In this paper we present two results regarding refinement operators. The first is that it does not exist a refinement operator that is both complete and optimal for the theta-subsumption ordering and for the language of full cla\USAl logic. The second regards the properties of the refinement operator implemented in Aleph's code by predicate auto\_refine/2. We think this operator is interesting for its simplicity and because it does not require the construction of a bottom-clause. In particular, the operator is useful in the cases where a bottom-clause can not be built, as for example in learning from interpretations. The properties of this operator are that it is locally finite, not proper nor complete but weakly complete. Moreover, the operator is also not optimal. However, it can be made complete by extending the specification of the language bias and by requiring that the language does not contain function symbols.
Two Results Regarding Refinement Operators
RIGUZZI, Fabrizio
2005
Abstract
In this paper we present two results regarding refinement operators. The first is that it does not exist a refinement operator that is both complete and optimal for the theta-subsumption ordering and for the language of full cla\USAl logic. The second regards the properties of the refinement operator implemented in Aleph's code by predicate auto\_refine/2. We think this operator is interesting for its simplicity and because it does not require the construction of a bottom-clause. In particular, the operator is useful in the cases where a bottom-clause can not be built, as for example in learning from interpretations. The properties of this operator are that it is locally finite, not proper nor complete but weakly complete. Moreover, the operator is also not optimal. However, it can be made complete by extending the specification of the language bias and by requiring that the language does not contain function symbols.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
