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),
Triangular Norms and Conorms. Scholarpedia, p.10029.
11.3.2014 Lecture cancelled because of a conference.
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.
For the following topics, see Lectures on classical and fuzzy logics.; Czech version.
Classical logic: syntax, axioms, deduction, theorems.
Classical logic: semantics, tautologies, completeness.
Fuzzy logic: axioms of basic logic.
Fuzzy logic: theorems of basic logic, semantics of basic logic, deduction in basic logic, completeness.
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.
Motivation of quantum probability in real-world situations
Models of probability including quantum uncertainty: classes of subsets, generalized probability spaces.
13.5.2014 Orthomodular lattices as a generalization of Boolean algebras.