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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Mathematical Logic

The course is not on the list Without time-table
Code Completion Credits Range Language
BIE-MLO Z,ZK 5 2P+2C English

It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has already completed the course BIE-DML.21 (mutually exclusive courses).

It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has already completed the course BIE-LOG.21 (mutually exclusive courses).

It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has previously completed the course BIE-DML.21 (mutually exclusive courses).

It is not possible to register for the course BIE-MLO if the student is concurrently registered for or has previously completed the course BIE-LOG.21 (mutually exclusive courses).

Garant předmětu:
Lecturer:
Tutor:
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/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-04-11
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