Authors: Ognjanović, Zoran 
Marković, Zoran 
Rašković, Miodrag 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Completeness theorem for a logic with imprecise and conditional probabilities
Journal: Publications de l'Institut Mathematique
Volume: 78
Issue: 92
First page: 35
Last page: 49
Issue Date: 1-Jan-2005
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM0578035O
We present a propositional probability logic which allows making formulas that speak about imprecise and conditional probabilities. A class of Kripke-like 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 ε, such that the probability is equal to r-ε (or r+ε). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem.
Keywords: Completeness | Conditional probability logic | Hardy field | Nonstandard values
Publisher: Mathematical Institute of the Serbian Academy of Sciences and Arts

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