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Course detail
FSI-SML-AAcad. year: 2023/2024
In the course, the basics of propositional and predicate logics will be taught. First, the students will get acquainted with the syntax and semantics of the logics, then the logics will be studied as formal theories with an emphasis on formula proving. The classical theorems on correctness, completeness and compactness will also be dealt with. After discussing the prenex forms of formulas, some properties and models of first-order theories will be studied. We will also deal with the undecidability of first-order theories resulting from the well-known Gödel incompleteness theorems.
Language of instruction
Number of ECTS credits
Mode of study
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Department
Entry knowledge
Rules for evaluation and completion of the course
The course unit credit is awarded on condition of having attended the seminars actively and passed a written test. The exam has a written and an oral part. The written part tests student's ability to deal with various problems using the knowledge and skills acquired in the course. In the oral part, the student has ro prove that he or she has mastered the related theory.
Aims
The aim of the course is to acquaint students with the basic methods of reasoning in mathematics. The students will learn about general principles of predicate logic and, consequently, acquire the ability of exact mathematical reasoning and expression. They will understand the general principles of construction of mathematical theories and proofs. The course will contribute students to better acquiring logical reasonong in mathematics and thus to better understanding mathematical knowledge.
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Elearning
Classification of course in study plans
Lecture
Teacher / Lecturer
Syllabus
1. Introduction to mathematical logic2. Propositions and their truth, logical connectives3. Language, formulas and semantics of propositional calculus4. Principle of duality, applications of propositional logic 5. Formal theory of the propositional logic 6. Provability in propositional logic, completeness theorem 7. Language of the (first-order) predicate logic, terms and formulas 8. Semantic of predicate logic9. Axiomatic theory of the first-order predicate logic 10.Provability in predicate logic 11.Prenex normal forms, first-order theories and their models 12. Theorems on compactness and completeness 13.Undecidability of the first-order theories, Gödel's incompleteness theorems
Exercise