The Well-Founded Semantics Is the Principle of Inductive Definition

摘要

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 differneces 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 uncertainty.