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Propositional logic, normal forms of propositional formulas,
predicate logic of first order,
prenex forms of formulas, completness theorems for
propositional and predicate logic,
models of first-order theories. The limits of formal
method, Goedel's theorems
Last update: G_I (05.06.2003)
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To present elements of propositional and predicate logic. Last update: Gregor Petr, doc. Mgr., Ph.D. (09.10.2017)
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The form of study verification is a course credit and an exam. Obtaining the course credit is a necessary condition for taking the exam, except in the case of early exam dates. Course credit is granted by the instructors of the individual tutorial groups on the basis of the point-based evaluation of the credit tests, or additionally a project, homework assignments, participation, etc. Each credit test may be retaken once. The nature of the other assessed components does not allow for a retake. Last update: Bulín Jakub, RNDr., Ph.D. (25.07.2026)
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A. Nerode, R. A. Shore, Logic for Applications, Springer, 2. vydání, 1997.
P. Pudlák, Logical Foundations of Mathematics and Computational Complexity - A Gentle Introduction, Springer, 2013. V. Švejdar, Logic: Incompleteness, Complexity, and Necessity, Academia, Praha, 2002. W. Hodges, Shorter Model Theory, Cambridge University Press, 1997. W. Rautenberg, A concise introduction to mathematical logic, Springer, 2009. Literature in Czech only: A. Sochor, Klasická matematická logika, Univerzita Karlova v Praze - Karolinum, 2001.J. Mlček, Výroková a predikátová logika, el. skripta, 2012. P. Štěpánek, Meze formální metody, el. skripta, 2000. Last update: Bulín Jakub, RNDr., Ph.D. (18.11.2019)
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The exam is oral with written preparation. Requirements for the exam correspond to the syllabus of the course in the extent that has been covered in the lecture. Last update: Gregor Petr, doc. Mgr., Ph.D. (20.09.2022)
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Propositional logic: elementary syntax and semantics, normal forms of propositional formulas, problem of satisfiability. Tableau method and resolution in propositional logic. Completeness theorem for propositional logic.
Predicate (first-order) logic: elementary syntax and semantics, prenex normal form of formulas, properties and models of first-order theories. Tableau method and resolution for predicate logic. Skolem's theorem, Herbrand's theorem. Completeness theorem for predicate logic, compactness.
Criteria for completeness, decidability. Limits of formal methods, Goedel's theorems. Last update: Gregor Petr, doc. Mgr., Ph.D. (09.10.2017)
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