On the Reconstruction of Proofs in Distributed Theorem Proving: a Modied Clause-Diusion Method
Maria Paola Bonacina · 1996
Proof reconstruction is the operation of extracting the computed proof from the trace of a theorem-proving run. We study the problem of proof reconstruction in distributed theorem proving: because of the distributed nature of the derivation and especially because of deletions of clauses by contraction, it may happen that a deductive process generates the empty clause, but does not have all the necessary information to reconstruct the proof. We analyze this problem and we present a method for distributed theorem proving, called Modie d Clause-Diusion , which guarantees that the deductive process that generates the empty clause will be able to reconstruct the distributed proof. This result is obtained without imposing a centralized control on the deductive processes or resorting to a round of post-processing with ad hoc communication. We prove that Modied Clause-Diusion is fair (hence complete) and guarantees proof reconstruction. First we dene a set of conditions, next we prove that they are sucien t for proof reconstruction, then we show that Modied Clause-Diusion satises them. Fairness is proved in the same way, which has the advantage that the sucien t conditions provide a treatment of the problem relevant for distributed theorem proving in general.