Mathematical Logic

SS 2018

Schedule

Type Date Location   Organizer
V3 Mo 14:15 – 15:30 1420|002 (Roter Hörsaal) Lecture E. Grädel
Fr 08:30 – 09:30 1420|001 (Grüner Hörsaal) Lecture E. Grädel
Fr 09:30 – 10:00 1420|001 (Grüner Hörsaal) Discussion E. Grädel
Ü2 Mo 08:30 – 10:00 1100|U101 (VT) Group A A. Kusidlo
Mo 10:15 – 11:45 1230|001 (WK) Group B Y. Rohde
Mo 12:15 – 13:45 2356|051 (AH VI) Group K F. Bloemers
Mo 16:15 – 17:45 2350|111 (AH II) Group C J. Segschneider
We 12:15 – 13:45 2350|009 (AH I) Group D M. Hoelzel
Th 08:30 – 10:00 2350|111 (AH II) Group E P. Selz
Th 10:15 – 11:45 2350|111 (AH II) Group F T. Polock
Th 16:15 – 17:45 2350|111 (AH II) Group G S. Schalthöfer
Th 16:15 – 17:45 2356|056 (5056) Group H L. Mrkonjic
Fr 12:15 – 13:45 2350|009 (AH I) Group I R. Wilke
Fr 14:15 – 15:45 1100|U101 (VT) Group L K. Dannert

Lecture Notes

  • Vollständiges Skript [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
  • 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

Richard Wilke, Erich Grädel