@TechReport{Horcik-TR-2003-05, IS = { zkontrolovano 23 Apr 2003 }, UPDATE = { 2003-02-19 }, author = {Hor{\v c}{\'\i }k, Rostislav}, title = {Mathematical Properties of Many-valued Logics -- PhD Thesis Proposal}, institution = {Center for Machine Perception, K333 FEE Czech Technical University}, address = {Prague, Czech Republic}, year = {2003}, month = {February}, type = {Research Report}, number = {{CTU--CMP--2003--05}}, issn = {1213-2365}, pages = {25}, figures = {1}, authorship = {100}, psurl = {[Horcik-TR-2003-05.ps.gz]}, project = {MSM 212300013, GACR 201/02/1540, CTU 0208613, CEEPUS SK-042}, annote = {This thesis proposal is concerned with propositional fuzzy logics. At the beginning we give a survey of R-fuzzy logics which are based on a continuous t-norm and its residuum. Then our results in this area are presented. Firstly we define a validation set of a formula in a fuzzy logic as the set of all truth values which this formula may achieve. Then we summarize characterizations of validation sets in R-fuzzy logics. Secondly we introduce PL logic which is an extension of {\L}ukasiewicz R-fuzzy logic by the product connective. Finally we discuss possible directions of future work on the thesis.}, keywords = {fuzzy logic, many-valued logic, Lukasiewicz logic, MV-algebras, product MV-algebras}, }