PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 78(92), pp. 35–49 (2005) 

COMPLETENESS THEOREM FOR A LOGIC WITH IMPRECISE AND CONDITIONAL PROBABILITIESZoran Ognjanovic, Zoran Markovic and Miodrag RaskovicMatematicki institut SANU, Beograd, Serbia and MontenegroAbstract: We present a propositional probability logic which allows making formulas that speak about imprecise and conditional probabilities. A class of Kripkelike probabilistic models is defined to give semantics to probabilistic formulas. Every possible world of such a model is equipped with a probability space. The corresponding probabilities may have nonstandard values. The proposition "the probability is close to $r$" means that there is an infinitesimal $\epsilon$, such that the probability is equal to $r\epsilon$ (or $r+\epsilon$). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem. Keywords: conditional probability logic; nonstandard values; Hardy field; completeness Classification (MSC2000): 03B70; 03B45; 68T37 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 2 Mar 2006. This page was last modified: 27 Oct 2006.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
