# Subject description - B0B01LGR

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
Roles:PV, P Extent of teaching:3P+2S
Department:13101 Language of teaching:CS
Guarantors:Demlová M. Completion:Z,ZK
Lecturers:Gollová A. Credits:5
Tutors:Dostál M., Gollová A. Semester:Z,L

Anotation:

This course covers basics of mathematical logic and graph theory. Syntax and semantics of propositional and predicate logic are introduced. The importance of the notion of semantic consequence andof the relationship between a formula and its model is stressed, Further, basic notions from graph theory are introduced.

Study targets:

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

Content:

 1 Syntax and semantics of propositional logic, formulas, truth valuation, a tautology, a contradiction, a satisfiable formula. 2 Tautological equivalence of two formulas. CNF and DNF, 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.

Course outlines:

 1 Syntax and semantics of propositional logic, formulas, truth valuation, a tautology, a contradiction, a satisfyable formula. 2 Tautological equivalence of two formulas. CNF and DNF, Boolean calculus. 3 Semantic consequence. The resolution method in propositional 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.

Exercises outline:

In the exercise classes students solve theoretical and algorithmic problems from logic and graph theory. Students strenghten and extend their knowledge and skills obtained from the lectures.

Literature:

 [1] M. Huth, M. Ryan: Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press, 2004. [2] J. A. Bondy, U. S. R. Murty: Graph theory with applications. Elsevier Science Ltd/North-Holland, 1976.

Requirements:

None.

Webpage:

http://math.feld.cvut.cz/dostamat/teaching/lgr1920.htm http://math.feld.cvut.cz/gollova/lgr.html

Keywords:

Propositional logic, predicate logic, semantic consequence, basic notions of graph theory, graph algorithms.

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPOI_BO_2018 Common courses P 2 BPOI4_2018 Computer Games and Graphics P 2 BPOI3_2018 Software P 2 BPOI2_2018 Internet things P 2 BPOI1_2018 Artificial Intelligence and Computer Science P 2 BPOI1_2016 Computer and Information Science P 2 BPOI_BO_2016 Common courses P 2 BPOI4_2016 Computer Games and Graphics P 2 BPOI3_2016 Software P 2 BPOI2_2016 Internet things P 2 BPBIO_2018 Common courses PV 5 BPKYR_2016 Common courses P 1

 Page updated 4.8.2020 17:51:40, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)