Mathematical Logic

Information for students:

On this web page you may find a lot of useful information: particular lessons, learning materials, exercises.
The page is updated regularly, which does not mean that an old info is useless.
Just opposite, I will add more and more useful info!

Logic is a joy, enjoy Logic!

Marie Duží

Lessons in English:

Lesson 1 (September 20) Introduction "What is the subject of logic?"
Lesson 2 (September 27) Propositional logic (language, semantics)
Lesson 3 (October 4) Propositional logic (normal forms, equivalent transformations, resolution method)
Lesson 4 (October 11) First-order Predicate Logic (FOL language, its syntax and intuitive semantics)
Lesson 5a Cantor's naive theory of sets; Lesson 5 (October 18) Relations, functions (mappings); countable and uncountable sets
Lesson 6 (October 25) Semantics of FOPL; models, interpretation; semantic proofs; semantic tableaus
Lesson 7 (November 1) Aristotelian Logic, Venn's diagrams
Lesson 8 (November 8) Resolution method in the First-Order Predicate Logic
Lesson 9 (November 15) Resolution method continuing
Lesson 10 (November 22) Foundations of Prolog programming
Lesson 12 (November 29)(December 6) Natural Deduction
Lesson 11 (December 6) Proof calculi; completeness vs. decidability
Lesson 14 (December 13) Gödel's incompleteness theorems

Additional material:

Lesson 13 Hilbert calculus
Lesson 15 Relational and Algebraic Theories

Proof calculi and formal theories summary
Gödel's results on completeness and incompleteness
Examples of written tests sample test 1; sample test 2; sample test 3; sample test 4
Examples of proofs

Exercises from previous years:

No 1, No 2, No 3, No 4, No 5, No 6, No 7, No 8

Exercises 2014:

Exercise 1
Resolution method: Exercise 4
Natural deduction: Exercise 5