Carles Noguera: Mathematical Fuzzy Logic 1 - A logical framework for graded reasoning
In this talk we introduce the general notion of graded predicates, distinguish several kinds of such predicates, and present mathematical fuzzy logic as a formal tool to deal with reasoning in their presence.
Libor Behounek: Mathematical Fuzzy Logic 2 - First-order fuzzy logic
The talk will present the apparatus of first-order fuzzy logic and its main metamathematical properties. Its stregth will be illustrated on two first-order theories of fuzzy sets: Hajek-Hanikova ZFC-style theory and Cantor-Lukasiewicz theory based on naive comprehension.
Petr Cintula: Mathematical Fuzzy Logic 3 - Foundations of fuzzy mathematics
We will present Fuzzy Class Theory, a foundational theory built over suitable fuzzy logic, which provides logical basis for the study of mathematics of fuzzy sets. We will illustrate the power of the theory with two particular examples from the theory of fuzzy relations: description of fuzzy partitions and Valerde representation theorem.
San Ming Wang：Mathematical Fuzzy Logic 4-The logic of pseudo-uninorms and their residua
Our method for density elimination is generalized to the non-commutative substructural logic GpsUL∗. Then the standard completeness of HpsUL∗ follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that HpsUL is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis.