Mathematical Logic

SS 2015

Schedule

Type Date Location   Organizer
V3 Mo 08:45 – 10:00 1420|002 (Ro) Lecture (Start April 13th) E. Grädel
We 14:15 – 15:15 1420|002 (Ro) Lecture E. Grädel
We 15:15 – 15:45 1420|002 (Ro) Discussion E. Grädel
Ü2 Thu 12:15 – 13:45 1010|213 (V) Gruppe A (Beginn 16.4.) E. Hüsgen
Thu 16:15 – 17:45 2350|009 (AH I) Gruppe B R. Lipp
Fri 12:15 – 13:45 2350|314.1 (AH III) Gruppe C F. Reinhardt
Fri 13:15 – 14:45 2350|111 (AH II) Gruppe D F. Abu Zaid/S. Schalthöfer
Mon 10:30 – 12:00 2350|111 (AH II) Gruppe E W. Pakusa
Mon 12:15 – 13:45 2356|051 (AH VI) Gruppe F C. Wagner
Mon 13:15 – 14:45 2350|314.1 (AH III) Gruppe G M. Voit
mo 16:15 – 17:45 2350|009 (AH I) Gruppe H A. Tollkötter
Tue 12:15 – 13:45 1010|213 (V) Gruppe I C. Hugenroth

Lecture Notes

  • 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]

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

Frederic Reinhardt, Erich Grädel