Topics in Modal Logic (Fall 2019)
This page concerns the course `Topics in Modal Logic', taught at the University
of Amsterdam from October - December 2019.
Contents of these pages
- We will make use of lecture notes, to be provided and updated (if needed)
during the course.
- Here is a complete version of the
lecture notes (version: 12 Dec).
- Here are earlier versions of the lecture notes
Here is some additional reading material:
- Jan Rutten,
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
- C. Cîrstea, A. Kurz, D. Pattinson, L. Schröder and Y. Venema,
Modal logics are coalgebraic,
The Computer Journal, 54 (2011) 31-41.
- In case you got interested in the algebra/coalgebra duality, you could
start reading the following:
- C Kupke, A Kurz and Y Venema.
Theoretical Computer Science 327 (2004) 109--134.
For the extended (report) version, click here.
Yde Venema (y dot venema at uva dot nl, phone: 525 5299)
- Homework grading:
Dates & location:
Classes run from 29 October until 12 December; there will be 13/14 classes
There are two classes weekly, on Tuesdays from 13.00 - 14.45,
and on Thursdays from 15.00 - 16.45,
both in room F2.19 (ILLC building, Science Park).
There is an exam on Tuesday 17 December, from 09.00 - 12.00, in room SP
Grading is primarily through homework assignments, and a written exam at the
end of the course.
For the later part of the course additional/alternative requirements may apply
(such as working out lecture notes).
See the separate page on grading for more details.
Modal languages are simple yet expressive and flexible tools for describing
all kinds of relational structures.
Thus modal logic finds applications in many disciplines such as computer
science, mathematics, linguistics or economics.
Notwithstanding this enormous diversity in appearance and application area,
modal logics have a great number of properties in common.
This common mathematical backbone form the content of this course, the exact
topics change from year to year.
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:
More information can be found in the literature mentioned above.
- universal coalgebra is a unifying theory for many state-based evolving
structures including deterministic finite automata, Kripke structures and
- universal coalgebra can be used to unify many different branches of
modal logic under the umbrella of coalgebraic modal logic.
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
The course is an advanced master course, and we assume that students possess
some mathematical maturity; some basic knowledge of algebra and topology
will be handy.
We do presuppose some basic skills and background knowledge on modal logic:
No previous exposure to category theory is assumed.
- 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
Comments, complaints, questions: mail