|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||Abstract:||
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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