Q: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Hybrid Probabilistic Programs (HPPs) are logic programs that allow the programmer to explicitly encode his knowledge of the de pendencies between events being described in the program. In this paper, we classify HPPs into three classes called H P P1, H P P2 and H P Pr, r 2: 3. For these classes, we pro vide three types of results for HPPs. First, we develop algorithms to compute the set of all ground consequences of an HPP. Then we provide algorithms and complexity results for the problems of entailment ("Given an HPP P and a query Q as input, is Q a logical con sequence of P?") and consistency ("Given an HPP Pas input, is P consistent?"). Our re sults provide a fine characterization of when polynomial algorithms exist for the above problems, and when these problems become intractable.
A:
Hybrid Probabilistic Programs: Algorithms and Complexity