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


Course material



Dates & location:


Course Description

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 mu-calculus, an extension of modal logic with explicit fixpoint operators, which was introduced in the early 1980s. The modal mu-calculus 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 automata-theoretic tools to understand and prove results about the modal mu-calculus.

Indicatively, we will discuss the following topics:


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 1.1-1.3, 2.1-2.3 of the Modal Logic book.
Next to this, we assume that students possess some mathematical maturity.
Comments, complaints, questions: mail Yde Venema