Mathematical Fuzzy Logic - ALGV00041

• Title: Mathematical Fuzzy Logic
• Guaranteed by: Department of Logic (21-KLOG)
• Faculty: Faculty of Arts
• Actual: from 2024
• Semester: summer
• Points: 0
• E-Credits: 5
• Examination process: summer s.:
• Hours per week, examination: summer s.:2/0, Ex [HT]
• Capacity: unlimited / unknown (15)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Additional information: http://logika.ff.cuni.cz/predmety/ALGV00041
• Note: course can be enrolled in outside the study plan; enabled for web enrollment
• Guarantor: Mgr. Marta Bílková, Ph.D.; Chun-Yu Lin
• Teacher(s): Chun-Yu Lin

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.

Last update: Verner Jonathan, Mgr., Ph.D. (06.06.2013)

Literature

Course notes will be distributed after each class. There are several references for this course :

• Petr Hajek, ”What is mathematical fuzzy logic.” Fuzzy sets and systems 157.5 (2006): 597-603.

• Petr Cintula, Petr H ́ajek and Carles Noguera eds.,Handbook of Mathematical Fuzzy Logic. Studies in Logic, vols. 37-38, College Publications, London, 2011.

• Petr Cintula, Christian Fermu ̈ller and Carles Noguera eds., Handbook of Mathematical Fuzzy Logic. Studies in Logic, vol. 58, College Publications, London, 2015.

• Petr Hajek. Metamathematics of fuzzy logic. Trends in logic, vol. 4. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1998, viii + 297 pp.

• George MetCalfe, Nicola Olivetti, and Dov M. Gabbay. Proof theory for fuzzy logics. Vol. 36. Springer Science & Business Media, 2008.

• Petr Hajek and Zuzana Hanikova, ”A set theory within fuzzy logic,” Proceedings 31st IEEE International Symposium on Multiple- Valued Logic, Warsaw, Poland, 2001, pp. 319-323.

Last update: Stejskalová Šárka, Mgr., Ph.D. (24.01.2023)

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

Last update: Stejskalová Šárka, Mgr., Ph.D. (24.01.2023)