Geodesic
Graded modal operators and fixed points
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 1, pp. 70-76

Voir la notice de l'article provenant de la source Math-Net.Ru

There is the well-known Fixed Point Theorem in the theory of modal logics. In the article this theorem is generalized from monomodal case to graded modalities. The following theorem is proved Theorem. For any graded modalized operator $F_\varphi$, there is unique fixed point of the operator $F_\varphi$ in every strictly partially ordered model with the ascending chain condition and there is a graded formula $\omega$, which defines the fixed point in every such model. The formula $\omega$ contains only those graded modalities, which are contained in $\varphi$. 
@article{VNGU_2006_6_1_a4,
     author = {S. I. Mardaev},
     title = {Graded modal operators and fixed points},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {70--76},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2006_6_1_a4/}
}
TY  - JOUR
AU  - S. I. Mardaev
TI  - Graded modal operators and fixed points
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2006
SP  - 70
EP  - 76
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VNGU_2006_6_1_a4/
LA  - ru
ID  - VNGU_2006_6_1_a4
ER  - 
%0 Journal Article
%A S. I. Mardaev
%T Graded modal operators and fixed points
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2006
%P 70-76
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VNGU_2006_6_1_a4/
%G ru
%F VNGU_2006_6_1_a4
S. I. Mardaev. Graded modal operators and fixed points. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 1, pp. 70-76. http://geodesic.mathdoc.fr/item/VNGU_2006_6_1_a4/