| Course Unit Code | 460-4034/02 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| DUZ48 | prof. RNDr. Marie Duží, CSc. |
| Summary |
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| The goal of the course is providing knowledge on particular methods of reasoning and automatic theorem proving. We focus on the development of these methods in the area of relational and algebraic theories and philosophy of mathematics. The course also aims at using the proof methods in theoretical computer science. |
| Learning Outcomes of the Course Unit |
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| The goal of the course is providing knowledge on particular methods of reasoning and automatic theorem proving. We focus on the development of these methods in the area of relational and algebraic theories and philosophy of mathematics. The course also aims at using the proof methods in theoretical computer science. |
| Course Contents |
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Lectures:
1) Proof calculi, consistence and completeness.
2) Hilbert-style proof calculus.
3) Logical theories; completeness and incompleteness of a theory, decidability.
4) Theory of relations; equivalence and orderings.
5) Algebraic theories; groups, rings and fields.
6) Lattice theory, conceptual lattices.
7) Theories of arithmetic, Gödel results; incompleteness theorems.
8) Theory of recursive functions and algorithms.
9) Sequent calculi
10) Intensional logics and Kripke semantics.
Seminars:
1) Proof calculi, consistence and completeness.
2) Hilbert-style proof calculus.
3) Logical theories; completeness and incompleteness of a theory, decidability.
4) Theory of relations; equivalence and orderings.
5) Algebraic theories; groups, rings and fields.
6) Lattice theory, conceptual lattices.
7) Theories of arithmetic, Gödel results; incompleteness theorems.
8) Theory of recursive functions and algorithms.
9) Sequent calculi
10) Intensional logics and Kripke semantics.
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| Recommended or Required Reading |
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| Required Reading: |
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E. Mendelson. Introduction to Mathematical Logic. Chapman & Hall/CRC, 2001.
P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998. |
1. M. Duží. Logika pro informatiky a příbuzné obory. VŠB-Technická universita Ostrava, 2012. ISBN 978-80-248-2662-2
2. M.Duží: Matematická logika. Učební texty VŠB Ostrava.
http://www.cs.vsb.cz/duzi/Mat-logika.html
3. Z. Manna: Matematická teorie programů. McGraw-Hill, 1974, SNTL Praha 1981.
4. Švejdar, V.: Logika (neúplnost, složitost, nutnost). Academia, Praha 2002.
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| Recommended Reading: |
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| P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998. |
| P. Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998. |
| Planned learning activities and teaching methods |
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| Lectures, Seminars, Individual consultations, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | | |
| Examination | Examination | 100 | 51 |