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

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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 
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     author = {Angelina Ili\'c Stepi\'c and Zoran Ognjanovi\'c},
     title = {Complex {Valued} {Probability} {Logics}},
     journal = {Publications de l'Institut Math\'ematique},
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     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/}
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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/