Mathematical Logic

SS 2016

Schedule

Type Date Location   Organizer
V3 Mo 12:15 – 13:15 1420|001 (Grüner Hörsaal) Lecture (Start April 18th) E. Grädel
Mo 13:15 – 13:45 1420|001 (Grüner Hörsaal) Discussion E. Grädel
We 08:45 – 10:00 1420|002 (Ro) Lecture (Start April 13th) E. Grädel
Ü2 Mo 10:15 – 11:45 2356|051 (AH VI) Gruppe A L. Bohn
Mo 16:15 – 17:45 2350|009 (AH I) Gruppe B R. Lipp
Tue 08:30 – 10:00 1010|141 (IV) Gruppe C C. Welzel
Tue 10:15 – 11:45 2356|051 (AH VI) Gruppe D S. Schalthöfer
Tue 12:15 – 13:45 1100|U101 (VT) Gruppe E R. Wilke
We 14:15 – 15:45 2350|111 (AH II) Gruppe F M. Hoelzel
Thu 12:00 – 13:30 1080|005 (R 5) Gruppe G T. Winkler
Fri 10:15 – 11:45 2350|111 (AH II) Gruppe H F. Reinhardt
Thu 16:15 – 17:45 2350|111 (AH II) Gruppe I F. Bier
Fri 12:15 – 13:45 2356|050 (AH V) Gruppe J C. Wagner
Fri 14:15 – 15:45 2356|051 (AH VI) Gruppe K C. Hugenroth

Lecture Notes

  • Alle Kapitel [pdf] [pdf-2up]
  • Chapter 0: Notation [pdf]
  • Chapter 1: Aussagenlogik [pdf]
  • Chapter 2: Syntax und Semantik der Prädikatenlogik [pdf]
  • Chapter 3: Definierbarkeit in der Prädikatenlogik [pdf]
  • Chapter 4: Vollständigkeitssatz, Kompaktheitssatz und Unentscheidbarkeit der Prädikatenlogik [pdf]
  • Chapter 5: Modallogik, temporale Logiken und monadische Logik [pdf]

Coursework

Content

  • Propositional logic (foundations, algorithmical questions, compactness, resolution, sequent calculus)
  • Structures, syntax und semantic of the Predicate logic
  • Introduction into other logics (modal and temporal Logics, higher order logics)
  • Evaluation games, model comparison games
  • Proof calculi, term structures, completeness theorem
  • Compactness theorem and applications
  • Decidability, undecidability and complexity of logical specifications

Literature

[1] S. Burris. Logic for Mathematics and Computer Science. Prentice Hall, 1998.
[2] R. Cori and D. Lascar. Logique mathématique. Masson, 1993.
[3] H. Ebbinghaus, J. Flum, and W. Thomas. Einführung in die mathematische Logik. Wissenschaftliche Buchgesellschaft, Darmstadt, 1986.
[4] M. Huth and M. Ryan. Logic in Computer Science. Modelling and reasoning about systems. Cambridge University Press, 2000.
[5] B. Heinemann and K. Weihrauch. Logik für Informatiker. Teubner, 1992.
[6] H. K. Büning and T. Lettman. Aussagenlogik: Deduktion und Algorithmen. Teubner, 1994.
[7] S. Popkorn. First Steps in Modal Logic. Cambridge University Press, 1994.
[8] W. Rautenberg. Einführung in die Mathematische Logik. Vieweg, 1996.
[9] U. Schöning. Logik für Informatiker. Spektrum Verlag, 1995.
[10] D. van Dalen. Logic and Structure. Springer, Berlin, Heidelberg, 1983.

Classification

  • Informatik (B.Sc.)/4. Semester
  • Mathematik (B.Sc.)/Mathematik (WS)/4. Semester
  • Mathematik (B.Sc.)/Mathematik (WS)/6. Semester
  • Mathematik (B.Sc.)/Mathematik (SS)/5. Semester
  • Mathematik (D)/Hauptstudium/Reine Mathematik
  • Informatik (S II)
  • Mathematik (S II)/Hauptstudium/B: Algebra und Grundlagen der Mathematik

Prerequisites

  • Basic mathematical knowledge from the lectures Discrete Structures and Linear Algebra
  • Basic knowledge about recursion theory and complexity theory

Successive Courses

  • Algorithmic Model Theory
  • Mathematical Logic II
  • Complexity Theory und Quantum Computing
  • Logic and Games
  • Other specialized lectures around the topic of Mathematical Logic

Recurrence

Every year in the summer term

Contact

Matthias Hoelzel, Erich Grädel