A Pruning Technique for Abduction on Model Generation Theorem Provers

Abstract

It has been presented that we can translate an abduction framework into a model generation problem. The translation method is called "Skip". The MGTP prover can generate the minimal models of a set of first-order clauses. A large amount of OR parallelism appears in the translated program. However, the number of model candidates generated by the MGTP prover is often exponential-order. Therefore, we need a pruning technique for the translated program. Since we usually require only the minimal explanations of a query from an abduction framework, non-minimal explanations are redundant. In parallel processing, it is difficult for the MGTP prover to find that model candidates are redundant at intermediate steps. This paper describes a pruning technique for the MGTP programs translated by the Skip method. Here, it is proved that we may omit model candidates containing multiple instances of an abducible predicate if no predicates in the given theory are multiple-dependent on the abducible predicate. This condition can be checked with information from dependency analysis among predicates. We can also use the MGTP prover as the dependency analyzer. If we make program containing negative clauses (called cut rules) for abducible predicates which satisfy the condition, then these cut rules automatically prune redundant model candidates on the MGTP prover. We illustrate that the cut rules dramatically reduce the number of model candidates generated by the MGTP prover with the translated program. This pruning technique involves no overheads in parallel processing and allows us good performance on the parallel inference machine PIM/m.