In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate $p$ that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of $p$. The second theorem shows that if a program has a signing then computing the positive part of $p$ under the well-founded semantics requires the computation of only one part of each predicate. This theorem suggests an analysis for query-answering under the well-founded semantics. In the process of proving these results, we use an alternative formulation of the well-founded semantics of logic programs, which might be of independent interest.
翻译:在本说明中,我们使用Kumen的签名概念来建立关于逻辑程序有根据的语义的两个理论,我们只(比如)只对作为程序后果的上游美元的积极字句感兴趣。第一个理论确定了有根据的和合适的语义与美元正数相匹配的一类程序。第二个理论表明,如果一个程序有签名,然后计算在有根据的语义下美元正数部分,则只需要计算每个词义的一部分。这个理论提出了在有根据的语义下进行问答的分析。在证明这些结果的过程中,我们使用一个有根据的逻辑语义的替代公式,这可能具有独立的兴趣。