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/}
}
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/