Lectures 2014:
Preliminaries: Printable version of lectures: English, Czech
18.2.2014
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
25.2.2014
Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.
4.3.2014
Fuzzy conjunctions (triangular norms),
Triangular Norms and Conorms. Scholarpedia, p.10029.
Representation theorems.
11.3.2014 Lecture cancelled because of a conference.
18.3.2014
Fuzzy disjunctions (triangular conorms), representation theorems.
Examples of fuzzy intersections and unions.
Exercises on fuzzy negations and conjunctions and their generators.
25.3.2014
Properties of fuzzy propositional and set operations.
Fuzzy implications and biimplications.
1.4.2014
For the following topics, see Lectures on classical and fuzzy logics.; Czech version.
Classical logic: syntax, axioms, deduction, theorems.
8.4.2014
Classical logic: semantics, tautologies, completeness.
Fuzzy logic: axioms of basic logic.
15.4.2014
Fuzzy logic: theorems of basic logic, semantics of basic logic, deduction in basic logic, completeness.
22.4.2014
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.
29.4.2014
Rational Pavelka logic.
Quantum logic:
6.5.2014
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.
20.5.2014