FI:MA007 Mathematical Logic - Course Information
MA007 Mathematical Logic
Faculty of InformaticsAutumn 2024
- Extent and Intensity
- 2/1/1. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
- Teacher(s)
- prof. RNDr. Antonín Kučera, Ph.D. (lecturer)
Dr. rer. nat. Achim Blumensath (seminar tutor)
Mgr. Vít Jelínek (seminar tutor)
RNDr. David Klaška (seminar tutor)
Bc. Filip Kučerák (seminar tutor)
Bc. Adam Štafa (seminar tutor) - Guaranteed by
- prof. RNDr. Antonín Kučera, Ph.D.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Antonín Kučera, Ph.D.
Supplier department: Department of Computer Science – Faculty of Informatics - Timetable
- Thu 19. 9. to Thu 12. 12. Thu 10:00–11:50 D1
- Timetable of Seminar Groups:
MA007/02: Mon 23. 9. to Mon 2. 12. each odd Monday 12:00–13:50 A319, A. Štafa
MA007/03: Tue 17. 9. to Tue 10. 12. each even Tuesday 12:00–13:50 A319, F. Kučerák - Prerequisites
- IB000 Math. Foundations of CS || PřF:M1120 Discrete Mathematics || PřF:M1125 Fundamentals of Mathematics
Students should have passed the course IB000 Mathematical Foundations of Computer Science or a course covering the foundations of mathematics at the Faculty of Science. - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Informatics (programme FI, B-INF) (2)
- Course objectives
- The course covers basic results about propositional and first order logic, including Gödel's completeness and incompleteness theorems.
- Learning outcomes
- At the end of this course, students should be able to:
understand the difference between formal notions and notions defined at a meta-level;
understand the difference between validity and provability;
understand the syntax and semantics of first-order logic;
understand and appreciate the fundamental ideas in the proofs of Gödel's completeness and incompleteness theorems. - Syllabus
- Propositional calculus: propositional formulas, truth, provability, completeness.
- First-order logic: syntax, semantics.
- A deductive system for first-order logic. Provability, correctness.
- Completeness theorem: theories, models, Gödel's completeness theorem
- Basic model theory, Löwenheim-Skolem theorem
- Gödel's incompleteness theorem.
- Literature
- MENDELSON, Elliott. Vvedenije v matematičeskuju logiku. Edited by Sergej Ivanovič Adjan, Translated by F. A. Kabakov. Izd. 2-oje, ispr. Moskva: Nauka. Glavnaja redakcija fiziko-matematičeskoj literatury, 1976, 320 s. info
- ŠTĚPÁNEK, Petr. Matematická logika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 281 s. info
- KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info
- Teaching methods
- Lectures and tutorials.
- Assessment methods
- Lectures: 2 hours/week. Tutorials: 1 hour/week.
Written exam. - Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/fi/autumn2024/MA007