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Completeness Theorem for a Logic With Imprecise and Conditional Probabilities
Publications de l'Institut Mathématique, _N_S_78 (2005) no. 92, p. 35

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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 $\epsilon$, such that the probability is equal to $r-\epsilon$ (or $r+\epsilon$). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem.
DOI : 10.2298/PIM0578035O
Classification : 03B70 03B45 68T37
Keywords: conditional probability logic, nonstandard values, Hardy field, completeness 
Zoran Ognjanović; Zoran Marković; Miodrag Rašković. Completeness Theorem for a Logic With Imprecise and Conditional Probabilities. Publications de l'Institut Mathématique, _N_S_78 (2005) no. 92, p. 35 . doi: 10.2298/PIM0578035O
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     title = {Completeness {Theorem} for a {Logic} {With} {Imprecise} and {Conditional} {Probabilities}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {35 },
     year = {2005},
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