Topics in Modal Logic (Fall 2022)
This page concerns the course `Topics in Modal Logic', taught at the University
of Amsterdam in November and December 2022.
Contents of these pages

Here is last year's exam.

Here is an updated overview of the class.

Starting 18 November, there is a weekly question hour on Friday,
from 11:00 to 12:00 in room F2.01 (PhD Meeting Room at ILLC).

This year's topic will be modal fixpoint logic; scroll down for more
information on Course Description and Prerequisites.
 There is no overlap between this year's edition of the course and the
edition of 2021.
Students can do both versions of the course for grades.

There will be some (but not much) overlap between this course and the course
on Logic, Games and Automata taught by Bahareh Afshari.
A special arrangement will apply to students who have attended mentioned
course; please contact the lecturer immediately in case this applies to you.
Staff
 Lecturer: Yde Venema (y dot venema at uva dot nl)
 Teaching assistant, grading: Johannes Kloibhofer (j dot kloibhofer
at uva dot nl)
Dates & location:

Classes run from 2 November until 15 December; there will be 14 classes
in total.

There are two classes weekly, on Wednesdays from 13.00  14.45,
and on Thursdays from 15.00  16.45.
Both classes will be on site in Science Park D1.115.

In addition, starting 18 November, there is a weekly question hour on Friday,
from 11:00 to 12:00 in room F2.01 (PhD Meeting Room at ILLC).

There is a written on site exam on Tuesday 20 December,
from 09.00  12.00, in Science Park L1.01.

Grading is primarily through homework assignments, and a written exam at the
end of the course.
Collection and submission proceeds via the Canvas pages 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 entirely to connections between modal
fixpoint logic and automata theory.
This is a classic field in theoretical computer science, which has led to
both seminal theoretical results such as Rabin's decidability theorem, and
practical applications in the field of specification and verification of
software.
More specifically, a large part of the course will focus on the modal
mucalculus, an extension of modal logic with explicit fixpoint operators, which
was introduced in the early 1980s.
The modal mucalculus shares many attractive properties with ordinary modal
logic, but has a much bigger expressive power.
A main theme of the course will be the use of automatatheoretic tools to
understand and prove results about the modal mucalculus.
Indicatively, we will discuss the following topics:
 modal mucalculus: syntax and semantics
 equivalence of gametheoretical and algebraic semantics
 algebraic theory of fixpoint operators
 bisimulation invariance and bounded tree model property
 size matters in the modal mucalculus
 automata for infinite words: basic definitions, acceptance conditions,
determinization
 theory of infinite games
 parity games: positional determinacy, complexity issues
 parity formulas and modal automata
 simulation theorem
 finite model property, complexity of the satisfiability problem
 uniform interpolation
 expressive completeness
Prerequisites
We presuppose some (but very little) basic background knowledge
on modal logic; roughly, what is needed is familiarity with the syntax and
semantics of modal languages, and the notion of bisimulation.
More precisely, we build on the basic material covered
in the course Introduction to Modal Logic, that is: the sections
1.11.3, 2.12.3 of the Modal Logic book.
Next to this, we assume that students possess some mathematical maturity.
Comments, complaints, questions: mail
Yde Venema