Geodesic
A Double Negation Operator in Logic $N^*$
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 68-83

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

An axiomatization of double Routley negation operator as a necessity operator in logic $N^*$ is obtained. Logic $N^{\sharp}$ describing the behavior of double Routley negation operator is introduced, its Kripke semantics is defined, completeness wrt to this semantics is proved as well as its finite approximation property and decidability. Constructive properties of logics $N^*$ and $N^{\sharp}$ are compared.
Keywords: modal logic, intuitionistic logic, Kripke semantics, Routley negation, necessity, constructive properties. 
@article{VNGU_2013_13_4_a4,
     author = {S. A. Drobyshevich},
     title = {A {Double} {Negation} {Operator} in {Logic} $N^*$},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {68--83},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a4/}
}
TY  - JOUR
AU  - S. A. Drobyshevich
TI  - A Double Negation Operator in Logic $N^*$
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2013
SP  - 68
EP  - 83
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a4/
LA  - ru
ID  - VNGU_2013_13_4_a4
ER  - 
%0 Journal Article
%A S. A. Drobyshevich
%T A Double Negation Operator in Logic $N^*$
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2013
%P 68-83
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a4/
%G ru
%F VNGU_2013_13_4_a4
S. A. Drobyshevich. A Double Negation Operator in Logic $N^*$. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 4, pp. 68-83. http://geodesic.mathdoc.fr/item/VNGU_2013_13_4_a4/