Metamathematics of Fuzzy Logic

Prof. Petr Hàjek
Department of Computer Science
Czech Academy of Sciences, Prague

Fuzzy logic in the broad sense covers many topics concerning vagueness (fuzziness), including fuzzy control etc. Fuzzy logic in the narrow sense is a part of formal (symbolic) logic, studying systems of many-valued logic relevant for reasoning under vagueness. It turns out that these systems have a nice and deep theory analogous to that of classical logic. Theoretical investigations of fuzzy logic in this sense may well serve as foundations of applications in the frame of fuzzy logic in the broad sense, but also have impact on our understanding of human reasoning under vagueness. The course will handle the following:

• Theory of continuous t-norms as basis for truth functions of many-valued logic.
• Many-valued propositional calculi: basic, Lukasiewicz, Gödel and product logic. Completeness theorems. The same for predicate logics.
• Logical analysis of Zadeh's approximate reasoning and of fuzzy control.
• Optional: the liar paradox in fuzzy logic.
• Questions of computational complexity.