Reasoning about time and probability
Keiji Kanazawa · 1992
ly, we could define a node for each such temporal relation used in a density function. In practice, this need not be done, however. In general, adding a node for such temporal relations only adds overhead, unless we know beforehand that the information is being sought. Temporal relations are not the only type of extensions that are possible in a continuous time net. In general, we may allow, recursively, arbitrary functions of dates and ranges, and functions of those functions, etc.. For instance, it is possible to represent the lifetime of a fact as a random variable. As before, the lifetime of a fact is naturally computed easily as the difference of the dates of its beginning and end. For instance, for a fact token representing the occurrence of a traffic jam ø , we would have the nodes beg ø and end ø . The lifetime has the conditional density ø (tjbeg ø = fi; end ø = ffl) = ffi ffl\\Gammafi (t) This is true in general for all fact tokens ø . Nothing prevents the creation of nodes ...