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Course Unit Code | 460-4088/02 | |||||
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Number of ECTS Credits Allocated | 4 ECTS credits | |||||

Type of Course Unit * | Optional | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | ||||||

Semester when the Course Unit is delivered | Winter Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech, English | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

DUZ48 | prof. RNDr. Marie Duží, CSc. | |||||

MEN059 | Mgr. Marek Menšík, Ph.D. | |||||

Summary | ||||||

The course deals with fundamentals of mathematical logic and formal proof calculi. The following main topics are covered: propositional logic, 1st-order predicate logic, 1st-order proof calculi of Gentzen and Hilbert style and general resolution method. These methods are used in many areas of informatics in order to achieve a rigorous formalisation of intuitive theories (automatic theorem proving and deduction, artificial intelligence, and many others). | ||||||

Learning Outcomes of the Course Unit | ||||||

The goal of the subject is to provide basic principles of logical proof calculi and axiomatic theories, and their application in the area of algebras and theory of lattices. A student should be able to exactly formulate and solve particular problems of computer science and applied mathematics. | ||||||

Course Contents | ||||||

Lectures:
1. Introduction: deductively valid arguments 2. Propositional logic: language (syntax and semantics) 3. Fuzzy logic 4. Proof methods in the propositional logic, resolution method 5. Naive set-theory; relation, function, countable/uncountable sets 6. First-order predicate logic (FOL): language (syntax and semantics) 7. Semantics of FOL language (interpretation and models) 8. Semantic tableaus in FOL 9. Aristotle logic. Venn's diagrams 10. General resolution method in FOL 11. Foundations of logic programming 12. Proof calculi, Natural deduction and sequent calculus Seminars: Deductively valid arguments Propositional logic, language and semantics Resolution method in propositional logic Naive theory of sets First-order predicate logic, language and semantics Relation, function, countable and uncountable sets Semantic tableau Aristotelle logic Resolution method in FOL Logic programming Proof calculi: natural deduction Sequent calculus | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

E. Mendelson. Introduction to Mathematical Logic, (4th edition). Chapman & Hall/CRC 1997. | ||||||

1. M. Duží: Logika pro informatiky a příbuzné obory. VŠB-Technická universita Ostrava, 2012. ISBN 978-80-248-2662-2
2. M.Duží: Matematická logika. Učební texty VŠB Ostrava. http://www.cs.vsb.cz/duzi/Mat-logika.html Z. Manna: Matematická teorie programů. McGraw-Hill, 1974, SNTL Praha 1981. | ||||||

Recommended Reading: | ||||||

Brown, J.R.: Philosophy of Mathematics. Routledge, 1999.
Thayse, A.: From Standard Logic to Logic Programming, John Wiley & Sons, 1988 Nerode, Anil - Shore, Richard A. Logic for applications. New York : Springer-Verlag, 1993. Texts and Monographs in Computer Science. Richards, T.: Clausal Form Logic. An Introduction to the Logic of Computer Reasoning. Adison-Wesley, 1989. | ||||||

Švejdar, V.: Logika (neúplnost, složitost, nutnost). Academia, Praha 2002.
Sochor, A.: Klasická matematická logika. Karolinum Praha, 2001. Brown, J.R.: Philosophy of Mathematics. Routledge, 1999. Thayse, A.: From Standard Logic to Logic Programming, John Wiley & Sons, 1988 Nerode, Anil - Shore, Richard A. Logic for applications. New York : Springer-Verlag, 1993. Texts and Monographs in Computer Science. Richards, T.: Clausal Form Logic. An Introduction to the Logic of Computer Reasoning. Adison-Wesley, 1989. Bibel, W.: Deduction (Automated Logic). Academia Press, 1993. Fitting, Melvin. First order logic and automated theorem proving [1996]. 2nd ed. New York : Springer, 1996. Graduate texts in computer science. | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Seminars, Individual consultations, Tutorials | ||||||

Assesment methods and criteria | ||||||

Tasks are not Defined |