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ECTS Course Overview



Mathematical Logic

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code460-4088/02
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
DUZ48prof. RNDr. Marie Duží, CSc.
MEN059Mgr. 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