### Curricula of the course Fuzzy Logic

Lectures 2023, winter semester:

Fuzzy sets

October 5
Basic notions. System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
Record of a former lecture, mp4, pdf

October 12
Fuzzy inclusion.
Fuzzy negations. Representation theorem for fuzzy negations.
Record of a former lecture, mp4, pdf

October 19
Fuzzy complements.
Fuzzy conjunctions (triangular norms), Triangular Norms and Conorms. Scholarpedia, p.10029. Representation theorem for strict conjunctions.
Record of a former lecture, mp4, pdf

October 26
Representation theorem for nilpotent conjunctions.
Fuzzy disjunctions (triangular conorms), representation theorems. Fuzzy algebras and their properties. Examples of fuzzy intersections and unions.
Properties of fuzzy propositional and set operations.
Record of a former lecture, mp4

November 2
Fuzzy implications and biimplications.

Fuzzy logic

November 9
Syntax of classical logic: formulas, axioms, deduction, theorems.
Record of this lecture, mp4, pdf

November 16
Deduction theorem in classical logic: Record of a former lecture, mp4, pdf
Semantics of classical logic: evaluation, tautologies. Interplay of syntax and semantics of classical logic: soundness, completeness.

Basic logic: axioms, theorems, semantics.
Record of this lecture, mp4, pdf
Record of a former lecture, mp4, pdf

November 23
Deduction in basic logic.
Record of this lecture, mp4, pdf

November 30
Completeness of basic logic.
Other types of fuzzy logics: Gödel logic.
Record of this lecture, mp4, pdf

December 7
Other types of fuzzy logics: product logic (its alternative axiomatization, formulas which are tautologies of product logic but not of Gödel or basic logic), Łukasiewicz logic and its alternative axiomatization.
Rational Pavelka logic.
Record of this lecture, mp4, pdf

December 14
Compactness of logics.
Testing tautologies in Gödel and Łukasiewicz logic.
Record of this lecture, mp4, pdf

December 21
No lecture, only individual consultations (possibly online).

January 11
Fuzzy predicate logics.