Mathematical Logic

Předmět nesmí být zapsán současně s:

Discrete Mathematics and Logic (BIE-DML.21)
Mathematical Logic (BIE-LOG.21)

Garant předmětu:

Kateřina Trlifajová

Přednášející:

Kateřina Trlifajová

Cvičící:

Kateřina Trlifajová

Předmět zajišťuje:

katedra aplikované matematiky

Anotace:

An introduction to propositional and predicate logic.

Požadavky:

Elementary arithmetics, basic understanding of formal languages.

Osnova přednášek:

1. Introduction. Propositional logic. Truth tables.

2. Satisfiability, tautology, contradiction. Logical equivalence. Basic laws of propositional logic. Complete systems of connectives.

3. Logical consequence. Disjunctive and conjunctive normal form. Full normal forms.

4. Theory and its logical consequences. Semantic trees. Resolution method.

5. Karnaugh maps. Compactness theorem. P vs. NP problem.

6. Predicate logic. Language, terms, formulas. Formalization of natural language.

7. Interpretation of the language. Logical truth, satisfiability, contradiction. Logical consequence and equivalence.

8. Semantic trees. Basic laws of predicate logic. The problem of decidability.

9. Prenex normal forms. Theories and its models. Isomorphism and elementary equivalence.

10. Examples of the first-order theories.

11. Boolean algebra. Models of Boolean algebra.

12. The isomorphism theorem. Correctness, completeness and consistency.

Osnova cvičení:

1. Formalization. Truth tables.

2. Satisfiability, tautology, contradiction. Logical equivalence. Universal systems of connectives.

3. Disjunctive and conjunctive normal forms. Full normal forms.

4. Logical consequence. Semantic trees. Satisfiable theories.

5. Resolution method. Karnaugh maps.

6. Predicate logic. Language, terms, formulas.

7. Interpretations. Logical truth, satisfiability, contradiction.

8. Logical consequence and equivalence.

9. Semantic trees. Logical consequence of a theory.

10. Theories and their models, equivalence, ordering, group theory.

11. Boolean algebras.

12. Repetition.

Cíle studia:

Predicate logic is a formal language of mathematics. The goal of a course is to learn students to formalize their thoughts and assertions in predicate logic, to deal correctly with formulas, theories and their models.

Studijní materiály:

Mendelson, E., Introduction to Mathematical Logic, Chapman and Hall, 1997.

Bergmann, M., Moor, J., Nelson, The Logic Book, McGraw-Hill, 2008.

Copi, I.M., Symbolic Logic, The Macmilian Company, London, 1967.

Smullyan, R., What is the Name of this Book?

Demlová, M., Mathematical Logic, ČVUT, Praha: Kernberg Publishing, 2008.

Starý, J., lecture notes (in progress).

Smith, N.J.J., Logic: The Laws of Truth, Princeton University Press, 2012.

Smith, N.J.J., Cusbert J., Logic: The Drill, http://www-personal.usyd.edu.au/~njjsmith/lawsoftruth/

Poznámka:

Information about the course and courseware are available at https://courses.fit.cvut.cz/BIE-MLO/

Další informace:

https://courses.fit.cvut.cz/BIE-MLO/

Rozvrh na zimní semestr 2022/2023:

Rozvrh není připraven

Rozvrh na letní semestr 2022/2023:

Rozvrh není připraven

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