Foundations of Fuzzy Logic.
Code  Completion  Credits  Range 

D01ZFL  ZK 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The course contains a presentation of mathematical fuzzy logic (propositional and predicate) as a formal manyvalued logical system, problems of axiomatizability, its semantics based on the notion f a continuous tnorm.
 Requirements:

knowledge of basic logical notions (conjunction etc.), ability of mathematical reasoning.
 Syllabus of lectures:

Continuous tnorm and its residuum as the standard semantics of conjunction and mplication, residuated lattices, BLalgebras, general semantics. The basic propositional fuzzy logic BL, three stronger logics: Lukasiewicz, Gödel and product logic. Examples of formal proofs. Problems of decidability.
Corresponding predicate logics, double semantics. Examples of formal proofs. Problems of decidability.
 Syllabus of tutorials:
 Study Objective:

to help the student to replace the usual understanding of fuzzy logic (as arbitrary use of fuzzy sets) by the deeper treatment of fuzzy logic as a particular manyvalued (formal) propositional and predicate logic with its axioms, formal proofs and welldefined sémantice. Clarify the relation of fuzzy logic to vagueness, probability and modal logic.
 Study materials:

Key references:
P. Hájek: Metamathematics of fuzzy logic. Kluwer 1998, 299 stran
OR AT LEAST
P. Hájek: What is mathematical fuzzy logic. Fuzzy sets and systems 157 (2006) 597603
Recommended references:
P.Cintula, F. Esteva, J.Gispert, L.Godo, C. Noguera: Distinguished algebraic semantcs for tnorm based fuzzy logics. Annals of pure and appl. logic
160 (2009) 5381
F. Esteva, J.Gispert, L.Godo, F. Montagna, C. Noguera:
Adding truth constants to logics of a continuous tnorm: axiomatization and completeness results. Fuzzy sets and systems 158 (2007)597618
F. Esteva, L. Godo: Monoidal tnorm based logic: towards to a logic for leftcontinuoujs tnorms.Fuzzy sets and systems 124 (2001)271288
P. Hájek: Fuzzy logics with noncommutative conjunctions. J. of logic and computation 13 (2003) 469479
P. Hájek: Arithmetical complexity of fuzzy predicate logics a survey. Soft computing 9 (2005) 935941
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: