Algebraic foundations and improved methods of induction or ripple-down rules

Ripple down rules (RDR), that is rules with hierarchical exceptions, are used in knowledge acquisition because they provide a well intelligible and modiiable representation for even very large expert systems. In this paper a formal semantics for RDRs is proposed, that covers rst order rules as well as attribute-value based rules. An algebraic foundation is proposed, including simpliication of RDRs and transformation of RDRs into at lists of rules and ripple down rule sets, hence these knowledge representation schemes are put into perspective. It is shown, that a RDR has a shorter description length than an equivalent decision list. Induction of rules with exceptions is characterized as bidirectional movement in the hypothesis space, while known algorithms for learning rules or decision trees either perform a top-down specialization of the most general or a bottom-up generalization of the most special hypothesis. Known algorithms for induction of RDRs are summarized and compared and a bidirectional algorithm is proposed, that handles continuous-valued attributes using an implication based generalization for attribute-value based representations, and shows good empirical results.

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