Lectures 2016:
Introduction
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.
Fuzzy conjunctions (triangular norms),
Triangular Norms and Conorms. Scholarpedia, p.10029.
Representation theorems.
Fuzzy disjunctions (triangular conorms), representation theorems.
Examples of fuzzy intersections and unions.
Exercises on fuzzy negations and conjunctions and their generators.
Properties of fuzzy propositional and set operations.
Fuzzy implications and biimplications.
Fuzzy logic
30.3. Syntax of classical logic: formulas.
Semantics of classical logic: evaluation, tautologies.
Syntax of classical logic 2: axioms, deduction, theorems.
Interplay of syntax and semantics of classical logic: soundness, completeness.
4.5. Basic logic: axioms, theorems, semantics, deduction in basic logic.
11.5. Completeness of basic logic.
18.5. 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.
1.6. Rational Pavelka logic. (the last lecture)