| Course title | Mathematical Logic |
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| Course code | KMI/ML |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | unspecified |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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Logic: logic and related disciplines, historical development, mathematical logic, logic in computer science. Propositional Logic (ProL): language of ProL, formulas, truth valuation, truth evaluation of formulas, semantic consequence, tautology, satisfiable formulas, normal forms, table method. Axiomatic system of ProL: axioms, deduction rules, proof, deduction theorem, provable formulas, selected theorems (substitution, equivalence, neutral formulas), theories, consistency, correctness theorem, completeness theorem. Predicate logic (PreL): language, terms, formulas, basic syntactic notions; semantics: structures for PreL, evaluation of terms and formulas, tautologies, satisfiable formulas, semantics consequence, basic semantic concepts, theories, models. Axiomatic system of PreL: axioms, deduction rules, proof, deduction theorem, extension and conservative extension, constants, provable formulas, variants, consistency. Completeness: correctness, Henkin theory, complete theory, completion theorem, models from constants, canonical structure, completeness theorem. Introduction to logic programming: resolution, completeness of resolution, relationship to Prolog. Representative examples of Prolog. Introduction to non-classical logics: fuzzy logic, modal logic, temporal logic. Examples and applications.
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| Learning activities and teaching methods |
| Lecture, Demonstration |
| Learning outcomes |
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The students become familiar with basic concepts of mathematical logic.
1. Knowledge Indetify differences in various types of entailment. |
| Prerequisites |
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unspecified
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| Assessment methods and criteria |
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Oral exam, Written exam
Active participation in class. Completion of assigned homeworks. Passing the oral (or written) exam. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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