COMPLETENESS THEOREM FOR A LOGIC WITH IMPRECISE AND CONDITIONAL PROBABILITIES

Zoran Ognjanovic, Zoran Markovic and Miodrag Raskovic

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 $\epsilon$, such that the probability is equal to $r-\epsilon$ (or $r+\epsilon$). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem.

Keywords: conditional probability logic; nonstandard values; Hardy field; completeness

Classification (MSC2000): 03B70; 03B45; 68T37

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