The second author has put forward a theory of incomplete interval probabilities meant to give a common framework to both interval probabilities and open-frame bodies of evidence, as obtained by application of the non-normalized (open-frame) Dempster rule. Below we re-describe this proposal and then compare two possible ways of "conditioning" based on the open-frame Dempster rule: namely, we condition the original (possibly incomplete) knowledge by pooling it with new evidence which assigns certainty to the conditioning event. The idea is trying to build a probabilistic theory which would be able to cope not only wth uncertainty and ignorance, but also with [forms of] contradictoriness, to be included into the description of a possible state of knowledge.
Keywords. Open-frame beliefs, Dempster conditioning, incomplete probabilities, interval probabilities
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Department of Mathematical Sciences