Algorithmic Model Theory

WS 2019/20

Schedule

Type Date Location   Organizer
V4 Mo 10:30 – 12:00 AH III Start 7th October E. Grädel
Tue 08:30 – 10:00 AH I Start 8th October E. Grädel
Ü2 Tue 10:30 – 12:00 AH III Start 15th October

News

  • Since it is still not possible to create a working registration for the exam in RWTHonline, please write an E-mail to dannert(at)logic.rwth-aachen.de if you want to participate in the exam. Once the registration in RWTHonline becomes possible I will use that list to register everyone by hand.
  • The exercise sheets are published every Tuesday and are due the following Tuesday at 10:30 am. They may be handed in during the lecture or at the beginning of the exercise class. Alternatively they can be put in the box at the institute.
  • You may work on the exercise sheets in groups of up to three students.
  • There will be no e-learning room for this course. All necessary information can be found on this website.
  • The distribution of points for exercise sheet 1 has been adjusted slightly.

Coursework

Lecture Notes

  • Chapter 1: The Classical Decision Problem for FO [pdf] [pdf-2up]
  • Chapter 2: Descriptive Complexity [pdf]
  • Chapter 3: LFP and Infinitary Logics [pdf]
  • Chapter 4: Expressive Power of First-Order Logic [pdf]
  • Chapter 5: Zero-one laws [pdf]
  • Chapter 6: Modal, Inflationary and Partial Fixed Points [pdf]

Content

  • Decidable and undecidable theories
  • Finite model property
  • Descriptive complexity: logical characterisation of complexity classes
  • Locality of first order logic, 0-1 laws
  • Logics with transitive closure, fixed-point logics

Learning Objectives

  • Understanding the relation between logical definability and algorithmic complexity (decidability of theories, evaluation algorithms, logical characterisations of complexity classes).
  • Learning the methods from model theory and algorithmic complexity theory to analyse the expressive power and complexity of logical specifications on finite or finitely representable structures.
  • Learning to work with fundamental logics of algorithmic model theory and in their application in concrete scenarios.

Literature

[1] S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.
[2] E. Börger, E. Grädel, and Y. Gurevich. The Classical Decision Problem. Springer-Verlag, 1997.
[3] H. Ebbinghaus and J. Flum. Finite Model Theory. Springer, 1999.
[4] E. Grädel, P. G. Kolaitis, L. Libkin, M. Marx, J. Spencer, M. Y. Vardi, Y. Venema, and S.Weinstein. Finite Model Theory and Its Applications. Springer-Verlag, 2007.
[5] E. Grädel. Finite Model Theory and Descriptive Complexity. In Finite Model Theory and Its Applications, pp. 125–230. Springer-Verlag, 2007.
[6] N. Immerman. Descriptive Complexity. Springer, 1999.
[7] L. Libkin. Elements of Finite Model Theory. Springer, 2004.

Prerequisites

  • Mathematical Logic

Classification

  • Computermathematik (D)/Hauptstudium/Hauptfach Computermathematik
  • Informatik (D)/Hauptstudium/Theoretische Informatik
  • Informatik (D)/Anwendungsfächer/Mathematik
  • Mathematik (D)/Hauptstudium/Reine Mathematik
  • Informatik (M.A.)/Hauptstudium
  • Mathematik (M.A.)
  • Technik-Kommunikation (M.A.)/2. Hauptfach (Technisches Fach)/Grundlagen der Informatik/Hauptstudium/Spezialisierung Informatik
  • Informatik (GYM+GS,SII)/Hauptstudium/C. Mathematische Methoden der Informatik
  • Informatik (M.Sc.)/Theoretische Informatik
  • Mathematik (M.Sc.)/Mathematik/Reine Mathematik
  • Software Systems Engineering (M.Sc.)/Theoretical Foundations of Software Systems Engineering
  • Software Systems Engineering (M.Sc.)/[MPO2010] Theoretical Computer Science

Contact

Erich Grädel