Publications de l'Institut Mathématique, Nouvelle Série Vol. 82(96), pp. 141–154 (2007) 

A LOGIC WITH HIGHER ORDER CONDITIONAL PROBABILITIESZoran Ognjanovic and Nebojsa IkodinovicMatematicki institut, Kneza Mihaila 36, 11000 Beograd p.p. 367, Serbia and Prirodnomatematicki fakultet, 34000 Kragujevac, SerbiaAbstract: We investigate probability logic with the conditional probability operators. This logic, denoted $LCP$, allows making statements such as: $P_{\geq s}\alpha$, $CP_{\geq s}(\alpha\mid\beta)$, $CP_{\leq 0}(\alpha\mid\beta)$ with the intended meaning "the probability of $\alpha$ is at least $s$", "the conditional probability of $\alpha$ given $\beta$ is at least $s$", "the conditional probability of $\alpha$ given $\beta$ at most $0$". A possibleworld approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: $P(\alpha\mid\beta)=\frac{P(\alpha\wedge\beta)}{P(\beta)}$, $P(\beta)>0$, by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. Infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved. Classification (MSC2000): 68T37; 68T27; 03B48; 03B70 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 20 Feb 2008. This page was last modified: 26 Feb 2008.
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