Logic 2: Modal Logic (Spring 2022)

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: Friday 11:00-12:00 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!

If you want to get a wider perspective, you may find one or more of the following books useful (listed in 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


  • Lecture 1: Wednesday 12:10-13:00, Appleton Tower Lecture Theatre 2
  • Lecture 2: Friday 13:10-14:00, 40 George Square Lecture Theatre B
  • Tutorial Group 1: Monday 11:10-13:00, Appleton Tower Room 2.12
  • Tutorial Group 2: Tuesday 11:10-13:00, Appleton Tower Room 2.12

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.


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 probably be released on Monday 28th February, to be completed by Thursday 3rd March.

The second take-home test will probably be released on Monday 28th March, to be completed by Thursday 31st March.

The final exam will probably take place in May. The precise date, time, and format of the exam are not yet known.

Provisional Syllabus

Week 1 (17/01): Modal Operators

Lecture notes for week 1 (PDF)

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

Week 2 (24/01): Possible Worlds

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

Week 3 (31/01): Accessibility

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

Week 4 (07/02): Models and Proofs

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

Week 5 (14/02): Epistemic Logic

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

Week 6 (28/02): Deontic Logic

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

Week 7 (07/03): Temporal Logic

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

Week 8 (14/03): Conditionals

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

Week 9 (21/03): Towards Modal Predicate Logic

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

Week 10 (28/03): Semantics for Modal Predicate Logic

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

Week 11 (04/04): Review Week