On the Reconstruction of Proofs in Distributed Theorem Proving: a Modified Clause-Diffusion Method
✍ Scribed by MARIA PAOLA BONACINA
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 541 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
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 analyse this problem and we present a method for distributed theorem proving, called Modified Clause-Diffusion, 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 Modified Clause-Diffusion is fair (hence complete) and guarantees proof reconstruction. First we define a set of conditions, next we prove that they are sufficient for proof reconstruction, then we show that Modified Clause-Diffusion satisfies them. Fairness is proved in the same way, which has the advantage that the sufficient conditions provide a treatment of the problem relevant for distributed theorem proving in general.