A Logic with Kolmogorov Style Conditional Probabilities ⋆

Abstract

Abstract. In this paper we investigate a probability logic with conditional probability operators. The logic (denoted LP P) allows making statements such as CP≥s(α | β), with the intended meaning ”the conditional probability of α given β is at least s”. Conditional probabilities are P (α∧β) P (β) defined in the usual Kolmogorv style: P (α | β) = , P (β)> 0. A possible-world approach is used to give semantics to probability formulas. An infinitary axiomatic system for our logic is given and the corresponding strong completeness theorem is proved. It is proved that the logic is decidable.