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 bou nds on the probabilities of the consequents of the defaults. Using a knowle dge base of default rules which are considered to be constraints on a proba bility distribution, the result of applying the rules of P gives us new con straints that were implicit in the knowledge base and their associated lowe r 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 a nd the kind of proofs that it can generate.