**Lectures 2022:**

**Quantum logics**

September 21: Basic principles of the classical and non-classical (quantum) measure theory, Banach–Tarski paradox. Countable additivity of measures.

October 5: Set-representable models of quantum events and random variables.

October 12: Non set-representable models of quantum events and observables (pp. 1-25 and 45-58).

October 19: Hilbert lattices and states (probability measures) on them, Kochen-Specker Theorem and its improvements.,
Record of the lecture,
mp4,
pdf

**Fuzzy sets**

October 26: Basic notions. System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.

November 2: Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.

November 9: Fuzzy conjunctions (triangular norms),
Triangular Norms and Conorms. Scholarpedia, p.10029.
Representation theorems.
Record of the lecture,
mp4,
pdf

November 16: Fuzzy disjunctions (triangular conorms), representation theorems. Fuzzy algebras and their properties.
Examples of fuzzy intersections and unions.
Record of the lecture,
mp4,
pdf

November 23: Exercises on fuzzy negations and conjunctions and their generators.
Properties of fuzzy propositional and set operations.
Fuzzy implications and biimplications.

**Fuzzy logic**

November 30: Syntax of classical logic: formulas, axioms, deduction, theorems.

December 7:
Deduction theorem in classical logic:
Record of the lecture,
mp4,
pdf

December 14: 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.
Record of the lecture,
mp4,
pdf

January 11: Deduction in basic logic.
Completeness of basic logic.

January 18: 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.

January 25: Checking tautologies in Gödel and £ukasiewicz logic.
Rational Pavelka logic.