On Non-monotonic Conditional Reasoning

This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is established by introducing conditioning notions by means of formal structures that do not rely on quantitative measures. The associated conditional logic, compatible with conditional probability evaluations, is non-monotonic relative to additional evidence. Computational aspects of conditional probability logic are mentioned. The importance of this development lies on its role to provide a conceptual basis for various forms of evidence combination and on its significance to unify multi-valued and non-monotonic logics