Logics in Artificial Intelligence

Existing formalisations of (transfinite) inductive definitions in constructive mathematics are reviewed and strong correspondences with LP under least model and perfect model semantics become apparent. I point to fundamental restrictions of these existing formalisations and argue that the well-founded semantics (wfs) overcomes these problems and hence, provides a superior formalisation of the principle of inductive definition. The contribution of this study for LP is that it (re-) introduces the knowledge theoretic interpretation of LP as a logic for representing definitional knowledge. I point to fundamental differences between this knowledge theoretic interpretation of LP and the more commonly known interpretations of LP as default theories or auto-epistemic theories. The relevance is that differences in knowledge theoretic interpretation have strong impact on knowledge representation methodology and on extensions of the LP formalism, for example for representing

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