XEP33FLO Fuzzy Logic

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In the summer semester 2025/26, the course will be held in English or in Czech, depending on the students subscribed. The time will be decided by a poll when the subscriptions are (almost) complete.
The curricula will contain a general introduction to fuzzy sets (about 5 weeks), followed by lectures on specific topics chosen by you from several options. Please, read the previous curricula and prepare your comments.

Basic notions. 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 complements. Fuzzy conjunctions (triangular norms).
Representation theorem for strict conjunctions. Representation theorem for nilpotent conjunctions. Fuzzy disjunctions (triangular conorms), representation theorems. Fuzzy algebras and their properties. Examples of fuzzy intersections and unions.
Fuzzy disjunctions, representation theorems. Examples of fuzzy intersections and unions. Properties of fuzzy propositional and set operations.
Fuzzy implications and biimplications.

Syntax of classical logic: formulas, axioms, deduction, theorems.
Deduction theorem in classical logic.
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.
Completeness of basic logic.
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), Łukasiewicz logic and its alternative axiomatization.
Rational Pavelka logic.
Compactness of logics.
Testing tautologies in Gödel and Łukasiewicz logic.