Lectures 2025, summer semester:
February 19
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
February 26
Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.
Record of a former lecture,
mp4,
pdf
Record of an older lecture,
mp4,
pdf
March 5
Fuzzy complements.
Fuzzy conjunctions (triangular norms),
Triangular Norms and Conorms. Scholarpedia, p.10029.
Record of a former lecture,
mp4,
pdf
Record of an older lecture,
mp4,
pdf
March 12
Representation theorem for strict conjunctions.
Representation theorem for nilpotent conjunctions.
Examples of fuzzy intersections.
Fuzzy disjunctions (triangular conorms).
Record of a former lecture,
mp4,
pdf
Record of an older lecture,
mp4
March 19
Representation theorems for fuzzy disjunctions.
Examples of fuzzy unions.
Properties of fuzzy propositional and set operations.
March 26
Fuzzy implications and biimplications.
Record of a former lecture,
mp4,
pdf
Probability of fuzzy events, old related lecture, new text under construction
Alternative definition of a sigma-algebra and probability on it.
April 2
Comparison to the Kolmogorov axiomatization of probability.
Fuzzifications of sigma-algebras.
Record of an older lecture,
mp4,
pdf
April 9
Properties of fuzzy sigma-algebras.
Motivation and definitions of probabilities of fuzzy events.
Properties and characterizations of probabilities on Gödel and Łukasiewicz tribes.
Record of an older lecture,
mp4,
pdf
April 16
Properties and characterizations of probabilities on product, Frank, and other tribes.
Syntax of classical logic: formulas, axioms, deduction, theorems.
Record of a former lecture,
mp4,
pdf
April 23
Deduction theorem in classical logic:
Record of an older lecture,
mp4,
pdf
Semantics of classical logic: evaluation, tautologies. Interplay of syntax and semantics of classical logic: soundness, completeness.
April 30
Basic logic: axioms, theorems, semantics.
Record of a former lecture,
mp4,
pdf
Record of an older lecture,
mp4,
pdf
Deduction in basic logic.
Record of a former lecture,
mp4,
pdf
May 7
Completeness of basic logic.
Other types of fuzzy logics: Gödel logic.
Record of a former lecture,
mp4,
pdf
May 14 Rector's Day; lecture cancelled.
May 21
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.
Record of a former lecture,
mp4,
pdf
Testing tautologies in Gödel and Łukasiewicz logic.
Record of a former lecture,
mp4,
pdf