Probabilistic Abduction in a Fuzzy Logic Framework

We study the problem of explaining observations about the probabilities of events such as ‘it rains 20% of the time’, ‘rain and snow are equally likely’, etc. We explain these statements with a probability distribution or a statement about probabilities of (other) events that are consistent with our knowledge and entail the observation. We formalise this problem in a fuzzy probabilistic logic FP. We define and motivate the notions of abduction problems and their solutions. We analyse the complexity of solution recognition and existence for a given abduction problem in FP for the case of full language and its disjunctive-clause fragments. We also obtain a translation of classical probabilistic abduction (finding the most likely explanation of a given event) to FP.