Mathematical Logic

The course cannot be taken simultaneously with:

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

Garant předmětu:

Kateřina Trlifajová

Lecturer:

Kateřina Trlifajová

Tutor:

Kateřina Trlifajová

Supervisor:

Department of Applied Mathematics

Synopsis:

An introduction to propositional and predicate logic.

Requirements:

Elementary arithmetics, basic understanding of formal languages.

Syllabus of lectures:

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 consistenc

Syllabus of tutorials:

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.

Study Objective:

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.

Study materials:

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/

Note:

Further information:

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

Time-table for winter semester 2022/2023:

Time-table is not available yet

Time-table for summer semester 2022/2023:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor branch Security and Information Technology, in English, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 2015-2020 (compulsory course in the program)
• Bachelor branch Computer Science, in English, 2015-2020 (compulsory course in the program)
• Bachelor branch Computer Science, in English, 2015-2020 original version (compulsory course in the program)