Name
Abstract | ||
|---|---|---|
In this paper we give a completeness theorem of an inductive inference rule inverse entailment proposed by Muggleton. Our main result is that a hypothesis clause H can be derived from an example E under a background theory B with inverse entailment iff H subsumes E relative to B in Plotkin's sense. The theory B can be any clausal theory, and the example E can be any clause which is neither a tautology nor implied by B. The derived hypothesis H is a clause which is not always definite. In order to prove the result we give a declarative semantics for arbitrary consistent clausal theories, and show that SB-resolution, which was originally introduced by Plotkin, is a complete procedural semantics. The completeness is shown as an extension of the completeness theorem of SLD-resolution. We also show that every hypothesis H derived with saturant generalization, proposed by Rouveirol, must subsume E w.r.t. B in Buntine's sense. Moreover we show that saturant generalization can be obtained from inverse entailment by giving some restriction to it. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1007/3540635149_58 | ILP |
Keywords | Field | DocType |
inverse entailment,inductive inference | Discrete mathematics,Inductive reasoning,Tautology (logic),Logical consequence,Gödel's completeness theorem,First-order logic,Preferential entailment,Rule of inference,Completeness (statistics),Mathematics | Conference |
ISBN | Citations | PageRank |
3-540-63514-9 | 37 | 2.29 |
References | Authors | |
8 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Akihiro Yamamoto | 1 | 95 | 11.23 |