Terminated in academic year 2014/2015

Mathematical Logic

Type of study	Follow-up Master
Language of instruction	Czech
Code	460-4004/01
Abbreviation	ML
Course title	Mathematical Logic
Credits	8
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. Proof methods in the propositional logic, resolution method
4. Naive set-theory; relation, function, countable/uncountable sets
5. First-order predicate logic (FOL): language (syntax and semantics)
6. Semantics of FOL language (interpretation and models)
7. Semantic tableaus in FOL
8. Aristotle logic. Venn's diagrams
9. General resolution method in FOL
10. Foundations of logic programming
11. Proof calculi
12. Natural deduction

Exercises:
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
Proof calculi: natural deduction

Literature

M.Duží: Mathematical logic.
http://www.cs.vsb.cz/duzi/Mat-logika.html
Z. Manna: Mathematical theory of Computer Science. McGraw-Hill, 1974.

Advised literature

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.

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