Foundations of Fuzzy Logic.

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course contains a presentation of mathematical fuzzy logic (propositional and predicate) as a formal many-valued logical system, problems of axiomatizability, its semantics based on the notion f a continuous t-norm.

Requirements:

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

Syllabus of lectures:

Continuous t-norm and its residuum as the standard semantics of conjunction and mplication, residuated lattices, BL-algebras, 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 many-valued (formal) propositional and predicate logic with its axioms, formal proofs and well-defined 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) 597-603

Recommended references:

P.Cintula, F. Esteva, J.Gispert, L.Godo, C. Noguera: Distinguished algebraic semantcs for t-norm based fuzzy logics. Annals of pure and appl. logic

160 (2009) 53-81

F. Esteva, J.Gispert, L.Godo, F. Montagna, C. Noguera:

Adding truth constants to logics of a continuous t-norm: axiomatization and completeness results. Fuzzy sets and systems 158 (2007)597-618

F. Esteva, L. Godo: Monoidal t-norm based logic: towards to a logic for left-continuoujs t-norms.Fuzzy sets and systems 124 (2001)271-288

P. Hájek: Fuzzy logics with non-commutative conjunctions. J. of logic and computation 13 (2003) 469-479

P. Hájek: Arithmetical complexity of fuzzy predicate logics- a survey. Soft computing 9 (2005) 935-941

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: