A first-order conditional probability logic with iterations

Milos Milosevic, Zoran Ognjanovic
2013 Publications de l'Institut Mathématique (Beograd)  
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 CP 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.
doi:10.2298/pim1307019m fatcat:zqedfirzpveexc7r47r6ep7nwe