Course detail
Mathematical Logic
FSI-SMLAcad. year: 2016/2017
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
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
E.Mendelson, Introduction to Mathematical Logic, Chapman&Hall, 2001 (EN)
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Propositions and their truth, logic operations
3. Language, formulas and semantics of propositional calculus
4. 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 logics
9. Axiomatic theory of the first-order predicate logic
10.Provability in predicate logic
11. Theorems on compactness and completeness, prenex normal forms
12.First-order theories and their models
13.Undecidabilitry of first-order theories, Gödel's incompleteness theorems
Exercise
Teacher / Lecturer
Syllabus
1. Sets, cardinal numbers and cardinal arithmetic
2. Sentences, propositional connectives, truth tables,tautologies and contradictions
3. Independence of propositional connectives, axioms of propositional logic
4. Deduction theorem and proving formulas of propositional logic
5. Terms and formulas of predicate logics
6. Interpretation, satisfiability and truth
7. Axioms and rules of inference of predicate logic
8. Deduction theorem and proving formulas of predicate logic
9. Transforming formulas into prenex normal forms
10.First-order theories and some of their models
11.Monadic logics SkS and WSkS
12.Intuitionistic, modal and temporal logics, Presburger arithmetics