Logic 2: Modal Logic (Autumn 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 11:00-12:00 and by appointment
My office is room 8.06, 40 George Square.

Course Secretary



  • Thursday 13:10-14:00, 7 George Square, room S.1
  • Friday 13:10-14:00, 7 George Square, room S.1


  • Group 1: Monday 11:10-13:00 Lister Learning and Teaching Centre, room 1.1
  • Group 2: Tuesday 12:10-14:00 40 George Square, room LG.09
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.

Logic 2 Lab:

  • Wednesday 12:10-14:00, Lister Learning and Teaching Centre, room G.10


  • First take-home test (20%), released Monday 16 Oct, due Thursday 19 Oct at 1pm
  • Second take-home test (30%), released Monday 20 Nov, due Thursday 23 Nov 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. You can also download the combined lecture notes for the whole course.

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


You can find the answers to all the exercises in the the combined lecture notes.

Week 1: Modal Operators

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

Week 2: Possible Worlds

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

Week 3: Accessibility

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

Week 4: Models and Proofs

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

Week 5: Epistemic Logic

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'.

Week 8: Conditionals

Material conditionals. Strict conditionals. Variably strict conditionals. If-clauses as restrictors.
Lecture 16 cancelled.

Week 9: Towards Modal Predicate Logic

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

Week 10: Semantics for Modal Predicate Logic

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

Week 11: Review Week