dugald Stewart Building, room 3.10


  • Group 1: Thursday 14:10-16:00. Location varies from week to week (sorry!):
    • Week 1: Appleton Tower, room 2.14
    • Weeks 3-5: Charteris Land, room 4.20
    • Weeks 6-11: Lister Learning and Teaching Centre, room 5.3
  • Group 2: Friday 11:10-13:00, Old College, room 03

Tutorials start in week 2. 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.


  • First take-home test (20%), released Monday 13/02, due Thursday 16/02 at 1pm
  • Second take-home test (30%), released Monday 20/03, due Thursday 23/03 at 1pm
  • Final exam (50%), date and location TBC


Lecture notes with exercises are made available each week in the syllabus below. They are the only required reading.

If you want to get a wider perspective or further help, you may find one or more of the following books useful (listed with increasing difficulty):

  • Rod Girle, Modal Logics and Philosophy, 2nd edition, 2009
  • Graham Priest, An Introduction to Non-Classical Logic, 2nd edition, 2008
  • G.E. Hughes and Max Cresswell, A New Introduction to Modal Logic, 1996


Week 1 (16/01): Modal Operators

The language of modal propositional logic. Reasoning about necessity and possibility. Flavours of modality. Axiomatic systems.

Lecture notes for week 1 (PDF)

Slides for lecture 1 (PDF)

Slides for lecture 2 (PDF)

Answers to the exercises (PDF)

Week 2 (23/01): Possible Worlds

Basic possible-worlds semantics for modal propositional logic. The tree method for establishing validity and finding counterexamples.

Lecture notes for week 2 (PDF)

Slides for lecture 3 (PDF)

Slides for lecture 4 (PDF)

Answers to the exercises (PDF)

Week 3 (30/01): Accessibility

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

Lecture notes for week 3 (PDF)

Optional bonus text: Natural deduction proofs (PDF)

Slides for lecture 5 (PDF)

Slides for lecture 6 (PDF)

Answers to the exercises (PDF)

Week 4 (06/02): Models and Proofs

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

Lecture notes for week 4 (PDF)

Slides for lecture 7 (PDF)

Slides for lecture 8 (PDF)

Answers to the exercises (PDF)

Week 5 (13/02): Epistemic Logic

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

Lecture notes for week 5 (PDF)

Slides for lecture 9 (PDF)

Slides for lecture 10 (PDF)

Answers to the exercises (PDF)

Week 6 (27/02): Deontic Logic

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

Lecture notes for week 6 (PDF)

Slides for lecture 11 (PDF)

Slides for lecture 12 (PDF)

Answers to the exercises (PDF)

Week 7 (06/03): Temporal Logic

The logic of past, present, and future. Worlds and times. Branching time. `Now'.

Lecture notes for week 7 (PDF)

Slides for lecture 13 (PDF)

Slides for lecture 14 (PDF)

Answers to the exercises (PDF)

Week 8 (13/03): Conditionals

Material conditionals. Strict conditionals. Variably strict conditionals. If-clauses as restrictors.

Lecture notes for week 8 (PDF)

Slides for lecture 15 (PDF)

Slides for lecture 16 (PDF)

Answers to the exercises (PDF)

Week 9 (20/03): Towards Modal Predicate Logic

Predicate logic recap. Modal fragments of predicate logic. Modality de dicto and de re. Identity and descriptions.

Lecture notes for week 9 (PDF)

Slides for lecture 17 (PDF)

Slides for lecture 18 (PDF)

Answers to the exercises (PDF)

Week 10 (27/03): Semantics for Modal Predicate Logic

Constant domain semantics and variable domain semantics. Quantification and existence. Trans-world identity.

Lecture notes for week 10 (PDF)

Slides for lecture 19 (PDF)

Slides for lecture 20 (PDF)

Week 11 (03/04): Review Week

Slides for lecture 21 (PDF)

Slides for lecture 22 (PDF)

All lecture notes in one file (PDF)