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On Proofs in System P

This paper investigates how the rules of System P might be used in order to construct proofs for default consequences which take into account the bounds on the probabilities of the consequents of the defaults. Using a knowledge base of default rules which are considered to be constraints on a probability distribution, the result of applying the rules of P gives us new constraints that were implicit in the knowledge base and their associated lower bounds. The paper defines a proof system for such constraints, shows that it is sound, and then discusses at length the completeness of the system and the kind of proofs that it can generate.