Geodesic
$L_{\bbA P}^{\text{rat}}$ logic and Completeness Theorem
Kragujevac Journal of Mathematics, Tome 32 (2009) no. 1.

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

To the list of axioms of $L_{\bbA P}$ logic is added axiom which will provide that measures on probability models have only rational values of $[0,1]$ interval. Completeness Theorem is proved. 
@article{KJM_2009_32_1_a14,
     author = {Vladimir Risti\'c},
     title = {$L_{\bbA P}^{\text{rat}}$ logic and {Completeness} {Theorem}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {149 - 156},
     publisher = {mathdoc},
     volume = {32},
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     year = {2009},
     zbl = {1224.03006},
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Vladimir Ristić. $L_{\bbA P}^{\text{rat}}$ logic and Completeness Theorem. Kragujevac Journal of Mathematics, Tome 32 (2009) no. 1. http://geodesic.mathdoc.fr/item/KJM_2009_32_1_a14/