Topics in Modal Logic (Fall 2023)
This page concerns the course `Topics in Modal Logic', taught at the University
of Amsterdam in November and December 2023.
Contents of these pages
Staff
 Lecturer: Yde Venema (y dot venema at uva dot nl)
 Teaching assistant, grading: Lide Grotenhuis (l dot m dot grotenhuis
at uva dot nl)
Dates & location:

Classes run from 1 November until 14 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.

In addition, Lide offers a weekly office hour on Thursday
mornings from noon  1pm in room F2.02 (ILLC building).

There is a written on site exam on Tuesday 19 December,
from 16.00  19.00, in Science Park C1.110.

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
 complexity measures 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
 modal automata
 simulation theorem
 finite model property
 uniform interpolation
 model theory
 expressive completeness
 tableaux, complexity of the satisfiability problem
 derivation systems
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