A first-order conditional probability logic with iterations

Abstract

We investigate a first-order conditional probability logic with equality, which is, up to our knowledge, the first treatise of such logic. The logic, denoted LFPOIC=, allows making statements such as: CP≥s((φ, θ), and CP6≤s((φ, θ), with the intended meaning that the conditional probability of φ given θ is at least (at most) s. The corresponding syntax, semantic, and axiomatic system are introduced, and Extended completeness theorem is proven.