### Curricula of the course Fuzzy Logic

**Lectures 2018:**

**Introduction**

28. 2. 2018
Basic notions. System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.

Fuzzy inclusion.

Fuzzy negations.

Representation theorem for fuzzy negations.

Fuzzy conjunctions (triangular norms),

Triangular Norms and Conorms. Scholarpedia, p.10029.

Representation theorems.

14. 3. 2018
Fuzzy disjunctions (triangular conorms), representation theorems.

Examples of fuzzy intersections and unions.

Exercises on fuzzy negations and conjunctions and their generators.

Properties of fuzzy propositional and set operations.

21. 3. 2018

Fuzzy implications and biimplications.

**Fuzzy logic**

Syntax of classical logic: formulas, axioms, deduction, theorems.

Semantics of classical logic: evaluation, tautologies.

Interplay of syntax and semantics of classical logic: soundness, completeness.

Basic logic: axioms, theorems, semantics, deduction in basic logic.

Completeness of basic logic.

Other types of fuzzy logics: Gödel logic, product logic (its alternative axiomatization, formulas which are tautologies of product logic but not of Gödel or basic logic), £ukasiewicz logic and its alternative axiomatization.

Rational Pavelka logic.