Počet kreditů 5 Vyučováno v Winter and summer Rozsah výuky 3+2 Garant předmětu Přednášející Cvičící

This course covers basics of mathematical logic and graph theory. Syntax and sematics of propositional and predicate logic is introduced. Stress is put on understanding of the notion of semantic consequent of sets of formulas. The relationship between a formula and its model and rezolution methods (both in propositional and predicate logic) are dealt with. Further, basic notions from graph theory are introduced.

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The aim of the course is to introduce students with basis of mathematical logic and graph theory.

1. Syntax and semantics of propositional logic, formulas, truth valuation, a tautology, a contradiction, a satisfiable formula.
2. Tautological equivalence of two formulas. CNF a ndDNF, Boolean calculus.
3. Semantic consequence. The rezolution method in propositionl logic.
4. Syntax of predicate logic, a sentence, an open formula.
5. Interpretation of predicate logic, tautological equivalence of sentences and semantic consequence.
6. The rezolution method in predicate logic.
7. Applications of rezolution method. Natural deduction as an example of a sound and complete deduction system.Theorem of completness.
8. Undirected and directed graphs, basic notions. Connectivity, trees, spanning trees.
9.Rooted trees, strong connectivity ,acyclic graphs, topological sort of vertices and edges.
10. Euler graphs and their applications.
11. Hamiltonian graphs and their applications.
12. Independent sets, cliques, vertex and edge cover, Graph coloring.
13. Plannar graphs.

1. Syntax and semantics of propositional logic, formulas, truth valuation, a tautology, a contradiction, a satisfiable formula.
2. Tautological equivalence of two formulas. CNF a ndDNF, Boolean calculus.
3. Semantic consequence. The rezolution method in propositionl logic.
4. Syntax of predicate logic, a sentence, an open formula.
5. Interpretation of predicate logic, tautological equivalence of sentences and semantic consequence.
6. The rezolution method in predicate logic.
7. Applications of rezolution method. Natural deduction as an example of a sound and complete deduction system.Theorem of completness.
8. Undirected and directed graphs, basic notions. Connectivity, trees, spanning trees.
9.Rooted trees, strong connectivity ,acyclic graphs, topological sort of vertices and edges.
10. Euler graphs and their applications.
11. Hamiltonian graphs and their applications.
12. Independent sets, cliques, vertex and edge cover, Graph coloring.
13. Plannar graphs.

 Hodel, R. E.: An Introduction to Mathematical Logic, 2013, ISBN-13 978-0-486-49785-3
 Diestel, R.: Graph Theory, Springer-Verlag, 4th edition, 2010, ISBN 978-3-642-14278-9

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