Topics in Modal Logic (Fall 2024)
This page concerns the course `Topics in Modal Logic', taught at the University
of Amsterdam in November and December 2024.
Contents of these pages
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The second homework assignment can be found on the Canvas course page.
Deadline for submission is Thursday, 14 November, 2pm.
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This year's topic will be modal fixpoint logic; scroll down for more
information on Course Description and Prerequisites.
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We will make use of lecture notes, to be provided (and updated if needed)
during the course, and possibly material from the literature.
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Here are the lecture notes of last
year.
(Don't print these --- a new version will be distributed during the course.)
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:
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Classes run from 30 Octobber until 12 December; there will be 14 classes
in total.
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There are two lectures 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.
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In addition, there is a tutorial session on Thursdays from 17.00 - 18.45.
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There is a written on site exam on Tuesday 17 December,
from 17.00 - 20.00, in Science Park D1.116.
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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
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:
- modal mu-calculus: syntax and semantics
- equivalence of game-theoretical and algebraic semantics
- algebraic theory of fixpoint operators
- bisimulation invariance and bounded tree model property
- complexity measures in the modal mu-calculus
- 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
1.1-1.3, 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