Publications de l'Institut Mathématique, Nouvelle Série Vol. 95[109], pp. 73–86 (2014) 

COMPLEX VALUED PROBABILITY LOGICSAngelina Ilic Stepic, Zoran OgnjanovicMathematical Institute of Serbian Academy of Sciences and Arts, Belgrade, SerbiaAbstract: 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 (MSC2000): 03B48; 68T37 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 31 Mar 2014. This page was last modified: 2 Apr 2014.
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