Lectures 2025, winter semester:
September 22
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
September 29
Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.
Record of a former lecture,
mp4,
pdf
Record of an older lecture,
mp4,
pdf
October 6
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
October 13
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
October 20
Representation theorems for fuzzy disjunctions.
Examples of fuzzy unions.
Properties of fuzzy propositional and set operations.
Definition and basic properties of fuzzy implications.
October 27
Fuzzy implications and biimplications.
Fuzzy logic
Syntax of classical logic: formulas, axioms, deduction, theorems.
Record of a former lecture,
mp4,
pdf
November 3
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.
November 10
Basic logic: axioms, theorems, semantics.
Record of a former lecture,
mp4,
pdf
Record of an older lecture,
mp4,
pdf
November 24
Deduction in basic logic.
Record of a former lecture,
mp4,
pdf
Completeness of basic logic.
Other types of fuzzy logics: Gödel logic.
Record of a former lecture,
mp4,
pdf
December 1
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.
December 8
Quantum logic
A brief introduction to quantum logic.
Record of this lecture,
mp4,
pdf