Geodesic
Complex Valued Probability Logics
Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 73 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We present two complex valued probabilistic logics, LCOMP$_B$ and LCOMP$_S$, which extend classical propositional logic. In LCOMP$_B$ one can express formulas of the form $B_{z,\rho}\alpha$ meaning that the probability of $\alpha$ is in the complex ball with the center $z$ and the radius $\rho$, while in LCOMP$_S$ one can make statements of the form $S_{z,\rho}\alpha$ with the intended meaning - the probability of propositional formula $\alpha$ is in the complex square with the center $z$ and the side $2\rho$. The corresponding strongly complete axiom systems are provided. Decidability of the logics are proved by reducing the satisfiability problem for LCOMP$_B$ (LCOMP$_S$) to the problem of solving systems of quadratic (linear) inequalities.
Classification : 03B48 68T37 
@article{PIM_2014_N_S_95_109_a4,
     author = {Angelina Ili\'c Stepi\'c and Zoran Ognjanovi\'c},
     title = {Complex {Valued} {Probability} {Logics}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {73 },
     publisher = {mathdoc},
     volume = {_N_S_95},
     number = {109},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a4/}
}
TY  - JOUR
AU  - Angelina Ilić Stepić
AU  - Zoran Ognjanović
TI  - Complex Valued Probability Logics
JO  - Publications de l'Institut Mathématique
PY  - 2014
SP  - 73 
VL  - _N_S_95
IS  - 109
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a4/
LA  - en
ID  - PIM_2014_N_S_95_109_a4
ER  - 
%0 Journal Article
%A Angelina Ilić Stepić
%A Zoran Ognjanović
%T Complex Valued Probability Logics
%J Publications de l'Institut Mathématique
%D 2014
%P 73 
%V _N_S_95
%N 109
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a4/
%G en
%F PIM_2014_N_S_95_109_a4
Angelina Ilić Stepić; Zoran Ognjanović. Complex Valued Probability Logics. Publications de l'Institut Mathématique, _N_S_95 (2014) no. 109, p. 73 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_95_109_a4/