Geodesic
A First-Order Conditional Probability Logic With Iterations
Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 19

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We investigate a first-order conditional probability logic with equ-ality, which is, up to our knowledge, the first treatise of such logic. The logic, denoted $\operatorname{LFPOIC}^{=}$, allows making statements such as: $CP_{\geq s}(\phi,\theta)$, and $CP_{\leq s}(\phi,\theta)$, with the intended meaning that the conditional probability of $\phi$ given $\theta$ is at least (at most) $s$. The corresponding syntax, semantic, and axiomatic system are introduced, and Extended completeness theorem is proven.
Classification : 03B48 03B042 03B45 
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     author = {Milo\v{s} Milo\v{s}evi\'c and Zoran Ognjanovi\'c},
     title = {A {First-Order} {Conditional} {Probability} {Logic} {With} {Iterations}},
     journal = {Publications de l'Institut Math\'ematique},
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     publisher = {mathdoc},
     volume = {_N_S_93},
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Miloš Milošević; Zoran Ognjanović. A First-Order Conditional Probability Logic With Iterations. Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 19 . http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a1/