Foundations of probabilistic inference with uncertain evidence

The extension is different from earlier probabilistic approaches such as Jeffrey's rule of probability kinematics and Cheeseman's rule of distributed meaning, by introducing two forms of evidential meaning representation are presented, for which non-probabilistic analogues are found in theories such as Evidence Theory and Possibility Theory. By viewing the statement of evidential meaning as a separate step in the inference process, a clear probabilistic interpretation can be given to these forms of representation, and a generalization of Bayes Theorem can be derived. This generalized rule of inference allows uncertain evidence to be incorporated into probabilistic inference procedures.