The extent of partially resolving uncertainty in assessing coherent conditional plausibilities

Handling uncertainty and reasoning under partial knowledge are challenging tasks that require to deal with coherent assessments and their extensions. Plausibility theory is shown to rest upon the principle of partially resolving uncertainty due to Jaffray, together with a systematically optimistic behavior. This means that we allow situations in which the agent may only acquire the information that a non-impossible event occurs, without knowing which is the true state of the world. This leads to assume that a target event is plausibly true if it is compatible with the acquired piece of information. The aim of the paper is to provide coherence conditions for a conditional plausibility assessment (namely, Pl-coherence), by referring to a suitable axiomatic definition based on the Dempster's rule of conditioning. We provide different equivalent notions of Pl-coherence in terms of consistency, betting scheme, and penalization that, as a by-product, highlight different interpretations. We then specialize the Pl-coherence conditions to the subclasses of (finitely additive) conditional probabilities and (finitely maxitive) conditional possibilities.