Geodesic
An extension of the probability logic $LPP_2$
Kragujevac Journal of Mathematics, Tome 33 (2010) no. 1

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In this paper we present a probability logic which allows Boolean combinations of formulas of the form of $a_1w(\varphi_1)+\cdots+a_kw(\varphi_k)\geq c$, where $\varphi_1,\ldots,\varphi_k$ are propositional formulas, $a_1,\ldots,a_k,c$ are rational numbers. The logic with such syntax was introduced in [1]. We present axiomatic system along with the ideas from [2, 3] and prove extended completeness, instead of simple completeness shown in [1]. 
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     author = {Tatjana Stojanovi\'c and Ana Kaplarevi\'c-Mali\v{s}i\'c and Zoran Ognjanovi\'c},
     title = {An extension of the probability logic $LPP_2$},
     journal = {Kragujevac Journal of Mathematics},
     pages = {45 - 62},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2010},
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Tatjana Stojanović; Ana Kaplarević-Mališić; Zoran Ognjanović. An extension of the probability logic $LPP_2$. Kragujevac Journal of Mathematics, Tome 33 (2010) no. 1. http://geodesic.mathdoc.fr/item/KJM_2010_33_1_a3/