Topics in Modal Logic (Fall 2026)

Contents of these pages

• Course Description and Prerequisites
• Practicalities
• Grading and requirements for passing
• Contents of classes

News

• It seems that there was a problem with the UvA mail on Friday. Please keep looking here for information about the oral exam.
• In case UvA mail is not working and you have an important message for us, you can send it to Lide's private e-mail address: lidesfullname at gmail dot com.
• On Friday afternoon we made some minor updates on the oral exam that you can find here.
  Most importantly, make sure that you are present at least five minutes before the scheduled start of your exam. We will pick you up from the ILLC common room.
• Here are the first four chapters of this year's lecture notes.
  (This version corrects an error in the earlier version of the notes.)
• You can find all information on the homework, presentations and the oral exam on this page, including the schedules.

Course material

• We will make use of lecture notes.
  • Here are the first four chapters of this year's lecture notes.
  • Here is an earlier version of the notes; an updated version of this year's notes will be supplied during the course.
• Here is some additional reading material:
  • Jan Rutten, The Method of Coalgebra: exercises in coinduction, CWI, Amsterdam, The Netherlands, 2019 (ISBN 978-90-6196-568-8).
  • Bart Jacobs, Introduction to Coalgebra: towards mathematics of states and observation, Tracts in Theoretical Computer Science, Cambridge University Press, 2016. (An earlier version is freely available here.)
  • C. Cîrstea, A. Kurz, D. Pattinson, L. Schröder and Y. Venema, Modal logics are coalgebraic, The Computer Journal, 54 (2011) 31-41.

Practicalities

Staff

• lecturer: Yde Venema (y dot venema at uva dot nl)
• teaching assistant: Lide Grotenhuis (l dot m dot grotenhuis at uva dot nl)

Dates & location:

• Classes run from 27 October until 10 December; there will be 14 lectures and 7 exercise sessions in total.
• There are two lectures weekly, on Tuesdays and Wednesdays, and one exercise session weekly, on Thursdays.
• There is an exam on Monday 14 December, from 13.00 - 16.00, in room SP G0.10 - G0.12 (Science Park).

Grading

• The principal assessment of student performance will be on the basis of a written exam at the end of the course, but there will also be oral exams in week 4, homework assignments (without grades) and student presentations (without grades). The exact requirements can be found here.

Course Description

This year, the course will be devoted to connections between coalgebra and modal logic. We will provide an introduction to the notion of a coalgebra and its connection with modal logic. In a nutshell, we will see how:

• universal coalgebra is a unifying theory for many state-based evolving structures including deterministic finite automata, Kripke structures and non-wellfounded sets;
• universal coalgebra can be used to unify many different branches of modal logic under the umbrella of coalgebraic modal logic.

Course Content Here is a tentative list of topics to be covered:

• introduction to coalgebra: definition and examples
• coalgebraic modal logic: examples
• final coalgebras and coinduction
• behavioral equivalence and bisimilarity
• covarieties and structural operations
• Moss' coalgebraic modality
• logics based on predicate liftings
• one-step coalgebraic logic
• properties and desiderata of coalgebraic logics
• finite models: filtration and finite model property
• completeness for coalgebraic modal logics
• coalgebraic fixpoint logics and coalgebra automata
• topological coalgebras and Stone-type dualities
• algebra & coalgebra: analogies & dualities

Prerequisites

We do presuppose some basic skills and background knowledge on modal logic:

• required: familiarity with the syntax and semantics of modal languages, and the notion of bisimulation. More precisely, we build on the material covered in the first weeks of the course Introduction to Modal Logic, corresponding to the sections 1.1-1.3, 2.1-2.3 of the Modal Logic book.
• recommended (but not strictly necessary): previous exposure to the completeness proof of modal logic, and in particular, to the notion of the canonical frame.