Curricula of the course Fuzzy Logic

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.