Ann Math Artif Intell DOI 10.1007/s10472-012-9307-9 A propositional probabilistic logic with discrete linear time for reasoning about evidence Zoran Ognjanovi´ c · Zoran Markovi´ c · Miodrag Raškovi´ c · Dragan Doder · Aleksandar Perovi´ c © Springer Science+Business Media B.V. 2012 Abstract The aim of the paper is to present a sound, strongly complete and decidable probabilistic temporal logic that can model reasoning about evidence. The formal system developed here is actually a solution of a problem proposed by Halpern and Pucella (J Artif Intell Res 26:1–34, 2006). Keywords Strong Completeness · Decidability · Temporal logic · Probabilistic logic · Evidence Mathematics Subject Classifications (2010) 03B44 · 03B48 · 68T37 Z. Ognjanovi ´ c · Z. Markovi´ c · M. Raškovi´ c Mathematical Institute of Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia Z. Ognjanovi ´ c e-mail: zorano@mi.sanu.ac.rs Z. Markovi´ c e-mail: zoranm@mi.sanu.ac.rs M. Raškovi´ c e-mail: miodragr@mi.sanu.ac.rs D. Doder (B ) University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia e-mail: ddoder@mas.bg.ac.rs A. Perovi ´ c University of Belgrade, Faculty of Transportation and Traffic Engineering, Vojvode Stepe 305, 11000 Belgrade, Serbia e-mail: pera@sf.bg.ac.rs