Mathematical Logic

Type of study	Follow-up Master
Language of instruction	English
Code	460-4088/02
Abbreviation	ML
Course title	Mathematical Logic
Credits	4
Coordinating department	Department of Computer Science
Course coordinator	prof. RNDr. Marie Duží, CSc.

Subject syllabus

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

E-learning

https://www.cs.vsb.cz/duzi/MatLog-English.html

Literature

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

Advised literature

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

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