MA007 Mathematical Logic

Faculty of Informatics
Autumn 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).
Taught in person.
Teacher(s)
prof. RNDr. Antonín Kučera, Ph.D. (lecturer)
Dr. rer. nat. Achim Blumensath (seminar tutor)
Bc. Vít Jelínek (seminar tutor)
RNDr. David Klaška (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
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
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.
The course is taught: every week.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
• Enrolment Statistics (Autumn 2024, recent)