# Mathematical Logic

## SS 2021

Note: This course was held in German.

### Exam

The course Mathematical Logic is completed by passing a written exam lasting 120 minutes.

For the exam admission, it suffices to obtain 50% of all exercise and eTest points.

### Content

• Propositional logic (foundations, algorithmical questions, compactness, resolution, sequent calculus)
• Structures, syntax and semantic of first-order 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

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

### Classification

• Grundlagen der Informatik (B.Sc.) / Themenmodule / Themenmodul Wahlpflicht Mathematik
• Informatik (B.Sc.) / Modulbereich Theoretische Informatik
• Mathematik (B.Sc.) / Wahlpflichtbereich

### Prerequisites

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

### Successive Courses

• Mathematical Logic II
• Logic and Games
• Algorithmic Model Theory
• other specialized lectures around the topic of Mathematical Logic

### Recurrence

every year in the summer term

### Contact

Erich Grädel, Lovro Mrkonjić