Preliminaries: Printable version of lectures: English, Czech
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
Representation theorem for fuzzy negations.
Fuzzy conjunctions (triangular norms), representation theorems.
Triangular Norms and Conorms. Scholarpedia, p.10029.
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.
Fuzzy implications and biimplications.
Classical logic: syntax, semantics, tautologies.
Classical logic: axioms, deduction, theorems, completeness.
Fuzzy logic: axioms and theorems of basic logic.
Fuzzy logic: semantics of basic logic.
Fuzzy logic: deduction in basic logic, completeness.
Other types of fuzzy logics: Gödel logic, product logic.
Other types of fuzzy logics: product logic (continued: 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.