Syllabus
This course will cover the following topics
• Lukasiewicz Logic, G ̈o del Logic, Product Logic, Monoidal t- norm logic, BL
• Predicate Fuzzy Logics
• Model theroy for MFL
• Proof theory for MFL
• Set theory within MFL
• Complexity of MFL
Annotation
Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, mathematical fuzzy logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth theories and challenging problems, thus continuing to attract an ever increasing number of researchers.
The goal of this course is to provide an up-to-date introduction to MFL. Starting with the motivations and historical origins of the area, we present MFL, its main methods, and its core agenda. In particular, we focus on some of its better known logic systems (\L ukasiewicz and G\"odel--Dummett logics, HL, MTL) and present a general theory of fuzzy logics. Finally, we give an overview of several currently active lines of research in the development and application of fuzzy logics.