Algorithmic Model Theory

SS 2024

Information

Schedule

Type Date Location   Organizer
V4 Mon 12:30 14:00 2350|111 (AH II) Lecture (Start 15th April) E. Grädel
Wed 12:30 14:00 2350|028 (AH I) Lecture (Start 10th April) E. Grädel
Ü2 Thu 16:30 18:00 1010|141 (IV) and online (link) Exercise Class (Start 25th April) M. Naaf, S. Brinke

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 and G. McColm. On the Power of Deterministic Transitive Closures. Information and Computation, vol. 119, pp. 129–135, 1995.
[6] E. Grädel. Finite Model Theory and Descriptive Complexity. In Finite Model Theory and Its Applications, pp. 125–230. , 2007.
[7] N. Immerman. Descriptive Complexity. Springer, 1999.
[8] L. Libkin. Elements of Finite Model Theory. Springer, 2004.

Prerequisites

  • Mathematical Logic

Classification

  • Informatik (B.Sc.) / Wahlpflichtbereich Theoretische Informatik
  • Mathematik (B.Sc.) / Wahlpflichtbereich
  • Informatik (M.Sc.) / Theoretische Informatik
  • Mathematik (M.Sc.) / Reine Mathematik
  • Data Science (M.Sc.) / Computer Science
  • Software Systems Engineering (M.Sc.) / Theoretical Foundations of Software Systems Engineering

Contact

Erich Grädel, Lovro Mrkonjić