# Mathematical Logic

## SS 2021

### Information

• All exam results are available via RWTHonline.

• We have published the exercises on this web page. Please note that you are not allowed to publish the course materials anywhere else.

• Exam registration: Please do not forget to register for the exam via RWTHonline (first exam date or second exam date). Note that each exam registration has a deadline.

• This course is held via the Moodle course page. Your points (and later, your exam results) are displayed to you in the MaLo-Portal. If you encounter any problems, please send an e-mail to Lovro Mrkonjić.

### → MaLo-Portal ←

The MaLo-Portal displays your current points and preliminary exam results, if available.

### Course Material

The current course material is available on the Moodle course page. Note that the preliminary material on this page will not be updated during the semester.

### Exam

Please refer to the Moodle course page or RWTHonline for current information about the exam and dates or visit the German version of this page.

### 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

  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

• 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

Lovro Mrkonjić, Erich Grädel