Authors: Ognjanović, Zoran 
Ikodinović, Nebojša
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A logic with higher order conditional probabilities
Journal: Publications de l'Institut Mathematique
Volume: 96
First page: 141
Last page: 154
Issue Date: 1-Jan-2007
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM0796141O
Abstract: 
We investigate probability logic with the conditional probability operators. This logic, denoted LCP, allows making statements such as: P≥sα, CP≥s,(α β), CP ≤0(α β) with the intended meaning "the probability of α is at least s", "the conditional probability of α given β is at least s", "the conditional probability of α given β at most 0". A possible-world 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(α β) = P(β)/P(αΛβ), P(β) > 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.
Publisher: Mathematical Institute of the SASA

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