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},